TSTP Solution File: SWW473+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW473+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:50:17 EDT 2023
% Result : Theorem 35.58s 5.54s
% Output : Proof 65.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW473+1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 20:09:33 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 9.76/2.08 Prover 1: Preprocessing ...
% 9.76/2.09 Prover 4: Preprocessing ...
% 9.76/2.12 Prover 5: Preprocessing ...
% 9.76/2.12 Prover 6: Preprocessing ...
% 9.76/2.12 Prover 3: Preprocessing ...
% 9.76/2.12 Prover 0: Preprocessing ...
% 9.76/2.12 Prover 2: Preprocessing ...
% 26.43/4.40 Prover 1: Warning: ignoring some quantifiers
% 26.43/4.48 Prover 3: Warning: ignoring some quantifiers
% 28.25/4.55 Prover 3: Constructing countermodel ...
% 28.25/4.56 Prover 1: Constructing countermodel ...
% 29.28/4.71 Prover 4: Warning: ignoring some quantifiers
% 29.85/4.75 Prover 6: Proving ...
% 31.15/4.94 Prover 4: Constructing countermodel ...
% 31.58/5.02 Prover 5: Proving ...
% 32.40/5.21 Prover 0: Proving ...
% 34.97/5.53 Prover 3: proved (4876ms)
% 35.58/5.53
% 35.58/5.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.58/5.54
% 35.58/5.55 Prover 6: stopped
% 35.58/5.55 Prover 0: stopped
% 35.58/5.56 Prover 5: stopped
% 35.90/5.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 35.90/5.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 35.90/5.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 35.90/5.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 39.88/6.18 Prover 7: Preprocessing ...
% 40.41/6.21 Prover 10: Preprocessing ...
% 41.07/6.30 Prover 11: Preprocessing ...
% 41.28/6.35 Prover 2: Proving ...
% 41.28/6.35 Prover 2: stopped
% 41.28/6.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 41.28/6.35 Prover 8: Preprocessing ...
% 44.00/6.70 Prover 13: Preprocessing ...
% 48.98/7.35 Prover 10: Warning: ignoring some quantifiers
% 48.98/7.37 Prover 8: Warning: ignoring some quantifiers
% 50.03/7.48 Prover 8: Constructing countermodel ...
% 50.03/7.52 Prover 10: Constructing countermodel ...
% 51.86/7.78 Prover 7: Warning: ignoring some quantifiers
% 51.86/7.83 Prover 7: Constructing countermodel ...
% 54.51/8.06 Prover 11: Warning: ignoring some quantifiers
% 55.08/8.16 Prover 11: Constructing countermodel ...
% 56.18/8.30 Prover 13: Warning: ignoring some quantifiers
% 56.85/8.41 Prover 13: Constructing countermodel ...
% 63.60/9.41 Prover 10: Found proof (size 118)
% 63.60/9.41 Prover 10: proved (3843ms)
% 63.60/9.41 Prover 11: stopped
% 63.60/9.41 Prover 13: stopped
% 63.60/9.41 Prover 1: stopped
% 63.60/9.41 Prover 4: stopped
% 63.60/9.41 Prover 8: stopped
% 63.60/9.41 Prover 7: stopped
% 63.60/9.41
% 63.60/9.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 63.60/9.41
% 64.77/9.43 % SZS output start Proof for theBenchmark
% 64.77/9.44 Assumptions after simplification:
% 64.77/9.44 ---------------------------------
% 64.77/9.45
% 64.77/9.45 (conj_0)
% 64.77/9.47 $i(u) & $i(finite_finite_pname) & ? [v0: $i] :
% 64.77/9.47 (hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 & $i(v0) & hBOOL(v0))
% 64.77/9.47
% 64.77/9.47 (conj_1)
% 64.77/9.47 $i(mgt_call) & $i(ord_le1311769555a_bool) & $i(u) & $i(g) & ? [v0: $i] : ?
