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 : n014.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 00:50:18 EDT 2023
% Result : Theorem 59.03s 8.83s
% Output : Proof 128.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n014.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 22:10:16 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 15.82/2.91 Prover 4: Preprocessing ...
% 15.82/2.92 Prover 1: Preprocessing ...
% 16.15/2.98 Prover 0: Preprocessing ...
% 16.15/2.98 Prover 5: Preprocessing ...
% 16.15/3.04 Prover 3: Preprocessing ...
% 16.15/3.06 Prover 2: Preprocessing ...
% 16.15/3.10 Prover 6: Preprocessing ...
% 46.52/7.04 Prover 3: Warning: ignoring some quantifiers
% 47.09/7.14 Prover 1: Warning: ignoring some quantifiers
% 47.48/7.24 Prover 3: Constructing countermodel ...
% 48.62/7.43 Prover 1: Constructing countermodel ...
% 50.07/7.53 Prover 6: Proving ...
% 50.27/7.62 Prover 4: Warning: ignoring some quantifiers
% 54.81/8.18 Prover 4: Constructing countermodel ...
% 57.14/8.50 Prover 5: Proving ...
% 58.11/8.59 Prover 0: Proving ...
% 58.68/8.82 Prover 3: proved (8201ms)
% 58.68/8.82
% 59.03/8.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.03/8.83
% 59.03/8.83 Prover 5: stopped
% 59.03/8.84 Prover 6: stopped
% 59.03/8.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 59.03/8.84 Prover 0: stopped
% 59.03/8.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 59.03/8.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 59.03/8.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 69.11/10.02 Prover 7: Preprocessing ...
% 69.61/10.09 Prover 10: Preprocessing ...
% 69.61/10.23 Prover 8: Preprocessing ...
% 69.61/10.26 Prover 11: Preprocessing ...
% 74.96/11.00 Prover 2: Proving ...
% 74.96/11.00 Prover 2: stopped
% 76.71/11.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 80.12/11.59 Prover 10: Warning: ignoring some quantifiers
% 80.73/11.69 Prover 13: Preprocessing ...
% 81.89/11.77 Prover 10: Constructing countermodel ...
% 83.54/11.96 Prover 8: Warning: ignoring some quantifiers
% 84.83/12.11 Prover 8: Constructing countermodel ...
% 85.57/12.24 Prover 7: Warning: ignoring some quantifiers
% 87.84/12.50 Prover 7: Constructing countermodel ...
% 89.31/12.70 Prover 11: Warning: ignoring some quantifiers
% 90.40/12.97 Prover 11: Constructing countermodel ...
% 93.59/13.25 Prover 13: Warning: ignoring some quantifiers
% 95.08/13.46 Prover 13: Constructing countermodel ...
% 109.32/15.35 Prover 13: stopped
% 109.32/15.36 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 114.16/15.98 Prover 1: stopped
% 114.39/15.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 115.88/16.24 Prover 16: Preprocessing ...
% 120.65/16.82 Prover 19: Preprocessing ...
% 121.59/17.13 Prover 10: Found proof (size 117)
% 121.59/17.13 Prover 10: proved (8295ms)
% 122.33/17.14 Prover 7: stopped
% 122.33/17.14 Prover 4: stopped
% 122.33/17.14 Prover 11: stopped
% 122.33/17.14 Prover 8: stopped
% 125.76/17.64 Prover 16: Warning: ignoring some quantifiers
% 126.07/17.73 Prover 16: Constructing countermodel ...
% 126.07/17.74 Prover 16: stopped
% 126.36/17.93 Prover 19: Warning: ignoring some quantifiers
% 126.74/18.03 Prover 19: Constructing countermodel ...
% 126.74/18.04 Prover 19: stopped
% 126.74/18.04
% 126.74/18.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 126.74/18.04
% 127.23/18.06 % SZS output start Proof for theBenchmark
% 127.39/18.08 Assumptions after simplification:
% 127.39/18.08 ---------------------------------
% 127.39/18.08
% 127.39/18.08 (conj_0)
% 127.39/18.10 $i(u) & $i(finite_finite_pname) & ? [v0: $i] :
% 127.39/18.10 (hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 & $i(v0) & hBOOL(v0))
% 127.39/18.10
% 127.39/18.10 (conj_1)
% 127.39/18.11 $i(mgt_call) & $i(ord_le1311769555a_bool) & $i(u) & $i(g) & ? [v0: $i] : ?
% 127.39/18.11 [v1: $i] : ? [v2: $i] : (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) =
% 127.39/18.11 v0 & hAPP_fun_a_bool_bool(v0, v1) = v2 & image_pname_a(mgt_call, u) = v1 &
% 127.39/18.11 $i(v2) & $i(v1) & $i(v0) & hBOOL(v2))
% 127.39/18.11
% 127.39/18.11 (conj_2)
% 127.39/18.11 $i(na) & $i(mgt_call) & $i(suc) & $i(finite_card_a) & $i(ord_less_eq_nat) &
% 127.39/18.11 $i(u) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 127.39/18.11 (hAPP_nat_nat(suc, na) = v0 & hAPP_fun_a_bool_nat(finite_card_a, v2) = v3 &
% 127.39/18.11 hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 & hAPP_nat_bool(v1, v3) =
% 127.39/18.11 v4 & image_pname_a(mgt_call, u) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 127.39/18.11 $i(v0) & hBOOL(v4))
% 127.39/18.11
% 127.39/18.11 (conj_3)
% 127.39/18.11 $i(na) & $i(mgt_call) & $i(suc) & $i(finite_card_a) & $i(u) & $i(g) & ? [v0:
% 127.39/18.11 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 127.39/18.11 (minus_minus_nat(v2) = v3 & hAPP_nat_nat(v3, v4) = v0 & hAPP_nat_nat(suc, na)
% 127.39/18.11 = v4 & hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 127.39/18.11 hAPP_fun_a_bool_nat(finite_card_a, g) = v0 & image_pname_a(mgt_call, u) = v1
% 127.39/18.11 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 127.39/18.11
% 127.39/18.11 (conj_4)
% 127.39/18.11 $i(member_pname) & $i(pn) & $i(u) & ? [v0: $i] : ? [v1: $i] :
% 127.39/18.11 (hAPP_f1664156314l_bool(v0, u) = v1 & hAPP_p338031245l_bool(member_pname, pn)
% 127.39/18.11 = v0 & $i(v1) & $i(v0) & hBOOL(v1))
% 127.39/18.11
% 127.39/18.11 (conj_5)
% 127.39/18.11 $i(mgt_call) & $i(member_a) & $i(pn) & $i(g) & ? [v0: $i] : ? [v1: $i] : ?
% 127.39/18.11 [v2: $i] : (hAPP_fun_a_bool_bool(v1, g) = v2 & hAPP_pname_a(mgt_call, pn) = v0
% 127.39/18.11 & hAPP_a85458249l_bool(member_a, v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ~
% 127.39/18.11 hBOOL(v2))
% 127.39/18.11
% 127.39/18.12 (conj_6)
% 127.39/18.12 $i(mgt_call) & $i(ord_le1311769555a_bool) & $i(pn) & $i(u) & $i(g) & ? [v0:
% 127.39/18.12 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 127.39/18.12 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2 &
% 127.39/18.12 hAPP_fun_a_bool_bool(v2, v3) = v4 & hAPP_pname_a(mgt_call, pn) = v0 &
% 127.39/18.12 insert_a(v0, g) = v1 & image_pname_a(mgt_call, u) = v3 & $i(v4) & $i(v3) &
% 127.39/18.12 $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v4))
% 127.39/18.12
% 127.39/18.12 (fact_154_finite__surj)
% 127.39/18.12 $i(ord_le1311769555a_bool) & $i(finite_finite_pname) & $i(finite_finite_a) &
% 127.39/18.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 127.39/18.12 $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v0) = v3) | ~
% 127.39/18.12 (hAPP_fun_a_bool_bool(v3, v4) = v5) | ~ (image_pname_a(v1, v2) = v4) | ~
% 127.39/18.12 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v5) | ? [v6: $i] : ? [v7: $i] :
% 127.39/18.12 ((hAPP_f1664156314l_bool(finite_finite_pname, v2) = v6 & $i(v6) & ~
% 127.39/18.12 hBOOL(v6)) | (hAPP_fun_a_bool_bool(finite_finite_a, v0) = v7 & $i(v7) &
% 127.39/18.12 hBOOL(v7))))
% 127.39/18.12
% 127.39/18.12 (fact_264_insert__absorb)
% 127.39/18.12 $i(member_pname) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 127.39/18.12 (hAPP_f1664156314l_bool(v2, v1) = v3) | ~
% 127.39/18.12 (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.39/18.12 hBOOL(v3) | ~ is_fun_pname_bool(v1) | insert_pname(v0, v1) = v1)
% 127.39/18.12
% 127.39/18.12 (fact_312_rev__image__eqI)
% 127.39/18.12 $i(member_a) & $i(member_pname) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.39/18.12 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 127.39/18.12 : ( ~ (hAPP_f1664156314l_bool(v4, v3) = v5) | ~ (hAPP_fun_a_bool_bool(v6, v7)
% 127.39/18.12 = v8) | ~ (hAPP_p338031245l_bool(member_pname, v2) = v4) | ~
% 127.39/18.12 (hAPP_a85458249l_bool(member_a, v0) = v6) | ~ (image_pname_a(v1, v3) = v7)
% 127.39/18.12 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v5) | hBOOL(v8) |
% 127.39/18.12 ? [v9: $i] : ( ~ (v9 = v0) & hAPP_pname_a(v1, v2) = v9 & $i(v9)))
% 127.39/18.12
% 127.39/18.12 (fact_324_insert__subset)
% 127.39/18.13 $i(member_a) & $i(ord_le1311769555a_bool) & ! [v0: $i] : ! [v1: $i] : !
% 127.39/18.13 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 127.39/18.13 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) = v4) | ~
% 127.39/18.13 (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ (insert_a(v0, v1) = v3) | ~ $i(v2)
% 127.39/18.13 | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8:
% 127.39/18.13 $i] : ? [v9: $i] : (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) =
% 127.39/18.13 v8 & hAPP_fun_a_bool_bool(v8, v2) = v9 & hAPP_fun_a_bool_bool(v6, v2) = v7
% 127.39/18.13 & hAPP_a85458249l_bool(member_a, v0) = v6 & $i(v9) & $i(v8) & $i(v7) &
% 127.39/18.13 $i(v6) & hBOOL(v9) & hBOOL(v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.39/18.13 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 127.39/18.13 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) = v4) | ~
% 127.39/18.13 (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ (insert_a(v0, v1) = v3) | ~ $i(v2)
% 127.39/18.13 | ~ $i(v1) | ~ $i(v0) | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8:
% 127.39/18.13 $i] : ? [v9: $i] : ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) =
% 127.39/18.13 v8 & hAPP_fun_a_bool_bool(v8, v2) = v9 & $i(v9) & $i(v8) & ~ hBOOL(v9))
% 127.39/18.13 | (hAPP_fun_a_bool_bool(v6, v2) = v7 & hAPP_a85458249l_bool(member_a, v0)
% 127.39/18.13 = v6 & $i(v7) & $i(v6) & ~ hBOOL(v7))))
% 127.39/18.13
% 127.39/18.13 (fact_359_subsetI)
% 127.39/18.13 $i(member_a) & $i(ord_le1311769555a_bool) & ! [v0: $i] : ! [v1: $i] : !