% 64.77/9.47 [v1: $i] : ? [v2: $i] : (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) =
% 64.77/9.47 v0 & hAPP_fun_a_bool_bool(v0, v1) = v2 & image_pname_a(mgt_call, u) = v1 &
% 64.77/9.47 $i(v2) & $i(v1) & $i(v0) & hBOOL(v2))
% 64.77/9.47
% 64.77/9.47 (conj_2)
% 64.77/9.47 $i(na) & $i(mgt_call) & $i(suc) & $i(finite_card_a) & $i(ord_less_eq_nat) &
% 64.77/9.47 $i(u) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 64.77/9.47 (hAPP_nat_nat(suc, na) = v0 & hAPP_fun_a_bool_nat(finite_card_a, v2) = v3 &
% 64.77/9.47 hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 & hAPP_nat_bool(v1, v3) =
% 64.77/9.47 v4 & image_pname_a(mgt_call, u) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 64.77/9.47 $i(v0) & hBOOL(v4))
% 64.77/9.47
% 64.77/9.47 (conj_3)
% 64.77/9.47 $i(na) & $i(mgt_call) & $i(suc) & $i(finite_card_a) & $i(u) & $i(g) & ? [v0:
% 64.77/9.48 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 64.77/9.48 (minus_minus_nat(v2) = v3 & hAPP_nat_nat(v3, v4) = v0 & hAPP_nat_nat(suc, na)
% 64.77/9.48 = v4 & hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 64.77/9.48 hAPP_fun_a_bool_nat(finite_card_a, g) = v0 & image_pname_a(mgt_call, u) = v1
% 64.77/9.48 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 64.77/9.48
% 64.77/9.48 (conj_4)
% 64.77/9.48 $i(member_pname) & $i(pn) & $i(u) & ? [v0: $i] : ? [v1: $i] :
% 64.77/9.48 (hAPP_f1664156314l_bool(v0, u) = v1 & hAPP_p338031245l_bool(member_pname, pn)
% 64.77/9.48 = v0 & $i(v1) & $i(v0) & hBOOL(v1))
% 64.77/9.48
% 64.77/9.48 (conj_5)
% 64.77/9.48 $i(mgt_call) & $i(member_a) & $i(pn) & $i(g) & ? [v0: $i] : ? [v1: $i] : ?
% 64.77/9.48 [v2: $i] : (hAPP_fun_a_bool_bool(v1, g) = v2 & hAPP_pname_a(mgt_call, pn) = v0
% 64.77/9.48 & hAPP_a85458249l_bool(member_a, v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ~
% 64.77/9.48 hBOOL(v2))
% 64.77/9.48
% 64.77/9.48 (conj_6)
% 64.77/9.48 $i(mgt_call) & $i(ord_le1311769555a_bool) & $i(pn) & $i(u) & $i(g) & ? [v0:
% 64.77/9.48 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 64.77/9.48 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2 &
% 64.77/9.48 hAPP_fun_a_bool_bool(v2, v3) = v4 & hAPP_pname_a(mgt_call, pn) = v0 &
% 64.77/9.48 insert_a(v0, g) = v1 & image_pname_a(mgt_call, u) = v3 & $i(v4) & $i(v3) &
% 64.77/9.48 $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v4))
% 64.77/9.48
% 64.77/9.48 (fact_102_card__insert__if)
% 64.77/9.48 $i(member_pname) & $i(suc) & $i(finite_card_pname) & $i(finite_finite_pname) &
% 64.77/9.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 64.77/9.48 (hAPP_f1664156314l_bool(v2, v1) = v3) | ~
% 64.77/9.48 (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 64.77/9.48 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 64.77/9.48 ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v4 & $i(v4) & ~
% 64.77/9.48 hBOOL(v4)) | (( ~ hBOOL(v3) | (v7 = v6 &
% 64.77/9.48 hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 64.77/9.48 hAPP_f921600141ol_nat(finite_card_pname, v1) = v6 & insert_pname(v0,
% 64.77/9.48 v1) = v5 & $i(v6) & $i(v5))) & (hBOOL(v3) | (v8 = v6 &
% 64.77/9.48 hAPP_nat_nat(suc, v7) = v6 &
% 64.77/9.48 hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 64.77/9.48 hAPP_f921600141ol_nat(finite_card_pname, v1) = v7 & insert_pname(v0,
% 64.77/9.48 v1) = v5 & $i(v7) & $i(v6) & $i(v5))))))
% 64.77/9.48
% 64.77/9.48 (fact_103_card__insert__if)
% 64.77/9.49 $i(member_a) & $i(suc) & $i(finite_card_a) & $i(finite_finite_a) & ! [v0: $i]
% 64.77/9.49 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_fun_a_bool_bool(v2, v1)
% 64.77/9.49 = v3) | ~ (hAPP_a85458249l_bool(member_a, v0) = v2) | ~ $i(v1) | ~