% 127.39/18.13 [v2: $i] : ! [v3: $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool,
% 127.39/18.13 v1) = v2) | ~ (hAPP_fun_a_bool_bool(v2, v0) = v3) | ~ $i(v1) | ~
% 127.39/18.13 $i(v0) | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 127.39/18.13 (hAPP_fun_a_bool_bool(v5, v1) = v6 & hAPP_fun_a_bool_bool(v5, v0) = v7 &
% 127.39/18.13 hAPP_a85458249l_bool(member_a, v4) = v5 & $i(v7) & $i(v6) & $i(v5) &
% 127.39/18.13 $i(v4) & hBOOL(v6) & is_a(v4) & ~ hBOOL(v7)))
% 127.39/18.13
% 127.39/18.13 (fact_64_card__insert__if)
% 127.39/18.13 $i(member_pname) & $i(suc) & $i(finite_card_pname) & $i(finite_finite_pname) &
% 127.39/18.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 127.39/18.13 (hAPP_f1664156314l_bool(v2, v1) = v3) | ~
% 127.39/18.13 (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 127.39/18.13 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 127.39/18.13 ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v4 & $i(v4) & ~
% 127.39/18.13 hBOOL(v4)) | (( ~ hBOOL(v3) | (v7 = v6 &
% 127.39/18.13 hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 127.39/18.13 hAPP_f921600141ol_nat(finite_card_pname, v1) = v6 & insert_pname(v0,
% 127.39/18.13 v1) = v5 & $i(v6) & $i(v5))) & (hBOOL(v3) | (v8 = v6 &
% 127.39/18.13 hAPP_nat_nat(suc, v7) = v6 &
% 127.39/18.13 hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 127.39/18.13 hAPP_f921600141ol_nat(finite_card_pname, v1) = v7 & insert_pname(v0,
% 127.39/18.13 v1) = v5 & $i(v7) & $i(v6) & $i(v5))))))
% 127.39/18.13
% 127.39/18.13 (fact_65_card__insert__if)
% 127.39/18.13 $i(member_a) & $i(suc) & $i(finite_card_a) & $i(finite_finite_a) & ! [v0: $i]
% 127.39/18.13 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_fun_a_bool_bool(v2, v1)
% 127.39/18.13 = v3) | ~ (hAPP_a85458249l_bool(member_a, v0) = v2) | ~ $i(v1) | ~
% 127.39/18.13 $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 127.39/18.13 : ((hAPP_fun_a_bool_bool(finite_finite_a, v1) = v4 & $i(v4) & ~ hBOOL(v4))
% 127.39/18.13 | (( ~ hBOOL(v3) | (v7 = v6 & hAPP_fun_a_bool_nat(finite_card_a, v5) = v6
% 127.39/18.13 & hAPP_fun_a_bool_nat(finite_card_a, v1) = v6 & insert_a(v0, v1) =
% 127.39/18.13 v5 & $i(v6) & $i(v5))) & (hBOOL(v3) | (v8 = v6 & hAPP_nat_nat(suc,
% 127.39/18.13 v7) = v6 & hAPP_fun_a_bool_nat(finite_card_a, v5) = v6 &
% 127.39/18.13 hAPP_fun_a_bool_nat(finite_card_a, v1) = v7 & insert_a(v0, v1) = v5
% 127.39/18.13 & $i(v7) & $i(v6) & $i(v5))))))
% 127.39/18.13
% 127.39/18.13 (gsy_v_U)
% 127.39/18.13 $i(u) & is_fun_pname_bool(u)
% 127.39/18.13
% 127.67/18.14 (function-axioms)
% 127.77/18.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.77/18.20 (hAPP_f1476298914l_bool(v3, v2) = v1) | ~ (hAPP_f1476298914l_bool(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (hAPP_f1748468828l_bool(v3, v2) = v1) | ~ (hAPP_f1748468828l_bool(v3, v2)
% 127.77/18.20 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 127.77/18.20 | ~ (hAPP_f198738859l_bool(v3, v2) = v1) | ~ (hAPP_f198738859l_bool(v3,
% 127.77/18.20 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 127.77/18.20 = v0 | ~ (hAPP_a1392362872l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_a1392362872l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p393069232l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_p393069232l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1006566506l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_n1006566506l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_fun_bool_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_a_fun_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (nat_case_bool(v3, v2) = v1) | ~
% 127.77/18.20 (nat_case_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (cOMBB_bool_bool_nat(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_bool_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_238756964t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_238756964t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1897541054_pname(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1897541054_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_472261505bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_472261505bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1137537805bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1137537805bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_743407885bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_743407885bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_a_fun_a_bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_a_fun_a_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_392435466_pname(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_392435466_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_408569982_pname(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_408569982_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_928955006_pname(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_928955006_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1823939024ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1823939024ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f282463732t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f282463732t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2117322052ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_2117322052ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1066163005t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1066163005t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2026977092ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_2026977092ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1885489796ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1885489796ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_fun_nat_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_a_fun_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_164527437a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_164527437a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1896684278e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1896684278e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1250273980t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1250273980t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_523834888_pname(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_523834888_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_pname_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_pname_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 127.77/18.20 ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1321347587bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1321347587bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_a_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (cOMBB_800536526ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_800536526ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1693087065a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1693087065a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_598082538e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_598082538e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1246832597l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1246832597l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_141086128t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_141086128t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p130839763l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_p130839763l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_542850580_pname(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_542850580_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_610033911bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_610033911bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f800510211t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f800510211t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1212655066ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1212655066ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p1499970991t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_p1499970991t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_b589554111l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_b589554111l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_fun_nat_bool(v3, v2) = v1) | ~
% 127.77/18.20 (image_a_fun_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_nat_nat(v3, v2) = v1) | ~
% 127.77/18.20 (image_nat_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (cOMBB_1015721476ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1015721476ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_nat_bool_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBS_nat_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_675860798_pname(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_675860798_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_338059395a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_338059395a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2095475776e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_2095475776e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_444170502t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_444170502t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_1187019125l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBS_1187019125l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1972296269bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_1972296269bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n215258509l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_n215258509l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f285962445l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f285962445l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f556039215l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f556039215l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1951378235l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1951378235l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_nat_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (image_pname_nat(v3, v2) = v1) | ~
% 127.77/18.20 (image_pname_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 127.77/18.20 ! [v3: $i] : (v1 = v0 | ~ (hAPP_f22106695ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f22106695ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2009550088ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f2009550088ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f55526627ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f55526627ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f696928925ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f696928925ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_fun_a_bool_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_fun_a_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1699378549t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_n1699378549t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f921600141ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f921600141ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_nat(v3, v2) = v1) | ~
% 127.77/18.20 (insert_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (insert_fun_nat_bool(v3, v2) = v1) | ~
% 127.77/18.20 (insert_fun_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_fun_a_bool_nat(v3, v2) = v1) | ~
% 127.77/18.20 (image_fun_a_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1551609309ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (image_1551609309ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_496248727ol_nat(v3, v2) = v1) | ~
% 127.77/18.20 (image_496248727ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_nat(v3, v2) = v1) | ~
% 127.77/18.20 (image_a_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (image_26036933t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (image_26036933t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_2129980159t_bool(v3, v2) = v1) | ~
% 127.77/18.20 (image_2129980159t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f103356543l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f103356543l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1434722111l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1434722111l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f510955609l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f510955609l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1772781669l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1772781669l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f937997336l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f937997336l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f389811538l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f389811538l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f292226953l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f292226953l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1637334154l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1637334154l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f559147733l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f559147733l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1935102916l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1935102916l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2117159681l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f2117159681l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f621171935l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f621171935l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f654413245e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f654413245e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1549043526a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1549043526a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f54304608l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f54304608l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1291551745_pname(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1291551745_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f434788991l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f434788991l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f759274231e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f759274231e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1051908748a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1051908748a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1664156314l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1664156314l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1297739591_pname(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1297739591_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1631501043l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1631501043l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1794073134e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1794073134e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2050579477a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f2050579477a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_fun_a_bool_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_fun_a_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1128469712_pname(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_f1128469712_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n850744903l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_n850744903l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1414589940l_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_n1414589940l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1025906991e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_n1025906991e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_fun_a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_nat_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_bool(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (hAPP_nat_pname(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_nat_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 127.77/18.20 ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_a(v3, v2) = v1) | ~ (hAPP_nat_a(v3, v2)
% 127.77/18.20 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 127.77/18.20 | ~ (hAPP_bool_bool(v3, v2) = v1) | ~ (hAPP_bool_bool(v3, v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.77/18.20 (hAPP_p338031245l_bool(v3, v2) = v1) | ~ (hAPP_p338031245l_bool(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (hAPP_p1824510254l_bool(v3, v2) = v1) | ~ (hAPP_p1824510254l_bool(v3, v2)
% 127.77/18.20 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 127.77/18.20 | ~ (hAPP_p61793385e_bool(v3, v2) = v1) | ~ (hAPP_p61793385e_bool(v3, v2)
% 127.77/18.20 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 127.77/18.20 | ~ (hAPP_p1534023578a_bool(v3, v2) = v1) | ~ (hAPP_p1534023578a_bool(v3,
% 127.77/18.20 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 127.77/18.20 = v0 | ~ (hAPP_pname_bool(v3, v2) = v1) | ~ (hAPP_pname_bool(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (hAPP_pname_pname(v3, v2) = v1) | ~ (hAPP_pname_pname(v3, v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.77/18.20 (hAPP_pname_a(v3, v2) = v1) | ~ (hAPP_pname_a(v3, v2) = v0)) & ! [v0: $i]
% 127.77/18.20 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.77/18.20 (hAPP_a217006258l_bool(v3, v2) = v1) | ~ (hAPP_a217006258l_bool(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (hAPP_a85458249l_bool(v3, v2) = v1) | ~ (hAPP_a85458249l_bool(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (hAPP_a93125764e_bool(v3, v2) = v1) | ~ (hAPP_a93125764e_bool(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (hAPP_a_fun_a_bool(v3, v2) = v1) | ~ (hAPP_a_fun_a_bool(v3, v2) = v0)) &
% 127.77/18.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.77/18.20 (hAPP_a_bool(v3, v2) = v1) | ~ (hAPP_a_bool(v3, v2) = v0)) & ! [v0: $i] :
% 127.77/18.20 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_pname(v3, v2) =
% 127.77/18.20 v1) | ~ (hAPP_a_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.20 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_a(v3, v2) = v1) | ~
% 127.77/18.20 (hAPP_a_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 127.77/18.20 $i] : (v1 = v0 | ~ (insert1325755072e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (insert1325755072e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_fun_a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (insert_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : ! [v3: $i] : (v1 = v0 | ~ (insert_pname(v3, v2) = v1) | ~
% 127.77/18.20 (insert_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (insert_a(v3, v2) = v1) | ~ (insert_a(v3, v2) = v0))
% 127.77/18.20 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.77/18.20 (image_1921560913_pname(v3, v2) = v1) | ~ (image_1921560913_pname(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (image_fun_nat_bool_a(v3, v2) = v1) | ~ (image_fun_nat_bool_a(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (image_1283814551_pname(v3, v2) = v1) | ~ (image_1283814551_pname(v3, v2)
% 127.77/18.20 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 127.77/18.20 | ~ (image_876012084bool_a(v3, v2) = v1) | ~ (image_876012084bool_a(v3,
% 127.77/18.20 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 127.77/18.20 = v0 | ~ (image_1854862208_pname(v3, v2) = v1) | ~
% 127.77/18.20 (image_1854862208_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_fun_a_bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (image_fun_a_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : ! [v3: $i] : (v1 = v0 | ~ (image_1655916159e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (image_1655916159e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_nat_fun_a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (image_nat_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_nat_pname(v3, v2) = v1) | ~
% 127.77/18.20 (image_nat_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 127.77/18.20 ! [v3: $i] : (v1 = v0 | ~ (image_nat_a(v3, v2) = v1) | ~ (image_nat_a(v3,
% 127.77/18.20 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 127.77/18.20 = v0 | ~ (image_47868345e_bool(v3, v2) = v1) | ~ (image_47868345e_bool(v3,
% 127.77/18.20 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 127.77/18.20 = v0 | ~ (image_112932426a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (image_112932426a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_pname_pname(v3, v2) = v1) | ~
% 127.77/18.20 (image_pname_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : ! [v3: $i] : (v1 = v0 | ~ (image_pname_a(v3, v2) = v1) | ~
% 127.77/18.20 (image_pname_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (image_819518260e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (image_819518260e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_fun_a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (image_a_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : ! [v3: $i] : (v1 = v0 | ~ (image_a_pname(v3, v2) = v1) | ~
% 127.77/18.20 (image_a_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.77/18.20 [v3: $i] : (v1 = v0 | ~ (image_a_a(v3, v2) = v1) | ~ (image_a_a(v3, v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 127.77/18.20 ~ (fun(v3, v2) = v1) | ~ (fun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 127.77/18.20 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_350070575l_bool(v3, v2) = v1)
% 127.77/18.20 | ~ (cOMBS_350070575l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.20 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_1035972772l_bool(v3, v2) = v1) |
% 127.77/18.20 ~ (cOMBS_1035972772l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.20 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_568398431l_bool(v3, v2) = v1) |
% 127.77/18.20 ~ (cOMBS_568398431l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.20 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_a_bool_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBS_a_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_307249310e_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_307249310e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2140588453a_bool(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_2140588453a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_647938656_pname(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_647938656_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_bool_bool_a(v3, v2) = v1) | ~
% 127.77/18.20 (cOMBB_bool_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (plus_plus_nat(v2) = v1) | ~ (plus_plus_nat(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (body(v2) = v1) | ~
% 127.77/18.20 (body(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (the_com(v2) = v1) | ~ (the_com(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.20 [v2: $i] : (v1 = v0 | ~ (cOMBK_a_pname(v2) = v1) | ~ (cOMBK_a_pname(v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBK_bool_nat(v2) = v1) | ~ (cOMBK_bool_nat(v2) = v0)) & ! [v0: $i] : !
% 127.77/18.20 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBK_1994329625t_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBK_1994329625t_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_pname_a_bool(v2) = v1) | ~ (cOMBC_pname_a_bool(v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_1834145417l_bool(v2) = v1) | ~ (cOMBC_1834145417l_bool(v2) = v0)) &
% 127.77/18.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_777206479l_bool(v2) = v1) | ~ (cOMBC_777206479l_bool(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_a_a_bool(v2) = v1)
% 127.77/18.20 | ~ (cOMBC_a_a_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 127.77/18.20 (v1 = v0 | ~ (cOMBC_445755039l_bool(v2) = v1) | ~ (cOMBC_445755039l_bool(v2)
% 127.77/18.20 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_267053842l_bool(v2) = v1) | ~ (cOMBC_267053842l_bool(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_1928494297l_bool(v2) = v1) | ~ (cOMBC_1928494297l_bool(v2) = v0)) &
% 127.77/18.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_386238098l_bool(v2) = v1) | ~ (cOMBC_386238098l_bool(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_nat_a_bool(v2) =
% 127.77/18.20 v1) | ~ (cOMBC_nat_a_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.20 [v2: $i] : (v1 = v0 | ~ (cOMBC_619334683t_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_619334683t_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_1666426608t_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_1666426608t_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_385542954t_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_385542954t_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_pname_nat_bool(v2) = v1) | ~ (cOMBC_pname_nat_bool(v2)
% 127.77/18.20 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_a_nat_bool(v2) = v1) | ~ (cOMBC_a_nat_bool(v2) = v0)) & ! [v0: $i]
% 127.77/18.20 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_1880041174l_bool(v2) = v1)
% 127.77/18.20 | ~ (cOMBC_1880041174l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.20 [v2: $i] : (v1 = v0 | ~ (cOMBC_1738168533e_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_1738168533e_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_1988546018l_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_1988546018l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_1004116266e_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_1004116266e_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_1245412066l_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_1245412066l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_615407716e_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_615407716e_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_1058051404l_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_1058051404l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_1149511130e_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_1149511130e_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_1355376034l_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_1355376034l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_a_pname_bool(v2) = v1) | ~ (cOMBC_a_pname_bool(v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_226598744l_bool(v2) = v1) | ~ (cOMBC_226598744l_bool(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_nat_pname_bool(v2)
% 127.77/18.20 = v1) | ~ (cOMBC_nat_pname_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 127.77/18.20 ! [v2: $i] : (v1 = v0 | ~ (cOMBC_nat_nat_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_nat_nat_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 127.77/18.20 (v1 = v0 | ~ (minus_minus_nat(v2) = v1) | ~ (minus_minus_nat(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (collect_nat(v2) = v1) |
% 127.77/18.20 ~ (collect_nat(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 127.77/18.20 v0 | ~ (cOMBC_1693257480l_bool(v2) = v1) | ~ (cOMBC_1693257480l_bool(v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (collect_fun_nat_bool(v2) = v1) | ~ (collect_fun_nat_bool(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_1284144636l_bool(v2) = v1) | ~ (cOMBC_1284144636l_bool(v2) = v0)) &
% 127.77/18.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_1732670874l_bool(v2) = v1) | ~ (cOMBC_1732670874l_bool(v2) = v0)) &
% 127.77/18.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (cOMBC_331553030l_bool(v2) = v1) | ~ (cOMBC_331553030l_bool(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (collec707592106l_bool(v2) = v1) | ~ (collec707592106l_bool(v2) = v0)) & !