% 64.77/9.49 $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 64.77/9.49 : ((hAPP_fun_a_bool_bool(finite_finite_a, v1) = v4 & $i(v4) & ~ hBOOL(v4))
% 64.77/9.49 | (( ~ hBOOL(v3) | (v7 = v6 & hAPP_fun_a_bool_nat(finite_card_a, v5) = v6
% 64.77/9.49 & hAPP_fun_a_bool_nat(finite_card_a, v1) = v6 & insert_a(v0, v1) =
% 64.77/9.49 v5 & $i(v6) & $i(v5))) & (hBOOL(v3) | (v8 = v6 & hAPP_nat_nat(suc,
% 64.77/9.49 v7) = v6 & hAPP_fun_a_bool_nat(finite_card_a, v5) = v6 &
% 64.77/9.49 hAPP_fun_a_bool_nat(finite_card_a, v1) = v7 & insert_a(v0, v1) = v5
% 64.77/9.49 & $i(v7) & $i(v6) & $i(v5))))))
% 64.77/9.49
% 64.77/9.49 (fact_169_finite__surj)
% 64.77/9.49 $i(ord_le1311769555a_bool) & $i(finite_finite_pname) & $i(finite_finite_a) &
% 64.77/9.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 64.77/9.49 $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v0) = v3) | ~
% 64.77/9.49 (hAPP_fun_a_bool_bool(v3, v4) = v5) | ~ (image_pname_a(v1, v2) = v4) | ~
% 64.77/9.49 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v5) | ? [v6: $i] : ? [v7: $i] :
% 64.77/9.49 ((hAPP_f1664156314l_bool(finite_finite_pname, v2) = v6 & $i(v6) & ~
% 64.77/9.49 hBOOL(v6)) | (hAPP_fun_a_bool_bool(finite_finite_a, v0) = v7 & $i(v7) &
% 64.77/9.49 hBOOL(v7))))
% 64.77/9.49
% 64.77/9.49 (fact_223_insert__absorb)
% 64.77/9.49 $i(member_pname) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 64.77/9.49 (hAPP_f1664156314l_bool(v2, v1) = v3) | ~
% 64.77/9.49 (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 64.77/9.49 hBOOL(v3) | ~ is_fun_pname_bool(v1) | insert_pname(v0, v1) = v1)
% 64.77/9.49
% 64.77/9.49 (fact_262_rev__image__eqI)
% 64.77/9.49 $i(member_a) & $i(member_pname) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 64.77/9.49 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 64.77/9.49 : ( ~ (hAPP_f1664156314l_bool(v4, v3) = v5) | ~ (hAPP_fun_a_bool_bool(v6, v7)
% 64.77/9.49 = v8) | ~ (hAPP_p338031245l_bool(member_pname, v2) = v4) | ~
% 64.77/9.49 (hAPP_a85458249l_bool(member_a, v0) = v6) | ~ (image_pname_a(v1, v3) = v7)
% 64.77/9.49 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v5) | hBOOL(v8) |
% 64.77/9.49 ? [v9: $i] : ( ~ (v9 = v0) & hAPP_pname_a(v1, v2) = v9 & $i(v9)))
% 64.77/9.49
% 64.77/9.49 (fact_274_insert__subset)
% 65.14/9.50 $i(member_a) & $i(ord_le1311769555a_bool) & ! [v0: $i] : ! [v1: $i] : !
% 65.14/9.50 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 65.14/9.50 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) = v4) | ~
% 65.14/9.50 (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ (insert_a(v0, v1) = v3) | ~ $i(v2)
% 65.14/9.50 | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8:
% 65.14/9.50 $i] : ? [v9: $i] : (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) =
% 65.14/9.50 v8 & hAPP_fun_a_bool_bool(v8, v2) = v9 & hAPP_fun_a_bool_bool(v6, v2) = v7
% 65.14/9.50 & hAPP_a85458249l_bool(member_a, v0) = v6 & $i(v9) & $i(v8) & $i(v7) &
% 65.14/9.50 $i(v6) & hBOOL(v9) & hBOOL(v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.50 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 65.14/9.50 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) = v4) | ~
% 65.14/9.50 (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ (insert_a(v0, v1) = v3) | ~ $i(v2)
% 65.14/9.50 | ~ $i(v1) | ~ $i(v0) | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8:
% 65.14/9.50 $i] : ? [v9: $i] : ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) =
% 65.14/9.50 v8 & hAPP_fun_a_bool_bool(v8, v2) = v9 & $i(v9) & $i(v8) & ~ hBOOL(v9))
% 65.14/9.50 | (hAPP_fun_a_bool_bool(v6, v2) = v7 & hAPP_a85458249l_bool(member_a, v0)
% 65.14/9.50 = v6 & $i(v7) & $i(v6) & ~ hBOOL(v7))))
% 65.14/9.50
% 65.14/9.50 (fact_290_subsetI)
% 65.14/9.50 $i(member_a) & $i(ord_le1311769555a_bool) & ! [v0: $i] : ! [v1: $i] : !
% 65.14/9.50 [v2: $i] : ! [v3: $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool,
% 65.14/9.50 v1) = v2) | ~ (hAPP_fun_a_bool_bool(v2, v0) = v3) | ~ $i(v1) | ~
% 65.14/9.50 $i(v0) | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 65.14/9.50 (hAPP_fun_a_bool_bool(v5, v1) = v6 & hAPP_fun_a_bool_bool(v5, v0) = v7 &
% 65.14/9.50 hAPP_a85458249l_bool(member_a, v4) = v5 & $i(v7) & $i(v6) & $i(v5) &
% 65.14/9.50 $i(v4) & hBOOL(v6) & is_a(v4) & ~ hBOOL(v7)))
% 65.14/9.50
% 65.14/9.50 (gsy_v_U)
% 65.14/9.50 $i(u) & is_fun_pname_bool(u)
% 65.14/9.50
% 65.14/9.50 (function-axioms)
% 65.14/9.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.54 (hAPP_f1476298914l_bool(v3, v2) = v1) | ~ (hAPP_f1476298914l_bool(v3, v2) =
% 65.14/9.54 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 65.14/9.54 ~ (hAPP_f1748468828l_bool(v3, v2) = v1) | ~ (hAPP_f1748468828l_bool(v3, v2)
% 65.14/9.54 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 65.14/9.54 | ~ (hAPP_f198738859l_bool(v3, v2) = v1) | ~ (hAPP_f198738859l_bool(v3,
% 65.14/9.54 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 65.14/9.54 = v0 | ~ (hAPP_p393069232l_bool(v3, v2) = v1) | ~
% 65.14/9.54 (hAPP_p393069232l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1006566506l_bool(v3, v2) = v1) | ~
% 65.14/9.54 (hAPP_n1006566506l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_fun_bool_bool(v3, v2) = v1) | ~
% 65.14/9.54 (hAPP_a_fun_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_b589554111l_bool(v3, v2) = v1) | ~
% 65.14/9.54 (hAPP_b589554111l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_238756964t_bool(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_238756964t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_bool_bool_nat(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_bool_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1246832597l_bool(v3, v2) = v1) | ~
% 65.14/9.54 (hAPP_f1246832597l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f800510211t_bool(v3, v2) = v1) | ~
% 65.14/9.54 (hAPP_f800510211t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1897541054_pname(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_1897541054_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1015721476ol_nat(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_1015721476ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_nat_bool_bool(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBS_nat_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_675860798_pname(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_675860798_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1972296269bool_a(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_1972296269bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_338059395a_bool(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_338059395a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2095475776e_bool(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_2095475776e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_444170502t_bool(v3, v2) = v1) | ~
% 65.14/9.54 (cOMBB_444170502t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_1187019125l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBS_1187019125l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n215258509l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_n215258509l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f285962445l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f285962445l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f556039215l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f556039215l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1951378235l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1951378235l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_nat_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 65.14/9.55 [v3: $i] : (v1 = v0 | ~ (hAPP_f1253658590ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1253658590ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f98387925ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f98387925ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1690079119ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1690079119ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2009550088ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f2009550088ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f55526627ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f55526627ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f696928925ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f696928925ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_fun_a_bool_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_fun_a_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f22106695ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f22106695ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1699378549t_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_n1699378549t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f921600141ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f921600141ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_fun_nat_bool(v3, v2) = v1) | ~
% 65.14/9.55 (insert_fun_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert1457093509l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (insert1457093509l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert1117693814l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (insert1117693814l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert2003652156l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (insert2003652156l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_nat(v3, v2) = v1) | ~
% 65.14/9.55 (insert_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 65.14/9.55 [v3: $i] : (v1 = v0 | ~ (image_pname_nat(v3, v2) = v1) | ~
% 65.14/9.55 (image_pname_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 65.14/9.55 ! [v3: $i] : (v1 = v0 | ~ (image_2129980159t_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_2129980159t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1420695166l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_1420695166l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1642285373l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_1642285373l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1154884483l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_1154884483l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_26036933t_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_26036933t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1208015684l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_1208015684l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1874789623l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_1874789623l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1607900221l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_1607900221l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_nat(v3, v2) = v1) | ~