% 127.77/18.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_7971162l_bool(v2)
% 127.77/18.20 = v1) | ~ (cOMBC_7971162l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 127.77/18.20 ! [v2: $i] : (v1 = v0 | ~ (collec1613912337l_bool(v2) = v1) | ~
% 127.77/18.20 (collec1613912337l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (cOMBC_595898202l_bool(v2) = v1) | ~
% 127.77/18.20 (cOMBC_595898202l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (collec1015864663l_bool(v2) = v1) | ~
% 127.77/18.20 (collec1015864663l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.20 : (v1 = v0 | ~ (wt(v2) = v1) | ~ (wt(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 127.77/18.20 : ! [v2: $i] : (v1 = v0 | ~ (mgt(v2) = v1) | ~ (mgt(v2) = v0)) & ! [v0:
% 127.77/18.20 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) =
% 127.77/18.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.20 (collec1974731493e_bool(v2) = v1) | ~ (collec1974731493e_bool(v2) = v0)) &
% 127.77/18.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (collect_fun_a_bool(v2)
% 127.77/18.20 = v1) | ~ (collect_fun_a_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.21 [v2: $i] : (v1 = v0 | ~ (collect_pname(v2) = v1) | ~ (collect_pname(v2) =
% 127.77/18.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.21 (collect_a(v2) = v1) | ~ (collect_a(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 127.77/18.21 : ! [v2: $i] : (v1 = v0 | ~ (undefi64961550l_bool(v2) = v1) | ~
% 127.77/18.21 (undefi64961550l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 127.77/18.21 (v1 = v0 | ~ (undefi1699038445l_bool(v2) = v1) | ~
% 127.77/18.21 (undefi1699038445l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.77/18.21 : (v1 = v0 | ~ (undefi17486888e_bool(v2) = v1) | ~ (undefi17486888e_bool(v2)
% 127.77/18.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.21 (undefined_fun_a_bool(v2) = v1) | ~ (undefined_fun_a_bool(v2) = v0)) & !
% 127.77/18.21 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (undefined_pname(v2) =
% 127.77/18.21 v1) | ~ (undefined_pname(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 127.77/18.21 $i] : (v1 = v0 | ~ (undefined_a(v2) = v1) | ~ (undefined_a(v2) = v0)) & !
% 127.77/18.21 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.21 (cOMBK_1857069011e_bool(v2) = v1) | ~ (cOMBK_1857069011e_bool(v2) = v0)) &
% 127.77/18.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 127.77/18.21 (cOMBK_324466864a_bool(v2) = v1) | ~ (cOMBK_324466864a_bool(v2) = v0)) & !
% 127.77/18.21 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBK_bool_pname(v2) =
% 127.77/18.21 v1) | ~ (cOMBK_bool_pname(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 127.77/18.21 [v2: $i] : (v1 = v0 | ~ (cOMBK_bool_a(v2) = v1) | ~ (cOMBK_bool_a(v2) = v0))
% 127.77/18.21
% 127.77/18.21 Further assumptions not needed in the proof:
% 127.77/18.21 --------------------------------------------
% 127.77/18.21 fact_0_assms_I1_J, fact_100_finite__insert, fact_101_finite__insert,
% 127.77/18.21 fact_102_finite__insert, fact_103_finite__subset, fact_104_finite__subset,
% 127.77/18.21 fact_105_finite__subset, fact_106_finite__subset, fact_107_finite__subset,
% 127.77/18.21 fact_108_finite__subset, fact_109_rev__finite__subset, fact_10_finite__imageI,
% 127.77/18.21 fact_110_rev__finite__subset, fact_111_rev__finite__subset,
% 127.77/18.21 fact_112_rev__finite__subset, fact_113_rev__finite__subset,
% 127.77/18.21 fact_114_rev__finite__subset, fact_115_Suc__leD, fact_116_le__SucE,
% 127.77/18.21 fact_117_le__SucI, fact_118_Suc__le__mono, fact_119_le__Suc__eq,
% 127.77/18.21 fact_11_finite__imageI, fact_120_not__less__eq__eq, fact_121_Suc__n__not__le__n,
% 127.77/18.21 fact_122_Suc__diff__diff, fact_123_diff__Suc__Suc, fact_124_le__diff__iff,
% 127.77/18.21 fact_125_Nat_Odiff__diff__eq, fact_126_eq__diff__iff,
% 127.77/18.21 fact_127_diff__diff__cancel, fact_128_diff__le__mono, fact_129_diff__le__mono2,
% 127.77/18.21 fact_12_finite__imageI, fact_130_diff__le__self, fact_131_finite__surj,
% 127.77/18.21 fact_132_finite__surj, fact_133_finite__surj, fact_134_finite__surj,
% 127.77/18.21 fact_135_finite__surj, fact_136_finite__surj, fact_137_finite__surj,
% 127.77/18.21 fact_138_finite__surj, fact_139_finite__surj, fact_13_finite__imageI,
% 127.77/18.21 fact_140_finite__surj, fact_141_finite__surj, fact_142_finite__surj,
% 127.77/18.21 fact_143_finite__surj, fact_144_finite__surj, fact_145_finite__surj,
% 127.77/18.21 fact_146_finite__surj, fact_147_finite__surj, fact_148_finite__surj,
% 127.77/18.21 fact_149_finite__surj, fact_14_finite__imageI, fact_150_finite__surj,
% 127.77/18.21 fact_151_finite__surj, fact_152_finite__surj, fact_153_finite__surj,
% 127.77/18.21 fact_155_finite__subset__image, fact_156_finite__subset__image,
% 127.77/18.21 fact_157_finite__subset__image, fact_158_finite__subset__image,
% 127.77/18.21 fact_159_finite__subset__image, fact_15_finite__imageI,
% 127.77/18.21 fact_160_finite__subset__image, fact_161_finite__subset__image,
% 127.77/18.21 fact_162_finite__subset__image, fact_163_finite__subset__image,
% 127.77/18.21 fact_164_finite__subset__image, fact_165_finite__subset__image,
% 127.77/18.21 fact_166_finite__subset__image, fact_167_finite__subset__image,
% 127.77/18.21 fact_168_finite__subset__image, fact_169_finite__subset__image,
% 127.77/18.21 fact_16_finite__imageI, fact_170_finite__subset__image,
% 127.77/18.21 fact_171_finite__subset__image, fact_172_finite__subset__image,
% 127.77/18.21 fact_173_finite__subset__image, fact_174_finite__subset__image,
% 127.77/18.21 fact_175_finite__subset__image, fact_176_finite__subset__image,
% 127.77/18.21 fact_177_finite__subset__image, fact_178_finite__subset__image,
% 127.77/18.21 fact_179_finite__subset__image, fact_17_finite__imageI,
% 127.77/18.21 fact_180_finite__subset__image, fact_181_finite__subset__image,
% 127.77/18.21 fact_182_lift__Suc__mono__le, fact_183_lift__Suc__mono__le,
% 127.77/18.21 fact_184_lift__Suc__mono__le, fact_185_lift__Suc__mono__le,
% 127.77/18.21 fact_186_lift__Suc__mono__le, fact_187_pigeonhole__infinite,
% 127.77/18.21 fact_188_pigeonhole__infinite, fact_189_pigeonhole__infinite,
% 127.77/18.21 fact_18_finite__imageI, fact_190_pigeonhole__infinite,
% 127.77/18.21 fact_191_pigeonhole__infinite, fact_192_pigeonhole__infinite,
% 127.77/18.21 fact_193_pigeonhole__infinite, fact_194_pigeonhole__infinite,
% 127.77/18.21 fact_195_pigeonhole__infinite, fact_196_pigeonhole__infinite,
% 127.77/18.21 fact_197_pigeonhole__infinite, fact_198_pigeonhole__infinite,
% 127.77/18.21 fact_199_pigeonhole__infinite, fact_19_finite__imageI,
% 127.77/18.21 fact_1_finite__Collect__subsets, fact_200_pigeonhole__infinite,
% 127.77/18.21 fact_201_pigeonhole__infinite, fact_202_pigeonhole__infinite,
% 127.77/18.21 fact_203_pigeonhole__infinite, fact_204_pigeonhole__infinite,
% 127.77/18.21 fact_205_pigeonhole__infinite, fact_206_pigeonhole__infinite,
% 127.77/18.21 fact_207_pigeonhole__infinite, fact_208_pigeonhole__infinite,
% 127.77/18.21 fact_209_pigeonhole__infinite, fact_20_finite__imageI,
% 127.77/18.21 fact_210_pigeonhole__infinite, fact_211_image__eqI, fact_212_image__eqI,
% 127.77/18.21 fact_213_image__eqI, fact_214_image__eqI, fact_215_image__eqI,
% 127.77/18.21 fact_216_equalityI, fact_217_equalityI, fact_218_equalityI, fact_219_subsetD,
% 127.77/18.21 fact_21_finite__imageI, fact_220_subsetD, fact_221_subsetD, fact_222_insertCI,
% 127.77/18.21 fact_223_insertCI, fact_224_insertCI, fact_225_insertE, fact_226_insertE,
% 127.77/18.21 fact_227_insertE, fact_228_zero__induct__lemma, fact_229_Suc__le__D,
% 127.77/18.21 fact_22_finite__imageI, fact_230_insertI1, fact_231_insertI1, fact_232_insertI1,
% 127.77/18.21 fact_233_insert__compr, fact_234_insert__compr, fact_235_insert__compr,
% 127.77/18.21 fact_236_insert__compr, fact_237_insert__compr, fact_238_insert__compr,
% 127.77/18.21 fact_239_insert__Collect, fact_23_finite_OinsertI, fact_240_insert__Collect,
% 127.77/18.21 fact_241_insert__Collect, fact_242_insert__Collect, fact_243_insert__Collect,
% 127.77/18.21 fact_244_insert__Collect, fact_245_insert__absorb2, fact_246_insert__absorb2,
% 127.77/18.21 fact_247_insert__absorb2, fact_248_insert__commute, fact_249_insert__commute,
% 127.77/18.21 fact_24_finite_OinsertI, fact_250_insert__commute, fact_251_insert__iff,
% 127.77/18.21 fact_252_insert__iff, fact_253_insert__iff, fact_254_insert__code,
% 127.77/18.21 fact_255_insert__code, fact_256_insert__code, fact_257_insert__ident,
% 127.77/18.21 fact_258_insert__ident, fact_259_insert__ident, fact_25_finite_OinsertI,
% 127.77/18.21 fact_260_insertI2, fact_261_insertI2, fact_262_insertI2,
% 127.77/18.21 fact_263_insert__absorb, fact_265_insert__absorb, fact_266_subset__refl,
% 127.77/18.21 fact_267_subset__refl, fact_268_subset__refl, fact_269_set__eq__subset,
% 127.77/18.21 fact_26_finite_OinsertI, fact_270_set__eq__subset, fact_271_set__eq__subset,
% 127.77/18.21 fact_272_equalityD1, fact_273_equalityD1, fact_274_equalityD1,
% 127.77/18.21 fact_275_equalityD2, fact_276_equalityD2, fact_277_equalityD2,
% 127.77/18.21 fact_278_in__mono, fact_279_in__mono, fact_27_finite_OinsertI,
% 127.77/18.21 fact_280_in__mono, fact_281_set__rev__mp, fact_282_set__rev__mp,
% 127.77/18.21 fact_283_set__rev__mp, fact_284_set__mp, fact_285_set__mp, fact_286_set__mp,
% 127.77/18.21 fact_287_mem__def, fact_288_mem__def, fact_289_mem__def,
% 127.77/18.21 fact_28_finite_OinsertI, fact_290_Collect__def, fact_291_Collect__def,
% 127.77/18.21 fact_292_Collect__def, fact_293_Collect__def, fact_294_Collect__def,
% 127.77/18.21 fact_295_Collect__def, fact_296_subset__trans, fact_297_subset__trans,
% 127.77/18.21 fact_298_subset__trans, fact_299_equalityE, fact_29_card__image__le,
% 127.77/18.21 fact_2_finite__Collect__subsets, fact_300_equalityE, fact_301_equalityE,
% 127.77/18.21 fact_302_image__iff, fact_303_imageI, fact_304_imageI, fact_305_imageI,
% 127.77/18.21 fact_306_imageI, fact_307_imageI, fact_308_rev__image__eqI,
% 127.77/18.21 fact_309_rev__image__eqI, fact_30_card__image__le, fact_310_rev__image__eqI,
% 127.77/18.21 fact_311_rev__image__eqI, fact_313_insert__compr__raw,
% 127.77/18.21 fact_314_insert__compr__raw, fact_315_insert__compr__raw,
% 127.77/18.21 fact_316_insert__compr__raw, fact_317_insert__compr__raw,
% 127.77/18.21 fact_318_insert__compr__raw, fact_319_subset__insertI, fact_31_card__image__le,
% 127.77/18.21 fact_320_subset__insertI, fact_321_subset__insertI, fact_322_insert__subset,