% 65.14/9.55 (image_a_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 65.14/9.55 [v3: $i] : (v1 = v0 | ~ (image_496248727ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (image_496248727ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1551609309ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (image_1551609309ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_fun_a_bool_nat(v3, v2) = v1) | ~
% 65.14/9.55 (image_fun_a_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1802975832ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (image_1802975832ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1079571347ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (image_1079571347ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_2089570637ol_nat(v3, v2) = v1) | ~
% 65.14/9.55 (image_2089570637ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1772781669l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1772781669l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f510955609l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f510955609l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1434722111l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1434722111l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1050622307l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1050622307l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1759205631l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1759205631l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f760187903l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f760187903l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f103356543l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f103356543l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1295398978l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1295398978l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f595608956l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f595608956l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1363661463l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1363661463l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f937997336l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f937997336l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f389811538l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f389811538l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f292226953l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f292226953l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1637334154l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1637334154l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f559147733l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f559147733l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1935102916l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1935102916l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2117159681l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f2117159681l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f621171935l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f621171935l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f54304608l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f54304608l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f434788991l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f434788991l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f759274231e_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f759274231e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1664156314l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1664156314l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1631501043l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f1631501043l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2050579477a_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_f2050579477a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_fun_a_bool_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_fun_a_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1025906991e_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_n1025906991e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_fun_a_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_nat_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 65.14/9.55 [v3: $i] : (v1 = v0 | ~ (hAPP_bool_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 65.14/9.55 ! [v3: $i] : (v1 = v0 | ~ (hAPP_p338031245l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_p338031245l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p61793385e_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_p61793385e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p1534023578a_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_p1534023578a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_pname_bool(v3, v2) = v1) | ~
% 65.14/9.55 (hAPP_pname_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 65.14/9.55 ! [v3: $i] : (v1 = v0 | ~ (hAPP_pname_a(v3, v2) = v1) | ~ (hAPP_pname_a(v3,
% 65.14/9.55 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 65.14/9.55 = v0 | ~ (hAPP_a85458249l_bool(v3, v2) = v1) | ~ (hAPP_a85458249l_bool(v3,
% 65.14/9.55 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 65.14/9.55 = v0 | ~ (hAPP_a93125764e_bool(v3, v2) = v1) | ~ (hAPP_a93125764e_bool(v3,
% 65.14/9.55 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 65.14/9.55 = v0 | ~ (hAPP_a_fun_a_bool(v3, v2) = v1) | ~ (hAPP_a_fun_a_bool(v3, v2) =
% 65.14/9.55 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 65.14/9.55 ~ (hAPP_a_bool(v3, v2) = v1) | ~ (hAPP_a_bool(v3, v2) = v0)) & ! [v0: $i]
% 65.14/9.55 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.55 (insert1325755072e_bool(v3, v2) = v1) | ~ (insert1325755072e_bool(v3, v2) =
% 65.14/9.55 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 65.14/9.55 ~ (insert_fun_a_bool(v3, v2) = v1) | ~ (insert_fun_a_bool(v3, v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.55 (insert_pname(v3, v2) = v1) | ~ (insert_pname(v3, v2) = v0)) & ! [v0: $i]
% 65.14/9.55 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_a(v3, v2) =
% 65.14/9.55 v1) | ~ (insert_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1604018183_pname(v3, v2) = v1) | ~
% 65.14/9.55 (image_1604018183_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_526090948bool_a(v3, v2) = v1) | ~
% 65.14/9.55 (image_526090948bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1705983821_pname(v3, v2) = v1) | ~
% 65.14/9.55 (image_1705983821_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_349102846bool_a(v3, v2) = v1) | ~
% 65.14/9.55 (image_349102846bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_990671762_pname(v3, v2) = v1) | ~
% 65.14/9.55 (image_990671762_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_573985017bool_a(v3, v2) = v1) | ~
% 65.14/9.55 (image_573985017bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1921560913_pname(v3, v2) = v1) | ~
% 65.14/9.55 (image_1921560913_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_fun_nat_bool_a(v3, v2) = v1) | ~
% 65.14/9.55 (image_fun_nat_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1283814551_pname(v3, v2) = v1) | ~
% 65.14/9.55 (image_1283814551_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_876012084bool_a(v3, v2) = v1) | ~