% 127.77/18.21 fact_323_insert__subset, fact_325_subset__insert, fact_326_subset__insert,
% 127.77/18.21 fact_327_subset__insert, fact_328_subset__insertI2, fact_329_subset__insertI2,
% 127.77/18.21 fact_32_card__image__le, fact_330_subset__insertI2, fact_331_insert__mono,
% 127.77/18.21 fact_332_insert__mono, fact_333_insert__mono, fact_334_image__insert,
% 127.77/18.21 fact_335_image__insert, fact_336_image__insert, fact_337_image__insert,
% 127.77/18.21 fact_338_insert__image, fact_339_insert__image, fact_33_card__image__le,
% 127.77/18.21 fact_340_insert__image, fact_341_insert__image, fact_342_insert__image,
% 127.77/18.21 fact_343_insert__image, fact_344_subset__image__iff,
% 127.77/18.21 fact_345_subset__image__iff, fact_346_subset__image__iff,
% 127.77/18.21 fact_347_subset__image__iff, fact_348_image__mono, fact_349_image__mono,
% 127.77/18.21 fact_34_card__image__le, fact_350_image__mono, fact_351_image__mono,
% 127.77/18.21 fact_352_imageE, fact_353_imageE, fact_354_imageE, fact_355_imageE,
% 127.77/18.21 fact_356_imageE, fact_357_subsetI, fact_358_subsetI, fact_35_card__image__le,
% 127.77/18.21 fact_360_image__subsetI, fact_361_image__subsetI, fact_362_image__subsetI,
% 127.77/18.21 fact_363_image__subsetI, fact_364_image__subsetI, fact_365_image__subsetI,
% 127.77/18.21 fact_366_image__subsetI, fact_367_order__refl, fact_368_order__refl,
% 127.77/18.21 fact_369_order__refl, fact_36_card__image__le, fact_370_order__refl,
% 127.77/18.21 fact_371_order__refl, fact_372_finite__nat__set__iff__bounded__le,
% 127.77/18.21 fact_373_assms_I3_J, fact_374_le__fun__def, fact_375_le__fun__def,
% 127.77/18.21 fact_376_le__fun__def, fact_377_le__funD, fact_378_le__funD, fact_379_le__funD,
% 127.77/18.21 fact_37_card__image__le, fact_380_le__funE, fact_381_le__funE,
% 127.77/18.21 fact_382_le__funE, fact_383_emptyE, fact_384_emptyE, fact_385_emptyE,
% 127.77/18.21 fact_386_finite_OemptyI, fact_387_finite_OemptyI, fact_388_finite_OemptyI,
% 127.77/18.21 fact_389_finite_OemptyI, fact_38_card__image__le, fact_390_finite_OemptyI,
% 127.77/18.21 fact_391_finite_OemptyI, fact_392_empty__subsetI, fact_393_empty__subsetI,
% 127.77/18.21 fact_394_empty__subsetI, fact_395_equals0D, fact_396_equals0D,
% 127.77/18.21 fact_397_equals0D, fact_398_Collect__empty__eq, fact_399_Collect__empty__eq,
% 127.77/18.21 fact_39_card__image__le, fact_3_finite__Collect__subsets,
% 127.77/18.21 fact_400_Collect__empty__eq, fact_401_Collect__empty__eq,
% 127.77/18.21 fact_402_Collect__empty__eq, fact_403_Collect__empty__eq, fact_404_empty__iff,
% 127.77/18.21 fact_405_empty__iff, fact_406_empty__iff, fact_407_empty__Collect__eq,
% 127.77/18.21 fact_408_empty__Collect__eq, fact_409_empty__Collect__eq,
% 127.77/18.21 fact_40_card__image__le, fact_410_empty__Collect__eq,
% 127.77/18.21 fact_411_empty__Collect__eq, fact_412_empty__Collect__eq, fact_413_ex__in__conv,
% 127.77/18.21 fact_414_ex__in__conv, fact_415_ex__in__conv, fact_416_all__not__in__conv,
% 127.77/18.21 fact_417_all__not__in__conv, fact_418_all__not__in__conv, fact_419_empty__def,
% 127.77/18.21 fact_41_card__image__le, fact_420_empty__def, fact_421_empty__def,
% 127.77/18.21 fact_422_empty__def, fact_423_empty__def, fact_424_empty__def,
% 127.77/18.21 fact_425_bot__fun__def, fact_426_bot__fun__def, fact_427_bot__fun__def,
% 127.77/18.21 fact_428_bot__apply, fact_429_bot__apply, fact_42_card__mono,
% 127.77/18.21 fact_430_bot__apply, fact_431_le__bot, fact_432_le__bot, fact_433_le__bot,
% 127.77/18.21 fact_434_le__bot, fact_435_le__bot, fact_436_bot__unique, fact_437_bot__unique,
% 127.77/18.21 fact_438_bot__unique, fact_439_bot__unique, fact_43_card__mono,
% 127.77/18.21 fact_440_bot__unique, fact_441_bot__least, fact_442_bot__least,
% 127.77/18.21 fact_443_bot__least, fact_444_bot__least, fact_445_bot__least,
% 127.77/18.21 fact_446_singleton__inject, fact_447_singleton__inject,
% 127.77/18.21 fact_448_singleton__inject, fact_449_singletonE, fact_44_card__mono,
% 127.77/18.21 fact_450_singletonE, fact_451_singletonE, fact_452_doubleton__eq__iff,
% 127.77/18.21 fact_453_doubleton__eq__iff, fact_454_doubleton__eq__iff,
% 127.77/18.21 fact_455_singleton__iff, fact_456_singleton__iff, fact_457_singleton__iff,
% 127.77/18.21 fact_458_insert__not__empty, fact_459_insert__not__empty, fact_45_card__mono,
% 127.77/18.21 fact_460_insert__not__empty, fact_461_empty__not__insert,
% 127.77/18.21 fact_462_empty__not__insert, fact_463_empty__not__insert,
% 127.77/18.21 fact_464_subset__empty, fact_465_subset__empty, fact_466_subset__empty,
% 127.77/18.21 fact_467_image__is__empty, fact_468_image__empty, fact_469_empty__is__image,
% 127.77/18.21 fact_46_card__mono, fact_470_Collect__conv__if, fact_471_Collect__conv__if,
% 127.77/18.21 fact_472_Collect__conv__if, fact_473_Collect__conv__if,
% 127.77/18.21 fact_474_Collect__conv__if, fact_475_Collect__conv__if,
% 127.77/18.21 fact_476_Collect__conv__if2, fact_477_Collect__conv__if2,
% 127.77/18.21 fact_478_Collect__conv__if2, fact_479_Collect__conv__if2, fact_47_card__mono,
% 127.77/18.21 fact_480_Collect__conv__if2, fact_481_Collect__conv__if2,
% 127.77/18.21 fact_482_singleton__conv, fact_483_singleton__conv, fact_484_singleton__conv,
% 127.77/18.21 fact_485_singleton__conv, fact_486_singleton__conv, fact_487_singleton__conv,
% 127.77/18.21 fact_488_singleton__conv2, fact_489_singleton__conv2, fact_48_card__seteq,
% 127.77/18.21 fact_490_singleton__conv2, fact_491_singleton__conv2, fact_492_singleton__conv2,
% 127.77/18.21 fact_493_singleton__conv2, fact_494_subset__singletonD,
% 127.77/18.21 fact_495_subset__singletonD, fact_496_subset__singletonD,
% 127.77/18.21 fact_497_image__constant, fact_498_image__constant__conv,
% 127.77/18.21 fact_499_linorder__le__cases, fact_49_card__seteq,
% 127.77/18.21 fact_4_finite__Collect__subsets, fact_500_xt1_I6_J, fact_501_xt1_I6_J,
% 127.77/18.21 fact_502_xt1_I6_J, fact_503_xt1_I6_J, fact_504_xt1_I6_J, fact_505_xt1_I5_J,
% 127.77/18.21 fact_506_xt1_I5_J, fact_507_xt1_I5_J, fact_508_xt1_I5_J, fact_509_xt1_I5_J,
% 127.77/18.21 fact_50_card__seteq, fact_510_order__trans, fact_511_order__trans,
% 127.77/18.21 fact_512_order__trans, fact_513_order__trans, fact_514_order__trans,
% 127.77/18.21 fact_515_order__antisym, fact_516_order__antisym, fact_517_order__antisym,
% 127.77/18.21 fact_518_order__antisym, fact_519_order__antisym, fact_51_card__seteq,
% 127.77/18.21 fact_520_xt1_I4_J, fact_521_xt1_I4_J, fact_522_xt1_I4_J, fact_523_xt1_I4_J,
% 127.77/18.21 fact_524_xt1_I4_J, fact_525_ord__le__eq__trans, fact_526_ord__le__eq__trans,
% 127.77/18.21 fact_527_ord__le__eq__trans, fact_528_ord__le__eq__trans,
% 127.77/18.21 fact_529_ord__le__eq__trans, fact_52_card__seteq, fact_530_xt1_I3_J,
% 127.77/18.21 fact_531_xt1_I3_J, fact_532_xt1_I3_J, fact_533_xt1_I3_J, fact_534_xt1_I3_J,
% 127.77/18.21 fact_535_ord__eq__le__trans, fact_536_ord__eq__le__trans,
% 127.77/18.21 fact_537_ord__eq__le__trans, fact_538_ord__eq__le__trans,
% 127.77/18.21 fact_539_ord__eq__le__trans, fact_53_card__seteq, fact_540_order__antisym__conv,
% 127.77/18.21 fact_541_order__antisym__conv, fact_542_order__antisym__conv,
% 127.77/18.21 fact_543_order__antisym__conv, fact_544_order__antisym__conv,
% 127.77/18.21 fact_545_order__eq__refl, fact_546_order__eq__refl, fact_547_order__eq__refl,
% 127.77/18.21 fact_548_order__eq__refl, fact_549_order__eq__refl, fact_54_card__insert__le,
% 127.77/18.21 fact_550_order__eq__iff, fact_551_order__eq__iff, fact_552_order__eq__iff,
% 127.77/18.21 fact_553_order__eq__iff, fact_554_order__eq__iff, fact_555_linorder__linear,
% 127.77/18.21 fact_556_finite__subset__induct, fact_557_finite__subset__induct,
% 127.77/18.21 fact_558_finite__subset__induct, fact_559_finite__subset__induct,
% 127.77/18.21 fact_55_card__insert__le, fact_560_finite__subset__induct,
% 127.77/18.21 fact_561_finite__subset__induct, fact_562_assms_I2_J, fact_563_finite__induct,
% 127.77/18.21 fact_564_finite__induct, fact_565_finite__induct, fact_566_finite__less__ub,
% 127.77/18.21 fact_567_assms_I4_J, fact_568_diff__Suc__eq__diff__pred, fact_569_diff__Suc__1,
% 127.77/18.21 fact_56_card__insert__le, fact_570_less__eq__nat_Osimps_I2_J,
% 127.77/18.21 fact_571_add__Suc__right, fact_572_add__Suc, fact_573_add__Suc__shift,
% 127.77/18.21 fact_574_nat__add__right__cancel, fact_575_nat__add__left__cancel,
% 127.77/18.21 fact_576_nat__add__assoc, fact_577_nat__add__left__commute,
% 127.77/18.21 fact_578_nat__add__commute, fact_579_diff__add__inverse2,
% 127.77/18.21 fact_57_card__insert__le, fact_580_diff__add__inverse,
% 127.77/18.21 fact_581_diff__diff__left, fact_582_diff__cancel, fact_583_diff__cancel2,
% 127.77/18.21 fact_584_le__add2, fact_585_le__add1, fact_586_le__iff__add,
% 127.77/18.21 fact_587_nat__add__left__cancel__le, fact_588_trans__le__add1,
% 127.77/18.21 fact_589_trans__le__add2, fact_58_card__insert__le, fact_590_add__le__mono1,
% 127.77/18.21 fact_591_add__le__mono, fact_592_add__leD2, fact_593_add__leD1,
% 127.77/18.21 fact_594_add__leE, fact_595_diff__add__assoc2, fact_596_add__diff__assoc2,
% 127.77/18.21 fact_597_diff__add__assoc, fact_598_le__imp__diff__is__add,
% 127.77/18.21 fact_599_le__add__diff__inverse2, fact_59_card__insert__le,
% 127.77/18.21 fact_5_finite__Collect__subsets, fact_600_le__diff__conv2,
% 127.77/18.21 fact_601_add__diff__assoc, fact_602_le__add__diff__inverse,
% 127.77/18.21 fact_603_le__add__diff, fact_604_le__diff__conv, fact_605_diff__diff__right,
% 127.77/18.21 fact_606_Suc__eq__plus1, fact_607_Suc__eq__plus1__left,
% 127.77/18.21 fact_608_diff__Suc__diff__eq2, fact_609_diff__Suc__diff__eq1,
% 127.77/18.21 fact_60_card__insert__if, fact_610_termination__basic__simps_I3_J,
% 127.77/18.21 fact_611_termination__basic__simps_I4_J, fact_612_lessI, fact_613_Suc__mono,
% 127.77/18.21 fact_614_finite__Collect__less__nat, fact_615_termination__basic__simps_I1_J,
% 127.77/18.21 fact_616_termination__basic__simps_I2_J, fact_617_add__lessD1,
% 127.77/18.21 fact_618_less__add__eq__less, fact_619_add__less__mono,
% 127.77/18.21 fact_61_card__insert__if, fact_620_add__less__mono1, fact_621_trans__less__add2,
% 127.77/18.21 fact_622_trans__less__add1, fact_623_nat__add__left__cancel__less,
% 127.77/18.21 fact_624_not__add__less2, fact_625_not__add__less1, fact_626_Suc__less__SucD,
% 127.77/18.21 fact_627_Suc__lessD, fact_628_less__SucE, fact_629_less__trans__Suc,
% 127.77/18.21 fact_62_card__insert__if, fact_630_Suc__lessI, fact_631_less__SucI,
% 127.77/18.21 fact_632_less__antisym, fact_633_not__less__less__Suc__eq,
% 127.77/18.21 fact_634_Suc__less__eq, fact_635_less__Suc__eq, fact_636_not__less__eq,
% 127.77/18.21 fact_637_less__or__eq__imp__le, fact_638_le__neq__implies__less,
% 127.77/18.21 fact_639_less__imp__le__nat, fact_63_card__insert__if,
% 127.77/18.21 fact_640_le__eq__less__or__eq, fact_641_nat__less__le,
% 127.77/18.21 fact_642_diff__less__mono2, fact_643_less__imp__diff__less,
% 127.77/18.21 fact_644_termination__basic__simps_I5_J, fact_645_less__not__refl,
% 127.77/18.21 fact_646_nat__neq__iff, fact_647_linorder__neqE__nat,
% 127.77/18.21 fact_648_less__irrefl__nat, fact_649_less__not__refl2,
% 127.77/18.21 fact_650_less__not__refl3, fact_651_nat__less__cases,
% 127.77/18.21 fact_652_finite__nat__set__iff__bounded, fact_653_card__Collect__less__nat,
% 127.77/18.21 fact_654_finite__M__bounded__by__nat, fact_655_less__add__Suc1,
% 127.77/18.21 fact_656_less__add__Suc2, fact_657_less__iff__Suc__add,
% 127.77/18.21 fact_658_less__eq__Suc__le, fact_659_less__Suc__eq__le, fact_660_Suc__le__eq,
% 127.77/18.21 fact_661_le__imp__less__Suc, fact_662_Suc__leI, fact_663_le__less__Suc__eq,
% 127.77/18.21 fact_664_Suc__le__lessD, fact_665_diff__less__Suc, fact_666_add__diff__inverse,
% 127.77/18.21 fact_667_less__diff__conv, fact_668_diff__less__mono, fact_669_less__diff__iff,
% 127.77/18.21 fact_66_card__insert__disjoint, fact_670_less__eq__Suc__le__raw,
% 127.77/18.21 fact_671_mono__nat__linear__lb, fact_672_inc__induct,
% 127.77/18.21 fact_673_less__imp__Suc__add, fact_674_bounded__nat__set__is__finite,
% 127.77/18.21 fact_675_less__mono__imp__le__mono, fact_676_Suc__lessE, fact_677_lessE,
% 127.77/18.21 fact_678_less__zeroE, fact_679_le0, fact_67_card__insert__disjoint,
% 127.77/18.21 fact_680_zero__less__Suc, fact_681_add__is__1, fact_682_one__is__add,
% 127.77/18.21 fact_683_diff__add__0, fact_684_diff__is__0__eq_H, fact_685_diff__is__0__eq,
% 127.77/18.21 fact_686_One__nat__def, fact_687_diffs0__imp__equal, fact_688_diff__self__eq__0,
% 127.77/18.21 fact_689_minus__nat_Odiff__0, fact_68_card__insert__disjoint,
% 127.77/18.21 fact_690_diff__0__eq__0, fact_691_Suc__neq__Zero, fact_692_Zero__neq__Suc,
% 127.77/18.21 fact_693_nat_Osimps_I3_J, fact_694_Suc__not__Zero, fact_695_nat_Osimps_I2_J,
% 127.77/18.21 fact_696_Zero__not__Suc, fact_697_bot__nat__def, fact_698_le__0__eq,
% 127.77/18.21 fact_699_less__eq__nat_Osimps_I1_J, fact_69_card__insert__disjoint,
% 127.77/18.21 fact_6_finite__Collect__subsets, fact_70_card__insert__disjoint,
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% 127.77/18.21 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024,
% 127.77/18.21 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn,
% 127.77/18.21 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona,
% 127.77/18.21 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,
% 127.77/18.21 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021,
% 127.77/18.21 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,
% 127.77/18.21 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 127.77/18.21 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,
% 127.77/18.21 help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U,
% 127.77/18.21 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U,
% 127.77/18.21 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,
% 127.77/18.21 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,
% 127.77/18.21 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U,
% 127.77/18.21 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,
% 127.77/18.21 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,
% 127.77/18.21 help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 127.77/18.21 help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 127.77/18.21 help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 127.77/18.21 help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_,
% 127.77/18.21 help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,
% 127.77/18.21 help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,
% 127.77/18.21 help_fFalse_1_1_T, help_fFalse_1_1_U, help_fNot_1_1_U, help_fNot_2_1_U,
% 127.77/18.21 help_fconj_1_1_U, help_fconj_2_1_U, help_fconj_3_1_U, help_fdisj_1_1_U,
% 127.77/18.21 help_fdisj_2_1_U, help_fdisj_3_1_U, help_fequal_1_1_fequal_000t__a_T,
% 127.77/18.21 help_fequal_1_1_fequal_000tc__Com__Opname_T,
% 127.77/18.21 help_fequal_1_1_fequal_000tc__Nat__Onat_T,
% 127.77/18.21 help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,
% 127.77/18.21 help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 127.77/18.21 help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,
% 127.77/18.21 help_fequal_2_1_fequal_000t__a_T, help_fequal_2_1_fequal_000tc__Com__Opname_T,
% 127.77/18.21 help_fequal_2_1_fequal_000tc__Nat__Onat_T,
% 127.77/18.21 help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,
% 127.77/18.21 help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 127.77/18.21 help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,
% 127.77/18.21 help_fimplies_1_1_U, help_fimplies_2_1_U, help_fimplies_3_1_U
% 127.77/18.21
% 127.77/18.21 Those formulas are unsatisfiable:
% 127.77/18.21 ---------------------------------
% 127.77/18.21
% 127.77/18.21 Begin of proof
% 127.77/18.21 |
% 127.77/18.21 | ALPHA: (gsy_v_U) implies:
% 127.77/18.22 | (1) is_fun_pname_bool(u)
% 127.77/18.22 |
% 127.77/18.22 | ALPHA: (fact_64_card__insert__if) implies:
% 128.07/18.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 128.07/18.22 | (hAPP_f1664156314l_bool(v2, v1) = v3) | ~
% 128.07/18.22 | (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~ $i(v1) | ~
% 128.07/18.22 | $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 128.07/18.22 | [v8: $i] : ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v4 &
% 128.07/18.22 | $i(v4) & ~ hBOOL(v4)) | (( ~ hBOOL(v3) | (v7 = v6 &
% 128.07/18.22 | hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 128.07/18.22 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v6 &
% 128.07/18.22 | insert_pname(v0, v1) = v5 & $i(v6) & $i(v5))) & (hBOOL(v3) |
% 128.07/18.22 | (v8 = v6 & hAPP_nat_nat(suc, v7) = v6 &
% 128.07/18.22 | hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 128.07/18.22 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v7 &
% 128.07/18.22 | insert_pname(v0, v1) = v5 & $i(v7) & $i(v6) & $i(v5))))))
% 128.07/18.22 |
% 128.07/18.22 | ALPHA: (fact_65_card__insert__if) implies:
% 128.07/18.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 128.07/18.22 | (hAPP_fun_a_bool_bool(v2, v1) = v3) | ~
% 128.07/18.22 | (hAPP_a85458249l_bool(member_a, v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 128.07/18.22 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 128.07/18.22 | ((hAPP_fun_a_bool_bool(finite_finite_a, v1) = v4 & $i(v4) & ~
% 128.07/18.22 | hBOOL(v4)) | (( ~ hBOOL(v3) | (v7 = v6 &
% 128.07/18.22 | hAPP_fun_a_bool_nat(finite_card_a, v5) = v6 &
% 128.07/18.22 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v6 & insert_a(v0,
% 128.07/18.22 | v1) = v5 & $i(v6) & $i(v5))) & (hBOOL(v3) | (v8 = v6 &
% 128.07/18.22 | hAPP_nat_nat(suc, v7) = v6 &
% 128.07/18.22 | hAPP_fun_a_bool_nat(finite_card_a, v5) = v6 &
% 128.07/18.22 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v7 & insert_a(v0,
% 128.07/18.22 | v1) = v5 & $i(v7) & $i(v6) & $i(v5))))))
% 128.07/18.22 |
% 128.07/18.22 | ALPHA: (fact_154_finite__surj) implies:
% 128.07/18.22 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 128.07/18.22 | ! [v5: $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v0) =
% 128.07/18.22 | v3) | ~ (hAPP_fun_a_bool_bool(v3, v4) = v5) | ~
% 128.07/18.22 | (image_pname_a(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 128.07/18.22 | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] :
% 128.07/18.22 | ((hAPP_f1664156314l_bool(finite_finite_pname, v2) = v6 & $i(v6) & ~
% 128.07/18.22 | hBOOL(v6)) | (hAPP_fun_a_bool_bool(finite_finite_a, v0) = v7 &
% 128.07/18.22 | $i(v7) & hBOOL(v7))))
% 128.07/18.22 |
% 128.07/18.22 | ALPHA: (fact_264_insert__absorb) implies:
% 128.07/18.22 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 128.07/18.22 | (hAPP_f1664156314l_bool(v2, v1) = v3) | ~
% 128.07/18.22 | (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~ $i(v1) | ~
% 128.07/18.22 | $i(v0) | ~ hBOOL(v3) | ~ is_fun_pname_bool(v1) | insert_pname(v0,
% 128.07/18.22 | v1) = v1)
% 128.07/18.22 |
% 128.07/18.22 | ALPHA: (fact_312_rev__image__eqI) implies:
% 128.07/18.22 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 128.07/18.22 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 128.07/18.22 | (hAPP_f1664156314l_bool(v4, v3) = v5) | ~ (hAPP_fun_a_bool_bool(v6,
% 128.07/18.22 | v7) = v8) | ~ (hAPP_p338031245l_bool(member_pname, v2) = v4) |
% 128.07/18.22 | ~ (hAPP_a85458249l_bool(member_a, v0) = v6) | ~ (image_pname_a(v1,
% 128.07/18.22 | v3) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 128.07/18.22 | hBOOL(v5) | hBOOL(v8) | ? [v9: $i] : ( ~ (v9 = v0) &
% 128.07/18.22 | hAPP_pname_a(v1, v2) = v9 & $i(v9)))
% 128.07/18.22 |
% 128.07/18.22 | ALPHA: (fact_324_insert__subset) implies:
% 128.07/18.22 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 128.07/18.22 | ! [v5: $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) =
% 128.07/18.22 | v4) | ~ (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ (insert_a(v0, v1)
% 128.07/18.22 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v5) | ? [v6: $i]
% 128.07/18.22 | : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 128.07/18.22 | ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v8 &
% 128.07/18.22 | hAPP_fun_a_bool_bool(v8, v2) = v9 & $i(v9) & $i(v8) & ~
% 128.07/18.22 | hBOOL(v9)) | (hAPP_fun_a_bool_bool(v6, v2) = v7 &
% 128.07/18.22 | hAPP_a85458249l_bool(member_a, v0) = v6 & $i(v7) & $i(v6) & ~
% 128.07/18.22 | hBOOL(v7))))
% 128.07/18.22 |
% 128.07/18.22 | ALPHA: (fact_359_subsetI) implies:
% 128.07/18.22 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 128.07/18.22 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2) | ~
% 128.07/18.22 | (hAPP_fun_a_bool_bool(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 128.07/18.22 | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 128.07/18.22 | (hAPP_fun_a_bool_bool(v5, v1) = v6 & hAPP_fun_a_bool_bool(v5, v0) =
% 128.07/18.22 | v7 & hAPP_a85458249l_bool(member_a, v4) = v5 & $i(v7) & $i(v6) &
% 128.07/18.22 | $i(v5) & $i(v4) & hBOOL(v6) & is_a(v4) & ~ hBOOL(v7)))
% 128.07/18.22 |
% 128.07/18.22 | ALPHA: (conj_0) implies:
% 128.07/18.22 | (9) ? [v0: $i] : (hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 &
% 128.07/18.22 | $i(v0) & hBOOL(v0))
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (conj_1) implies:
% 128.07/18.23 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.07/18.23 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v0 &
% 128.07/18.23 | hAPP_fun_a_bool_bool(v0, v1) = v2 & image_pname_a(mgt_call, u) = v1
% 128.07/18.23 | & $i(v2) & $i(v1) & $i(v0) & hBOOL(v2))
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (conj_2) implies:
% 128.07/18.23 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 128.07/18.23 | (hAPP_nat_nat(suc, na) = v0 & hAPP_fun_a_bool_nat(finite_card_a, v2) =
% 128.07/18.23 | v3 & hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 &
% 128.07/18.23 | hAPP_nat_bool(v1, v3) = v4 & image_pname_a(mgt_call, u) = v2 &
% 128.07/18.23 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v4))
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (conj_3) implies:
% 128.07/18.23 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 128.07/18.23 | (minus_minus_nat(v2) = v3 & hAPP_nat_nat(v3, v4) = v0 &
% 128.07/18.23 | hAPP_nat_nat(suc, na) = v4 & hAPP_fun_a_bool_nat(finite_card_a, v1)
% 128.07/18.23 | = v2 & hAPP_fun_a_bool_nat(finite_card_a, g) = v0 &
% 128.07/18.23 | image_pname_a(mgt_call, u) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 128.07/18.23 | & $i(v0))
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (conj_4) implies:
% 128.07/18.23 | (13) ? [v0: $i] : ? [v1: $i] : (hAPP_f1664156314l_bool(v0, u) = v1 &
% 128.07/18.23 | hAPP_p338031245l_bool(member_pname, pn) = v0 & $i(v1) & $i(v0) &
% 128.07/18.23 | hBOOL(v1))
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (conj_5) implies:
% 128.07/18.23 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_fun_a_bool_bool(v1, g)
% 128.07/18.23 | = v2 & hAPP_pname_a(mgt_call, pn) = v0 &
% 128.07/18.23 | hAPP_a85458249l_bool(member_a, v0) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 128.07/18.23 | ~ hBOOL(v2))
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (conj_6) implies:
% 128.07/18.23 | (15) $i(g)
% 128.07/18.23 | (16) $i(u)
% 128.07/18.23 | (17) $i(pn)
% 128.07/18.23 | (18) $i(mgt_call)
% 128.07/18.23 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 128.07/18.23 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2 &
% 128.07/18.23 | hAPP_fun_a_bool_bool(v2, v3) = v4 & hAPP_pname_a(mgt_call, pn) = v0
% 128.07/18.23 | & insert_a(v0, g) = v1 & image_pname_a(mgt_call, u) = v3 & $i(v4) &
% 128.07/18.23 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v4))
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (function-axioms) implies:
% 128.07/18.23 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 128.07/18.23 | (image_pname_a(v3, v2) = v1) | ~ (image_pname_a(v3, v2) = v0))
% 128.07/18.23 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 128.07/18.23 | (insert_pname(v3, v2) = v1) | ~ (insert_pname(v3, v2) = v0))
% 128.07/18.23 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 128.07/18.23 | (hAPP_a85458249l_bool(v3, v2) = v1) | ~ (hAPP_a85458249l_bool(v3,
% 128.07/18.23 | v2) = v0))
% 128.07/18.23 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 128.07/18.23 | (hAPP_pname_a(v3, v2) = v1) | ~ (hAPP_pname_a(v3, v2) = v0))
% 128.07/18.23 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 128.07/18.23 | (hAPP_fun_a_bool_bool(v3, v2) = v1) | ~ (hAPP_fun_a_bool_bool(v3,
% 128.07/18.23 | v2) = v0))
% 128.07/18.23 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 128.07/18.23 | (hAPP_f1631501043l_bool(v3, v2) = v1) | ~
% 128.07/18.23 | (hAPP_f1631501043l_bool(v3, v2) = v0))
% 128.07/18.23 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 128.07/18.23 | (hAPP_f1664156314l_bool(v3, v2) = v1) | ~
% 128.07/18.23 | (hAPP_f1664156314l_bool(v3, v2) = v0))
% 128.07/18.23 |
% 128.07/18.23 | DELTA: instantiating (9) with fresh symbol all_802_0 gives:
% 128.07/18.23 | (27) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_802_0 &
% 128.07/18.23 | $i(all_802_0) & hBOOL(all_802_0)
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (27) implies:
% 128.07/18.23 | (28) hBOOL(all_802_0)
% 128.07/18.23 | (29) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_802_0
% 128.07/18.23 |
% 128.07/18.23 | DELTA: instantiating (13) with fresh symbols all_823_0, all_823_1 gives:
% 128.07/18.23 | (30) hAPP_f1664156314l_bool(all_823_1, u) = all_823_0 &
% 128.07/18.23 | hAPP_p338031245l_bool(member_pname, pn) = all_823_1 & $i(all_823_0) &
% 128.07/18.23 | $i(all_823_1) & hBOOL(all_823_0)
% 128.07/18.23 |
% 128.07/18.23 | ALPHA: (30) implies:
% 128.07/18.24 | (31) hBOOL(all_823_0)
% 128.07/18.24 | (32) hAPP_p338031245l_bool(member_pname, pn) = all_823_1
% 128.07/18.24 | (33) hAPP_f1664156314l_bool(all_823_1, u) = all_823_0
% 128.07/18.24 |
% 128.07/18.24 | DELTA: instantiating (10) with fresh symbols all_879_0, all_879_1, all_879_2
% 128.07/18.24 | gives:
% 128.07/18.24 | (34) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_879_2 &
% 128.07/18.24 | hAPP_fun_a_bool_bool(all_879_2, all_879_1) = all_879_0 &
% 128.07/18.24 | image_pname_a(mgt_call, u) = all_879_1 & $i(all_879_0) & $i(all_879_1)
% 128.07/18.24 | & $i(all_879_2) & hBOOL(all_879_0)
% 128.07/18.24 |
% 128.07/18.24 | ALPHA: (34) implies:
% 128.07/18.24 | (35) hBOOL(all_879_0)
% 128.07/18.24 | (36) image_pname_a(mgt_call, u) = all_879_1
% 128.07/18.24 | (37) hAPP_fun_a_bool_bool(all_879_2, all_879_1) = all_879_0
% 128.07/18.24 | (38) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_879_2
% 128.07/18.24 |
% 128.07/18.24 | DELTA: instantiating (14) with fresh symbols all_886_0, all_886_1, all_886_2
% 128.07/18.24 | gives:
% 128.07/18.24 | (39) hAPP_fun_a_bool_bool(all_886_1, g) = all_886_0 &
% 128.07/18.24 | hAPP_pname_a(mgt_call, pn) = all_886_2 &
% 128.07/18.24 | hAPP_a85458249l_bool(member_a, all_886_2) = all_886_1 & $i(all_886_0)
% 128.07/18.24 | & $i(all_886_1) & $i(all_886_2) & ~ hBOOL(all_886_0)
% 128.07/18.24 |
% 128.07/18.24 | ALPHA: (39) implies:
% 128.07/18.24 | (40) ~ hBOOL(all_886_0)
% 128.07/18.24 | (41) hAPP_a85458249l_bool(member_a, all_886_2) = all_886_1
% 128.07/18.24 | (42) hAPP_pname_a(mgt_call, pn) = all_886_2
% 128.07/18.24 | (43) hAPP_fun_a_bool_bool(all_886_1, g) = all_886_0
% 128.07/18.24 |
% 128.07/18.24 | DELTA: instantiating (19) with fresh symbols all_899_0, all_899_1, all_899_2,
% 128.07/18.24 | all_899_3, all_899_4 gives:
% 128.07/18.24 | (44) hAPP_f1631501043l_bool(ord_le1311769555a_bool, all_899_3) = all_899_2
% 128.07/18.24 | & hAPP_fun_a_bool_bool(all_899_2, all_899_1) = all_899_0 &
% 128.07/18.24 | hAPP_pname_a(mgt_call, pn) = all_899_4 & insert_a(all_899_4, g) =
% 128.07/18.24 | all_899_3 & image_pname_a(mgt_call, u) = all_899_1 & $i(all_899_0) &
% 128.07/18.24 | $i(all_899_1) & $i(all_899_2) & $i(all_899_3) & $i(all_899_4) & ~
% 128.07/18.24 | hBOOL(all_899_0)
% 128.07/18.24 |
% 128.07/18.24 | ALPHA: (44) implies:
% 128.07/18.24 | (45) ~ hBOOL(all_899_0)
% 128.07/18.24 | (46) $i(all_899_4)
% 128.07/18.24 | (47) $i(all_899_3)
% 128.07/18.24 | (48) $i(all_899_1)
% 128.07/18.24 | (49) image_pname_a(mgt_call, u) = all_899_1
% 128.07/18.24 | (50) insert_a(all_899_4, g) = all_899_3
% 128.07/18.24 | (51) hAPP_pname_a(mgt_call, pn) = all_899_4
% 128.07/18.24 | (52) hAPP_fun_a_bool_bool(all_899_2, all_899_1) = all_899_0
% 128.07/18.24 | (53) hAPP_f1631501043l_bool(ord_le1311769555a_bool, all_899_3) = all_899_2
% 128.07/18.24 |
% 128.07/18.24 | DELTA: instantiating (12) with fresh symbols all_901_0, all_901_1, all_901_2,
% 128.07/18.24 | all_901_3, all_901_4 gives:
% 128.07/18.24 | (54) minus_minus_nat(all_901_2) = all_901_1 & hAPP_nat_nat(all_901_1,
% 128.07/18.24 | all_901_0) = all_901_4 & hAPP_nat_nat(suc, na) = all_901_0 &
% 128.07/18.24 | hAPP_fun_a_bool_nat(finite_card_a, all_901_3) = all_901_2 &
% 128.07/18.24 | hAPP_fun_a_bool_nat(finite_card_a, g) = all_901_4 &
% 128.07/18.24 | image_pname_a(mgt_call, u) = all_901_3 & $i(all_901_0) & $i(all_901_1)
% 128.07/18.24 | & $i(all_901_2) & $i(all_901_3) & $i(all_901_4)
% 128.07/18.24 |
% 128.07/18.24 | ALPHA: (54) implies:
% 128.07/18.24 | (55) image_pname_a(mgt_call, u) = all_901_3
% 128.07/18.24 |
% 128.07/18.24 | DELTA: instantiating (11) with fresh symbols all_903_0, all_903_1, all_903_2,
% 128.07/18.24 | all_903_3, all_903_4 gives:
% 128.07/18.24 | (56) hAPP_nat_nat(suc, na) = all_903_4 & hAPP_fun_a_bool_nat(finite_card_a,
% 128.07/18.24 | all_903_2) = all_903_1 & hAPP_n1699378549t_bool(ord_less_eq_nat,
% 128.07/18.24 | all_903_4) = all_903_3 & hAPP_nat_bool(all_903_3, all_903_1) =
% 128.07/18.24 | all_903_0 & image_pname_a(mgt_call, u) = all_903_2 & $i(all_903_0) &
% 128.07/18.24 | $i(all_903_1) & $i(all_903_2) & $i(all_903_3) & $i(all_903_4) &
% 128.07/18.24 | hBOOL(all_903_0)
% 128.07/18.24 |
% 128.07/18.24 | ALPHA: (56) implies:
% 128.07/18.24 | (57) image_pname_a(mgt_call, u) = all_903_2
% 128.07/18.24 |
% 128.07/18.24 | GROUND_INST: instantiating (20) with all_879_1, all_901_3, u, mgt_call,
% 128.07/18.24 | simplifying with (36), (55) gives:
% 128.07/18.24 | (58) all_901_3 = all_879_1
% 128.07/18.24 |
% 128.07/18.24 | GROUND_INST: instantiating (20) with all_901_3, all_903_2, u, mgt_call,
% 128.07/18.24 | simplifying with (55), (57) gives:
% 128.07/18.24 | (59) all_903_2 = all_901_3
% 128.07/18.24 |
% 128.07/18.24 | GROUND_INST: instantiating (20) with all_899_1, all_903_2, u, mgt_call,
% 128.07/18.24 | simplifying with (49), (57) gives:
% 128.07/18.24 | (60) all_903_2 = all_899_1
% 128.07/18.24 |
% 128.07/18.24 | GROUND_INST: instantiating (23) with all_886_2, all_899_4, pn, mgt_call,
% 128.07/18.24 | simplifying with (42), (51) gives:
% 128.07/18.24 | (61) all_899_4 = all_886_2
% 128.07/18.24 |
% 128.07/18.24 | COMBINE_EQS: (59), (60) imply:
% 128.07/18.24 | (62) all_901_3 = all_899_1
% 128.07/18.24 |
% 128.07/18.24 | SIMP: (62) implies:
% 128.07/18.24 | (63) all_901_3 = all_899_1
% 128.07/18.24 |
% 128.07/18.24 | COMBINE_EQS: (58), (63) imply:
% 128.07/18.24 | (64) all_899_1 = all_879_1
% 128.07/18.24 |
% 128.07/18.24 | REDUCE: (52), (64) imply:
% 128.07/18.24 | (65) hAPP_fun_a_bool_bool(all_899_2, all_879_1) = all_899_0
% 128.07/18.24 |
% 128.07/18.24 | REDUCE: (50), (61) imply:
% 128.07/18.24 | (66) insert_a(all_886_2, g) = all_899_3
% 128.07/18.24 |
% 128.07/18.24 | REDUCE: (48), (64) imply:
% 128.07/18.24 | (67) $i(all_879_1)
% 128.07/18.24 |
% 128.07/18.24 | REDUCE: (46), (61) imply:
% 128.07/18.24 | (68) $i(all_886_2)
% 128.07/18.24 |
% 128.07/18.24 | GROUND_INST: instantiating (3) with all_886_2, g, all_886_1, all_886_0,