% 65.14/9.55 (image_876012084bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1854862208_pname(v3, v2) = v1) | ~
% 65.14/9.55 (image_1854862208_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_fun_a_bool_a(v3, v2) = v1) | ~
% 65.14/9.55 (image_fun_a_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.55 : ! [v3: $i] : (v1 = v0 | ~ (image_1655916159e_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_1655916159e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_nat_fun_a_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_nat_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_nat_pname(v3, v2) = v1) | ~
% 65.14/9.55 (image_nat_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 65.14/9.55 ! [v3: $i] : (v1 = v0 | ~ (image_nat_a(v3, v2) = v1) | ~ (image_nat_a(v3,
% 65.14/9.55 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 65.14/9.55 = v0 | ~ (image_47868345e_bool(v3, v2) = v1) | ~ (image_47868345e_bool(v3,
% 65.14/9.55 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 65.14/9.55 = v0 | ~ (image_112932426a_bool(v3, v2) = v1) | ~
% 65.14/9.55 (image_112932426a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_pname_pname(v3, v2) = v1) | ~
% 65.14/9.55 (image_pname_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.55 : ! [v3: $i] : (v1 = v0 | ~ (image_pname_a(v3, v2) = v1) | ~
% 65.14/9.55 (image_pname_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 65.14/9.55 [v3: $i] : (v1 = v0 | ~ (image_a_pname(v3, v2) = v1) | ~ (image_a_pname(v3,
% 65.14/9.55 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 65.14/9.55 = v0 | ~ (image_a_a(v3, v2) = v1) | ~ (image_a_a(v3, v2) = v0)) & ! [v0:
% 65.14/9.55 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (fun(v3, v2) =
% 65.14/9.55 v1) | ~ (fun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 65.14/9.55 ! [v3: $i] : (v1 = v0 | ~ (cOMBS_350070575l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBS_350070575l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_1035972772l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBS_1035972772l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_568398431l_bool(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBS_568398431l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_a_bool_bool(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBS_a_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.55 : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_307249310e_bool(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBB_307249310e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2140588453a_bool(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBB_2140588453a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_647938656_pname(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBB_647938656_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_bool_bool_a(v3, v2) = v1) | ~
% 65.14/9.55 (cOMBB_bool_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.55 : (v1 = v0 | ~ (cOMBC_1880041174l_bool(v2) = v1) | ~
% 65.14/9.55 (cOMBC_1880041174l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.55 : (v1 = v0 | ~ (cOMBC_1988546018l_bool(v2) = v1) | ~
% 65.14/9.55 (cOMBC_1988546018l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.55 : (v1 = v0 | ~ (cOMBC_1245412066l_bool(v2) = v1) | ~
% 65.14/9.55 (cOMBC_1245412066l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.55 : (v1 = v0 | ~ (cOMBC_a_a_bool(v2) = v1) | ~ (cOMBC_a_a_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_1355376034l_bool(v2) = v1) | ~ (cOMBC_1355376034l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_1149511130e_bool(v2) = v1) | ~ (cOMBC_1149511130e_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_226598744l_bool(v2) = v1) | ~ (cOMBC_226598744l_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_1058051404l_bool(v2) = v1) | ~ (cOMBC_1058051404l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_pname_a_bool(v2)
% 65.14/9.55 = v1) | ~ (cOMBC_pname_a_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 65.14/9.55 [v2: $i] : (v1 = v0 | ~ (cOMBC_nat_nat_bool(v2) = v1) | ~
% 65.14/9.55 (cOMBC_nat_nat_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 65.14/9.55 (v1 = v0 | ~ (minus_minus_nat(v2) = v1) | ~ (minus_minus_nat(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (collect_nat(v2) = v1) |
% 65.14/9.55 ~ (collect_nat(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 65.14/9.55 v0 | ~ (cOMBC_595898202l_bool(v2) = v1) | ~ (cOMBC_595898202l_bool(v2) =
% 65.14/9.55 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collec1015864663l_bool(v2) = v1) | ~ (collec1015864663l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_7971162l_bool(v2) = v1) | ~ (cOMBC_7971162l_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collec1613912337l_bool(v2) = v1) | ~ (collec1613912337l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_331553030l_bool(v2) = v1) | ~ (cOMBC_331553030l_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collec707592106l_bool(v2) = v1) | ~ (collec707592106l_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_636888218l_bool(v2) = v1) | ~ (cOMBC_636888218l_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collec1635217238l_bool(v2) = v1) | ~ (collec1635217238l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_336095980l_bool(v2) = v1) | ~ (cOMBC_336095980l_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collec792590109l_bool(v2) = v1) | ~ (collec792590109l_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_1269652216l_bool(v2) = v1) | ~ (cOMBC_1269652216l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collec1874991203l_bool(v2) = v1) | ~ (collec1874991203l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_1732670874l_bool(v2) = v1) | ~ (cOMBC_1732670874l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_1284144636l_bool(v2) = v1) | ~ (cOMBC_1284144636l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (cOMBC_1693257480l_bool(v2) = v1) | ~ (cOMBC_1693257480l_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collect_fun_nat_bool(v2) = v1) | ~ (collect_fun_nat_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2)
% 65.14/9.55 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collec1974731493e_bool(v2) = v1) | ~ (collec1974731493e_bool(v2) = v0)) &
% 65.14/9.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (collect_fun_a_bool(v2)
% 65.14/9.55 = v1) | ~ (collect_fun_a_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 65.14/9.55 [v2: $i] : (v1 = v0 | ~ (collect_pname(v2) = v1) | ~ (collect_pname(v2) =
% 65.14/9.55 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (collect_a(v2) = v1) | ~ (collect_a(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 65.14/9.55 : ! [v2: $i] : (v1 = v0 | ~ (undefi64961550l_bool(v2) = v1) | ~
% 65.14/9.55 (undefi64961550l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 65.14/9.55 (v1 = v0 | ~ (undefi1699038445l_bool(v2) = v1) | ~
% 65.14/9.55 (undefi1699038445l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 65.14/9.55 : (v1 = v0 | ~ (undefi17486888e_bool(v2) = v1) | ~ (undefi17486888e_bool(v2)
% 65.14/9.55 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 65.14/9.55 (undefined_fun_a_bool(v2) = v1) | ~ (undefined_fun_a_bool(v2) = v0)) & !