% 128.07/18.24 | simplifying with (15), (41), (43), (68) gives:
% 128.07/18.24 | (69) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 128.07/18.24 | ((hAPP_fun_a_bool_bool(finite_finite_a, g) = v0 & $i(v0) & ~
% 128.07/18.24 | hBOOL(v0)) | (( ~ hBOOL(all_886_0) | (v3 = v2 &
% 128.07/18.24 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 128.07/18.24 | hAPP_fun_a_bool_nat(finite_card_a, g) = v2 &
% 128.07/18.24 | insert_a(all_886_2, g) = v1 & $i(v2) & $i(v1))) &
% 128.07/18.24 | (hBOOL(all_886_0) | (v4 = v2 & hAPP_nat_nat(suc, v3) = v2 &
% 128.07/18.24 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 128.07/18.24 | hAPP_fun_a_bool_nat(finite_card_a, g) = v3 &
% 128.07/18.24 | insert_a(all_886_2, g) = v1 & $i(v3) & $i(v2) & $i(v1)))))
% 128.07/18.24 |
% 128.07/18.25 | GROUND_INST: instantiating (4) with g, mgt_call, u, all_879_2, all_879_1,
% 128.07/18.25 | all_879_0, simplifying with (15), (16), (18), (35), (36), (37),
% 128.07/18.25 | (38) gives:
% 128.07/18.25 | (70) ? [v0: $i] : ? [v1: $i] :
% 128.07/18.25 | ((hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 & $i(v0) & ~
% 128.07/18.25 | hBOOL(v0)) | (hAPP_fun_a_bool_bool(finite_finite_a, g) = v1 &
% 128.07/18.25 | $i(v1) & hBOOL(v1)))
% 128.07/18.25 |
% 128.07/18.25 | GROUND_INST: instantiating (7) with all_886_2, g, all_879_1, all_899_3,
% 128.07/18.25 | all_899_2, all_899_0, simplifying with (15), (45), (53), (65),
% 128.07/18.25 | (66), (67), (68) gives:
% 128.07/18.25 | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 128.07/18.25 | ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v2 &
% 128.07/18.25 | hAPP_fun_a_bool_bool(v2, all_879_1) = v3 & $i(v3) & $i(v2) & ~
% 128.07/18.25 | hBOOL(v3)) | (hAPP_fun_a_bool_bool(v0, all_879_1) = v1 &
% 128.07/18.25 | hAPP_a85458249l_bool(member_a, all_886_2) = v0 & $i(v1) & $i(v0) &
% 128.07/18.25 | ~ hBOOL(v1)))
% 128.07/18.25 |
% 128.07/18.25 | GROUND_INST: instantiating (8) with all_879_1, all_899_3, all_899_2,
% 128.07/18.25 | all_899_0, simplifying with (45), (47), (53), (65), (67) gives:
% 128.07/18.25 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 128.07/18.25 | (hAPP_fun_a_bool_bool(v1, all_899_3) = v2 & hAPP_fun_a_bool_bool(v1,
% 128.07/18.25 | all_879_1) = v3 & hAPP_a85458249l_bool(member_a, v0) = v1 & $i(v3)
% 128.07/18.25 | & $i(v2) & $i(v1) & $i(v0) & hBOOL(v2) & is_a(v0) & ~ hBOOL(v3))
% 128.07/18.25 |
% 128.07/18.25 | GROUND_INST: instantiating (5) with pn, u, all_823_1, all_823_0, simplifying
% 128.07/18.25 | with (1), (16), (17), (31), (32), (33) gives:
% 128.07/18.25 | (73) insert_pname(pn, u) = u
% 128.07/18.25 |
% 128.07/18.25 | GROUND_INST: instantiating (2) with pn, u, all_823_1, all_823_0, simplifying
% 128.07/18.25 | with (16), (17), (32), (33) gives:
% 128.07/18.25 | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 128.07/18.25 | ((hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 & $i(v0) & ~
% 128.07/18.25 | hBOOL(v0)) | (( ~ hBOOL(all_823_0) | (v3 = v2 &
% 128.07/18.25 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v2 &
% 128.07/18.25 | hAPP_f921600141ol_nat(finite_card_pname, u) = v2 &
% 128.07/18.25 | insert_pname(pn, u) = v1 & $i(v2) & $i(v1))) &
% 128.07/18.25 | (hBOOL(all_823_0) | (v4 = v2 & hAPP_nat_nat(suc, v3) = v2 &
% 128.07/18.25 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v2 &
% 128.07/18.25 | hAPP_f921600141ol_nat(finite_card_pname, u) = v3 &
% 128.07/18.25 | insert_pname(pn, u) = v1 & $i(v3) & $i(v2) & $i(v1)))))
% 128.07/18.25 |
% 128.07/18.25 | DELTA: instantiating (70) with fresh symbols all_1147_0, all_1147_1 gives:
% 128.07/18.25 | (75) (hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1147_1 &
% 128.07/18.25 | $i(all_1147_1) & ~ hBOOL(all_1147_1)) |
% 128.07/18.25 | (hAPP_fun_a_bool_bool(finite_finite_a, g) = all_1147_0 &
% 128.07/18.25 | $i(all_1147_0) & hBOOL(all_1147_0))
% 128.07/18.25 |
% 128.07/18.25 | DELTA: instantiating (72) with fresh symbols all_1159_0, all_1159_1,
% 128.07/18.25 | all_1159_2, all_1159_3 gives:
% 128.07/18.25 | (76) hAPP_fun_a_bool_bool(all_1159_2, all_899_3) = all_1159_1 &
% 128.07/18.25 | hAPP_fun_a_bool_bool(all_1159_2, all_879_1) = all_1159_0 &
% 128.07/18.25 | hAPP_a85458249l_bool(member_a, all_1159_3) = all_1159_2 &
% 128.07/18.25 | $i(all_1159_0) & $i(all_1159_1) & $i(all_1159_2) & $i(all_1159_3) &
% 128.07/18.25 | hBOOL(all_1159_1) & is_a(all_1159_3) & ~ hBOOL(all_1159_0)
% 128.07/18.25 |
% 128.07/18.25 | ALPHA: (76) implies:
% 128.07/18.25 | (77) ~ hBOOL(all_1159_0)
% 128.07/18.25 | (78) $i(all_1159_3)
% 128.07/18.25 | (79) hAPP_a85458249l_bool(member_a, all_1159_3) = all_1159_2
% 128.07/18.25 | (80) hAPP_fun_a_bool_bool(all_1159_2, all_879_1) = all_1159_0
% 128.07/18.25 |
% 128.07/18.25 | DELTA: instantiating (71) with fresh symbols all_1161_0, all_1161_1,
% 128.07/18.25 | all_1161_2, all_1161_3 gives:
% 128.07/18.25 | (81) (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_1161_1 &
% 128.07/18.25 | hAPP_fun_a_bool_bool(all_1161_1, all_879_1) = all_1161_0 &
% 128.07/18.25 | $i(all_1161_0) & $i(all_1161_1) & ~ hBOOL(all_1161_0)) |
% 128.07/18.25 | (hAPP_fun_a_bool_bool(all_1161_3, all_879_1) = all_1161_2 &
% 128.07/18.25 | hAPP_a85458249l_bool(member_a, all_886_2) = all_1161_3 &
% 128.07/18.25 | $i(all_1161_2) & $i(all_1161_3) & ~ hBOOL(all_1161_2))
% 128.07/18.25 |
% 128.07/18.25 | DELTA: instantiating (69) with fresh symbols all_1168_0, all_1168_1,
% 128.07/18.25 | all_1168_2, all_1168_3, all_1168_4 gives:
% 128.07/18.25 | (82) (hAPP_fun_a_bool_bool(finite_finite_a, g) = all_1168_4 &
% 128.07/18.25 | $i(all_1168_4) & ~ hBOOL(all_1168_4)) | (( ~ hBOOL(all_886_0) |
% 128.07/18.25 | (all_1168_1 = all_1168_2 & hAPP_fun_a_bool_nat(finite_card_a,
% 128.07/18.25 | all_1168_3) = all_1168_2 & hAPP_fun_a_bool_nat(finite_card_a,
% 128.07/18.25 | g) = all_1168_2 & insert_a(all_886_2, g) = all_1168_3 &
% 128.07/18.25 | $i(all_1168_2) & $i(all_1168_3))) & (hBOOL(all_886_0) |
% 128.07/18.25 | (all_1168_0 = all_1168_2 & hAPP_nat_nat(suc, all_1168_1) =
% 128.07/18.25 | all_1168_2 & hAPP_fun_a_bool_nat(finite_card_a, all_1168_3) =
% 128.07/18.25 | all_1168_2 & hAPP_fun_a_bool_nat(finite_card_a, g) = all_1168_1
% 128.07/18.25 | & insert_a(all_886_2, g) = all_1168_3 & $i(all_1168_1) &
% 128.07/18.25 | $i(all_1168_2) & $i(all_1168_3))))
% 128.07/18.25 |
% 128.07/18.25 | DELTA: instantiating (74) with fresh symbols all_1169_0, all_1169_1,
% 128.07/18.25 | all_1169_2, all_1169_3, all_1169_4 gives:
% 128.07/18.25 | (83) (hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1169_4 &
% 128.07/18.25 | $i(all_1169_4) & ~ hBOOL(all_1169_4)) | (( ~ hBOOL(all_823_0) |
% 128.07/18.25 | (all_1169_1 = all_1169_2 &
% 128.07/18.25 | hAPP_f921600141ol_nat(finite_card_pname, all_1169_3) =
% 128.07/18.25 | all_1169_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 128.07/18.25 | all_1169_2 & insert_pname(pn, u) = all_1169_3 & $i(all_1169_2) &
% 128.07/18.25 | $i(all_1169_3))) & (hBOOL(all_823_0) | (all_1169_0 = all_1169_2
% 128.07/18.25 | & hAPP_nat_nat(suc, all_1169_1) = all_1169_2 &
% 128.07/18.25 | hAPP_f921600141ol_nat(finite_card_pname, all_1169_3) =
% 128.07/18.25 | all_1169_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 128.07/18.25 | all_1169_1 & insert_pname(pn, u) = all_1169_3 & $i(all_1169_1) &
% 128.07/18.25 | $i(all_1169_2) & $i(all_1169_3))))
% 128.07/18.25 |
% 128.07/18.25 | BETA: splitting (83) gives:
% 128.07/18.25 |
% 128.07/18.25 | Case 1:
% 128.07/18.25 | |
% 128.07/18.25 | | (84) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1169_4 &
% 128.07/18.25 | | $i(all_1169_4) & ~ hBOOL(all_1169_4)
% 128.07/18.25 | |
% 128.07/18.25 | | ALPHA: (84) implies:
% 128.07/18.26 | | (85) ~ hBOOL(all_1169_4)
% 128.07/18.26 | | (86) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1169_4
% 128.07/18.26 | |
% 128.07/18.26 | | GROUND_INST: instantiating (26) with all_802_0, all_1169_4, u,
% 128.07/18.26 | | finite_finite_pname, simplifying with (29), (86) gives:
% 128.07/18.26 | | (87) all_1169_4 = all_802_0
% 128.07/18.26 | |
% 128.07/18.26 | | REDUCE: (85), (87) imply:
% 128.07/18.26 | | (88) ~ hBOOL(all_802_0)
% 128.07/18.26 | |
% 128.07/18.26 | | PRED_UNIFY: (28), (88) imply:
% 128.07/18.26 | | (89) $false
% 128.07/18.26 | |
% 128.07/18.26 | | CLOSE: (89) is inconsistent.
% 128.07/18.26 | |
% 128.07/18.26 | Case 2:
% 128.07/18.26 | |
% 128.07/18.26 | | (90) ( ~ hBOOL(all_823_0) | (all_1169_1 = all_1169_2 &
% 128.07/18.26 | | hAPP_f921600141ol_nat(finite_card_pname, all_1169_3) =
% 128.07/18.26 | | all_1169_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 128.07/18.26 | | all_1169_2 & insert_pname(pn, u) = all_1169_3 & $i(all_1169_2) &
% 128.07/18.26 | | $i(all_1169_3))) & (hBOOL(all_823_0) | (all_1169_0 = all_1169_2
% 128.07/18.26 | | & hAPP_nat_nat(suc, all_1169_1) = all_1169_2 &
% 128.07/18.26 | | hAPP_f921600141ol_nat(finite_card_pname, all_1169_3) =
% 128.07/18.26 | | all_1169_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 128.07/18.26 | | all_1169_1 & insert_pname(pn, u) = all_1169_3 & $i(all_1169_1) &
% 128.07/18.26 | | $i(all_1169_2) & $i(all_1169_3)))
% 128.07/18.26 | |
% 128.07/18.26 | | ALPHA: (90) implies:
% 128.07/18.26 | | (91) ~ hBOOL(all_823_0) | (all_1169_1 = all_1169_2 &
% 128.07/18.26 | | hAPP_f921600141ol_nat(finite_card_pname, all_1169_3) = all_1169_2
% 128.07/18.26 | | & hAPP_f921600141ol_nat(finite_card_pname, u) = all_1169_2 &
% 128.07/18.26 | | insert_pname(pn, u) = all_1169_3 & $i(all_1169_2) &
% 128.07/18.26 | | $i(all_1169_3))
% 128.07/18.26 | |
% 128.07/18.26 | | BETA: splitting (75) gives:
% 128.07/18.26 | |
% 128.07/18.26 | | Case 1:
% 128.07/18.26 | | |
% 128.25/18.26 | | | (92) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1147_1 &
% 128.25/18.26 | | | $i(all_1147_1) & ~ hBOOL(all_1147_1)
% 128.25/18.26 | | |
% 128.25/18.26 | | | ALPHA: (92) implies:
% 128.25/18.26 | | | (93) ~ hBOOL(all_1147_1)
% 128.25/18.26 | | | (94) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1147_1
% 128.25/18.26 | | |
% 128.25/18.26 | | | GROUND_INST: instantiating (26) with all_802_0, all_1147_1, u,
% 128.25/18.26 | | | finite_finite_pname, simplifying with (29), (94) gives:
% 128.25/18.26 | | | (95) all_1147_1 = all_802_0
% 128.25/18.26 | | |
% 128.25/18.26 | | | REDUCE: (93), (95) imply:
% 128.25/18.26 | | | (96) ~ hBOOL(all_802_0)
% 128.25/18.26 | | |
% 128.25/18.26 | | | PRED_UNIFY: (28), (96) imply:
% 128.25/18.26 | | | (97) $false
% 128.25/18.26 | | |
% 128.25/18.26 | | | CLOSE: (97) is inconsistent.
% 128.25/18.26 | | |
% 128.25/18.26 | | Case 2:
% 128.25/18.26 | | |
% 128.25/18.26 | | | (98) hAPP_fun_a_bool_bool(finite_finite_a, g) = all_1147_0 &
% 128.25/18.26 | | | $i(all_1147_0) & hBOOL(all_1147_0)
% 128.25/18.26 | | |
% 128.25/18.26 | | | ALPHA: (98) implies:
% 128.25/18.26 | | | (99) hBOOL(all_1147_0)
% 128.25/18.26 | | | (100) hAPP_fun_a_bool_bool(finite_finite_a, g) = all_1147_0
% 128.25/18.26 | | |
% 128.25/18.26 | | | BETA: splitting (81) gives:
% 128.25/18.26 | | |
% 128.25/18.26 | | | Case 1:
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | (101) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_1161_1
% 128.25/18.26 | | | | & hAPP_fun_a_bool_bool(all_1161_1, all_879_1) = all_1161_0 &
% 128.25/18.26 | | | | $i(all_1161_0) & $i(all_1161_1) & ~ hBOOL(all_1161_0)
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | ALPHA: (101) implies:
% 128.25/18.26 | | | | (102) ~ hBOOL(all_1161_0)
% 128.25/18.26 | | | | (103) hAPP_fun_a_bool_bool(all_1161_1, all_879_1) = all_1161_0
% 128.25/18.26 | | | | (104) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_1161_1
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | GROUND_INST: instantiating (25) with all_879_2, all_1161_1, g,
% 128.25/18.26 | | | | ord_le1311769555a_bool, simplifying with (38), (104) gives:
% 128.25/18.26 | | | | (105) all_1161_1 = all_879_2
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | REDUCE: (103), (105) imply:
% 128.25/18.26 | | | | (106) hAPP_fun_a_bool_bool(all_879_2, all_879_1) = all_1161_0
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | GROUND_INST: instantiating (24) with all_879_0, all_1161_0, all_879_1,
% 128.25/18.26 | | | | all_879_2, simplifying with (37), (106) gives:
% 128.25/18.26 | | | | (107) all_1161_0 = all_879_0
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | REDUCE: (102), (107) imply:
% 128.25/18.26 | | | | (108) ~ hBOOL(all_879_0)
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | PRED_UNIFY: (35), (108) imply:
% 128.25/18.26 | | | | (109) $false
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | CLOSE: (109) is inconsistent.
% 128.25/18.26 | | | |
% 128.25/18.26 | | | Case 2:
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | (110) hAPP_fun_a_bool_bool(all_1161_3, all_879_1) = all_1161_2 &
% 128.25/18.26 | | | | hAPP_a85458249l_bool(member_a, all_886_2) = all_1161_3 &
% 128.25/18.26 | | | | $i(all_1161_2) & $i(all_1161_3) & ~ hBOOL(all_1161_2)
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | ALPHA: (110) implies:
% 128.25/18.26 | | | | (111) ~ hBOOL(all_1161_2)
% 128.25/18.26 | | | | (112) hAPP_a85458249l_bool(member_a, all_886_2) = all_1161_3
% 128.25/18.26 | | | | (113) hAPP_fun_a_bool_bool(all_1161_3, all_879_1) = all_1161_2
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | BETA: splitting (91) gives:
% 128.25/18.26 | | | |
% 128.25/18.26 | | | | Case 1:
% 128.25/18.26 | | | | |
% 128.25/18.26 | | | | | (114) ~ hBOOL(all_823_0)
% 128.25/18.26 | | | | |
% 128.25/18.26 | | | | | PRED_UNIFY: (31), (114) imply:
% 128.25/18.26 | | | | | (115) $false
% 128.25/18.26 | | | | |
% 128.25/18.26 | | | | | CLOSE: (115) is inconsistent.
% 128.25/18.26 | | | | |
% 128.25/18.26 | | | | Case 2:
% 128.25/18.26 | | | | |
% 128.25/18.26 | | | | | (116) all_1169_1 = all_1169_2 &
% 128.25/18.26 | | | | | hAPP_f921600141ol_nat(finite_card_pname, all_1169_3) =
% 128.25/18.26 | | | | | all_1169_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 128.25/18.26 | | | | | all_1169_2 & insert_pname(pn, u) = all_1169_3 &
% 128.25/18.26 | | | | | $i(all_1169_2) & $i(all_1169_3)
% 128.25/18.26 | | | | |
% 128.25/18.26 | | | | | ALPHA: (116) implies:
% 128.25/18.26 | | | | | (117) $i(all_1169_3)
% 128.25/18.26 | | | | | (118) insert_pname(pn, u) = all_1169_3
% 128.25/18.26 | | | | |
% 128.25/18.26 | | | | | BETA: splitting (82) gives:
% 128.25/18.26 | | | | |
% 128.25/18.26 | | | | | Case 1:
% 128.25/18.26 | | | | | |
% 128.25/18.26 | | | | | | (119) hAPP_fun_a_bool_bool(finite_finite_a, g) = all_1168_4 &
% 128.25/18.26 | | | | | | $i(all_1168_4) & ~ hBOOL(all_1168_4)
% 128.25/18.26 | | | | | |
% 128.25/18.26 | | | | | | ALPHA: (119) implies:
% 128.25/18.26 | | | | | | (120) ~ hBOOL(all_1168_4)
% 128.25/18.26 | | | | | | (121) hAPP_fun_a_bool_bool(finite_finite_a, g) = all_1168_4
% 128.25/18.26 | | | | | |
% 128.25/18.26 | | | | | | GROUND_INST: instantiating (24) with all_1147_0, all_1168_4, g,
% 128.25/18.26 | | | | | | finite_finite_a, simplifying with (100), (121) gives:
% 128.25/18.26 | | | | | | (122) all_1168_4 = all_1147_0
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | | REDUCE: (120), (122) imply:
% 128.25/18.27 | | | | | | (123) ~ hBOOL(all_1147_0)
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | | PRED_UNIFY: (99), (123) imply:
% 128.25/18.27 | | | | | | (124) $false
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | | CLOSE: (124) is inconsistent.
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | Case 2:
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | | (125) ( ~ hBOOL(all_886_0) | (all_1168_1 = all_1168_2 &
% 128.25/18.27 | | | | | | hAPP_fun_a_bool_nat(finite_card_a, all_1168_3) =
% 128.25/18.27 | | | | | | all_1168_2 & hAPP_fun_a_bool_nat(finite_card_a, g) =
% 128.25/18.27 | | | | | | all_1168_2 & insert_a(all_886_2, g) = all_1168_3 &
% 128.25/18.27 | | | | | | $i(all_1168_2) & $i(all_1168_3))) & (hBOOL(all_886_0) |
% 128.25/18.27 | | | | | | (all_1168_0 = all_1168_2 & hAPP_nat_nat(suc, all_1168_1)
% 128.25/18.27 | | | | | | = all_1168_2 & hAPP_fun_a_bool_nat(finite_card_a,
% 128.25/18.27 | | | | | | all_1168_3) = all_1168_2 &
% 128.25/18.27 | | | | | | hAPP_fun_a_bool_nat(finite_card_a, g) = all_1168_1 &
% 128.25/18.27 | | | | | | insert_a(all_886_2, g) = all_1168_3 & $i(all_1168_1) &
% 128.25/18.27 | | | | | | $i(all_1168_2) & $i(all_1168_3)))
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | | ALPHA: (125) implies:
% 128.25/18.27 | | | | | | (126) hBOOL(all_886_0) | (all_1168_0 = all_1168_2 &
% 128.25/18.27 | | | | | | hAPP_nat_nat(suc, all_1168_1) = all_1168_2 &
% 128.25/18.27 | | | | | | hAPP_fun_a_bool_nat(finite_card_a, all_1168_3) =
% 128.25/18.27 | | | | | | all_1168_2 & hAPP_fun_a_bool_nat(finite_card_a, g) =
% 128.25/18.27 | | | | | | all_1168_1 & insert_a(all_886_2, g) = all_1168_3 &
% 128.25/18.27 | | | | | | $i(all_1168_1) & $i(all_1168_2) & $i(all_1168_3))
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | | BETA: splitting (126) gives:
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | | Case 1:
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | (127) hBOOL(all_886_0)
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | PRED_UNIFY: (40), (127) imply:
% 128.25/18.27 | | | | | | | (128) $false
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | CLOSE: (128) is inconsistent.
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | Case 2:
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | GROUND_INST: instantiating (21) with u, all_1169_3, u, pn,
% 128.25/18.27 | | | | | | | simplifying with (73), (118) gives:
% 128.25/18.27 | | | | | | | (129) all_1169_3 = u
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | GROUND_INST: instantiating (22) with all_886_1, all_1161_3,
% 128.25/18.27 | | | | | | | all_886_2, member_a, simplifying with (41), (112)
% 128.25/18.27 | | | | | | | gives:
% 128.25/18.27 | | | | | | | (130) all_1161_3 = all_886_1
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | REDUCE: (113), (130) imply:
% 128.25/18.27 | | | | | | | (131) hAPP_fun_a_bool_bool(all_886_1, all_879_1) = all_1161_2
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | GROUND_INST: instantiating (6) with all_886_2, mgt_call, pn, u,
% 128.25/18.27 | | | | | | | all_823_1, all_823_0, all_886_1, all_879_1,
% 128.25/18.27 | | | | | | | all_1161_2, simplifying with (16), (17), (18), (31),
% 128.25/18.27 | | | | | | | (32), (33), (36), (41), (68), (111), (131) gives:
% 128.25/18.27 | | | | | | | (132) ? [v0: any] : ( ~ (v0 = all_886_2) &
% 128.25/18.27 | | | | | | | hAPP_pname_a(mgt_call, pn) = v0 & $i(v0))
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | GROUND_INST: instantiating (6) with all_1159_3, mgt_call, pn, u,
% 128.25/18.27 | | | | | | | all_823_1, all_823_0, all_1159_2, all_879_1,
% 128.25/18.27 | | | | | | | all_1159_0, simplifying with (16), (17), (18), (31),
% 128.25/18.27 | | | | | | | (32), (33), (36), (77), (78), (79), (80) gives:
% 128.25/18.27 | | | | | | | (133) ? [v0: any] : ( ~ (v0 = all_1159_3) &
% 128.25/18.27 | | | | | | | hAPP_pname_a(mgt_call, pn) = v0 & $i(v0))
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | DELTA: instantiating (132) with fresh symbol all_1262_0 gives:
% 128.25/18.27 | | | | | | | (134) ~ (all_1262_0 = all_886_2) & hAPP_pname_a(mgt_call, pn)
% 128.25/18.27 | | | | | | | = all_1262_0 & $i(all_1262_0)
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | ALPHA: (134) implies:
% 128.25/18.27 | | | | | | | (135) ~ (all_1262_0 = all_886_2)
% 128.25/18.27 | | | | | | | (136) hAPP_pname_a(mgt_call, pn) = all_1262_0
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | DELTA: instantiating (133) with fresh symbol all_1280_0 gives:
% 128.25/18.27 | | | | | | | (137) ~ (all_1280_0 = all_1159_3) & hAPP_pname_a(mgt_call, pn)
% 128.25/18.27 | | | | | | | = all_1280_0 & $i(all_1280_0)
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | ALPHA: (137) implies:
% 128.25/18.27 | | | | | | | (138) hAPP_pname_a(mgt_call, pn) = all_1280_0
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | GROUND_INST: instantiating (23) with all_886_2, all_1280_0, pn,
% 128.25/18.27 | | | | | | | mgt_call, simplifying with (42), (138) gives:
% 128.25/18.27 | | | | | | | (139) all_1280_0 = all_886_2
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | GROUND_INST: instantiating (23) with all_1262_0, all_1280_0, pn,
% 128.25/18.27 | | | | | | | mgt_call, simplifying with (136), (138) gives:
% 128.25/18.27 | | | | | | | (140) all_1280_0 = all_1262_0
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | COMBINE_EQS: (139), (140) imply:
% 128.25/18.27 | | | | | | | (141) all_1262_0 = all_886_2
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | REDUCE: (135), (141) imply:
% 128.25/18.27 | | | | | | | (142) $false
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | | CLOSE: (142) is inconsistent.
% 128.25/18.27 | | | | | | |
% 128.25/18.27 | | | | | | End of split
% 128.25/18.27 | | | | | |
% 128.25/18.27 | | | | | End of split
% 128.25/18.27 | | | | |
% 128.25/18.27 | | | | End of split
% 128.25/18.27 | | | |
% 128.25/18.27 | | | End of split
% 128.25/18.27 | | |
% 128.25/18.27 | | End of split
% 128.25/18.27 | |
% 128.25/18.27 | End of split
% 128.25/18.27 |
% 128.25/18.27 End of proof
% 128.25/18.27 % SZS output end Proof for theBenchmark
% 128.25/18.27
% 128.25/18.27 17676ms
%------------------------------------------------------------------------------