% 65.14/9.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (undefined_pname(v2) =
% 65.14/9.55 v1) | ~ (undefined_pname(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 65.14/9.55 $i] : (v1 = v0 | ~ (undefined_a(v2) = v1) | ~ (undefined_a(v2) = v0))
% 65.14/9.55
% 65.14/9.55 Further assumptions not needed in the proof:
% 65.14/9.55 --------------------------------------------
% 65.14/9.55 fact_0_assms_I1_J, fact_100_card__insert__if, fact_101_card__insert__if,
% 65.14/9.55 fact_104_card__insert__disjoint, fact_105_card__insert__disjoint,
% 65.14/9.55 fact_106_card__insert__disjoint, fact_107_card__insert__disjoint,
% 65.14/9.55 fact_108_card__insert__disjoint, fact_109_card__insert__disjoint,
% 65.14/9.55 fact_10_finite__imageI, fact_110_finite__Collect__conjI,
% 65.14/9.55 fact_111_finite__Collect__conjI, fact_112_finite__Collect__conjI,
% 65.14/9.55 fact_113_finite__Collect__conjI, fact_114_finite__Collect__conjI,
% 65.14/9.55 fact_115_finite__Collect__conjI, fact_116_Suc__diff__le,
% 65.14/9.55 fact_117_finite__Collect__le__nat, fact_118_card__Collect__le__nat,
% 65.14/9.55 fact_119_Suc__inject, fact_11_finite__imageI, fact_120_nat_Oinject,
% 65.14/9.55 fact_121_Suc__n__not__n, fact_122_n__not__Suc__n, fact_123_le__antisym,
% 65.14/9.55 fact_124_le__trans, fact_125_eq__imp__le, fact_126_nat__le__linear,
% 65.14/9.55 fact_127_le__refl, fact_128_diff__commute, fact_129_finite__Collect__disjI,
% 65.14/9.55 fact_12_finite__imageI, fact_130_finite__Collect__disjI,
% 65.14/9.55 fact_131_finite__Collect__disjI, fact_132_finite__Collect__disjI,
% 65.14/9.55 fact_133_finite__Collect__disjI, fact_134_finite__Collect__disjI,
% 65.14/9.55 fact_135_finite__insert, fact_136_finite__insert, fact_137_finite__insert,
% 65.14/9.55 fact_138_finite__insert, fact_139_finite__insert, fact_13_finite__imageI,
% 65.14/9.55 fact_140_finite__insert, fact_141_finite__subset, fact_142_finite__subset,
% 65.14/9.55 fact_143_finite__subset, fact_144_finite__subset, fact_145_finite__subset,
% 65.14/9.55 fact_146_finite__subset, fact_147_rev__finite__subset,
% 65.14/9.55 fact_148_rev__finite__subset, fact_149_rev__finite__subset,
% 65.14/9.55 fact_14_finite__imageI, fact_150_rev__finite__subset,
% 65.14/9.55 fact_151_rev__finite__subset, fact_152_rev__finite__subset, fact_153_Suc__leD,
% 65.14/9.55 fact_154_le__SucE, fact_155_le__SucI, fact_156_Suc__le__mono,
% 65.14/9.55 fact_157_le__Suc__eq, fact_158_not__less__eq__eq, fact_159_Suc__n__not__le__n,
% 65.14/9.55 fact_15_finite__imageI, fact_160_Suc__diff__diff, fact_161_diff__Suc__Suc,
% 65.14/9.55 fact_162_le__diff__iff, fact_163_Nat_Odiff__diff__eq, fact_164_eq__diff__iff,
% 65.14/9.55 fact_165_diff__diff__cancel, fact_166_diff__le__mono, fact_167_diff__le__mono2,
% 65.14/9.55 fact_168_diff__le__self, fact_16_finite__imageI, fact_170_finite__subset__image,
% 65.14/9.55 fact_171_lift__Suc__mono__le, fact_172_lift__Suc__mono__le,
% 65.14/9.55 fact_173_lift__Suc__mono__le, fact_174_lift__Suc__mono__le,
% 65.14/9.55 fact_175_pigeonhole__infinite, fact_176_image__eqI, fact_177_equalityI,
% 65.14/9.55 fact_178_equalityI, fact_179_equalityI, fact_17_finite__imageI,
% 65.14/9.55 fact_180_subsetD, fact_181_subsetD, fact_182_subsetD, fact_183_insertCI,
% 65.14/9.55 fact_184_insertCI, fact_185_insertCI, fact_186_insertE, fact_187_insertE,
% 65.14/9.55 fact_188_insertE, fact_189_insertI1, fact_18_finite__imageI, fact_190_insertI1,
% 65.14/9.55 fact_191_insertI1, fact_192_insert__compr, fact_193_insert__compr,
% 65.14/9.55 fact_194_insert__compr, fact_195_insert__compr, fact_196_insert__compr,
% 65.14/9.55 fact_197_insert__compr, fact_198_insert__Collect, fact_199_insert__Collect,
% 65.14/9.55 fact_19_finite__imageI, fact_1_finite__Collect__subsets,
% 65.14/9.55 fact_200_insert__Collect, fact_201_insert__Collect, fact_202_insert__Collect,
% 65.14/9.55 fact_203_insert__Collect, fact_204_insert__absorb2, fact_205_insert__absorb2,
% 65.14/9.55 fact_206_insert__absorb2, fact_207_insert__commute, fact_208_insert__commute,
% 65.14/9.55 fact_209_insert__commute, fact_20_finite__imageI, fact_210_insert__iff,
% 65.14/9.55 fact_211_insert__iff, fact_212_insert__iff, fact_213_insert__code,
% 65.14/9.55 fact_214_insert__code, fact_215_insert__code, fact_216_insert__ident,
% 65.14/9.55 fact_217_insert__ident, fact_218_insert__ident, fact_219_insertI2,
% 65.14/9.55 fact_21_finite__imageI, fact_220_insertI2, fact_221_insertI2,
% 65.14/9.55 fact_222_insert__absorb, fact_224_insert__absorb, fact_225_subset__refl,
% 65.14/9.55 fact_226_subset__refl, fact_227_subset__refl, fact_228_set__eq__subset,
% 65.14/9.55 fact_229_set__eq__subset, fact_22_finite__imageI, fact_230_set__eq__subset,
% 65.14/9.55 fact_231_equalityD1, fact_232_equalityD1, fact_233_equalityD1,
% 65.14/9.55 fact_234_equalityD2, fact_235_equalityD2, fact_236_equalityD2,
% 65.14/9.55 fact_237_in__mono, fact_238_in__mono, fact_239_in__mono, fact_23_finite__imageI,
% 65.14/9.55 fact_240_set__rev__mp, fact_241_set__rev__mp, fact_242_set__rev__mp,
% 65.14/9.55 fact_243_set__mp, fact_244_set__mp, fact_245_set__mp, fact_246_subset__trans,
% 65.14/9.55 fact_247_subset__trans, fact_248_subset__trans, fact_249_equalityE,
% 65.14/9.55 fact_24_finite__imageI, fact_250_equalityE, fact_251_equalityE,
% 65.14/9.55 fact_252_mem__def, fact_253_mem__def, fact_254_mem__def, fact_255_Collect__def,
% 65.14/9.55 fact_256_Collect__def, fact_257_Collect__def, fact_258_Collect__def,
% 65.14/9.55 fact_259_Collect__def, fact_25_finite__imageI, fact_260_image__iff,
% 65.14/9.55 fact_261_imageI, fact_263_insert__compr__raw, fact_264_insert__compr__raw,
% 65.14/9.55 fact_265_insert__compr__raw, fact_266_insert__compr__raw,
% 65.14/9.55 fact_267_insert__compr__raw, fact_268_insert__compr__raw,
% 65.14/9.55 fact_269_subset__insertI, fact_26_finite__imageI, fact_270_subset__insertI,
% 65.14/9.55 fact_271_subset__insertI, fact_272_insert__subset, fact_273_insert__subset,
% 65.14/9.55 fact_275_subset__insert, fact_276_subset__insert, fact_277_subset__insert,
% 65.14/9.55 fact_278_subset__insertI2, fact_279_subset__insertI2, fact_27_finite__imageI,
% 65.14/9.55 fact_280_subset__insertI2, fact_281_insert__mono, fact_282_insert__mono,
% 65.14/9.55 fact_283_insert__mono, fact_284_image__insert, fact_285_insert__image,
% 65.14/9.55 fact_286_subset__image__iff, fact_287_image__mono, fact_288_imageE,
% 65.14/9.55 fact_289_subsetI, fact_28_finite__imageI, fact_291_subsetI,
% 65.14/9.55 fact_292_zero__induct__lemma, fact_293_Suc__le__D, fact_294_image__subsetI,
% 65.14/9.55 fact_295_order__refl, fact_296_order__refl, fact_297_order__refl,
% 65.14/9.55 fact_298_order__refl, fact_299_finite__nat__set__iff__bounded__le,
% 65.14/9.55 fact_29_finite__imageI, fact_2_finite__Collect__subsets, fact_30_finite__imageI,
% 65.14/9.55 fact_31_finite__imageI, fact_32_finite__imageI, fact_33_finite__imageI,
% 65.14/9.55 fact_34_finite__imageI, fact_35_finite__imageI, fact_36_finite__imageI,
% 65.14/9.55 fact_37_finite__imageI, fact_38_finite__imageI, fact_39_finite__imageI,
% 65.14/9.55 fact_3_finite__Collect__subsets, fact_40_finite__imageI, fact_41_finite__imageI,
% 65.14/9.55 fact_42_finite__imageI, fact_43_finite__imageI, fact_44_finite__imageI,
% 65.14/9.55 fact_45_finite_OinsertI, fact_46_finite_OinsertI, fact_47_finite_OinsertI,
% 65.14/9.55 fact_48_finite_OinsertI, fact_49_finite_OinsertI,
% 65.14/9.55 fact_4_finite__Collect__subsets, fact_50_finite_OinsertI,
% 65.14/9.55 fact_51_finite_OinsertI, fact_52_finite_OinsertI, fact_53_finite_OinsertI,
% 65.14/9.55 fact_54_card__image__le, fact_55_card__image__le, fact_56_card__image__le,
% 65.14/9.55 fact_57_card__image__le, fact_58_card__image__le, fact_59_card__image__le,
% 65.14/9.55 fact_5_finite__Collect__subsets, fact_60_card__image__le,
% 65.14/9.55 fact_61_card__image__le, fact_62_card__image__le, fact_63_card__image__le,
% 65.14/9.55 fact_64_card__image__le, fact_65_card__image__le, fact_66_card__image__le,
% 65.14/9.55 fact_67_card__image__le, fact_68_card__image__le, fact_69_card__image__le,
% 65.14/9.55 fact_6_finite__Collect__subsets, fact_70_card__image__le,
% 65.14/9.55 fact_71_card__image__le, fact_72_card__image__le, fact_73_card__image__le,
% 65.14/9.55 fact_74_card__image__le, fact_75_card__image__le, fact_76_card__image__le,
% 65.14/9.55 fact_77_card__image__le, fact_78_card__image__le, fact_79_card__image__le,
% 65.14/9.55 fact_7_finite__Collect__subsets, fact_80_card__mono, fact_81_card__mono,
% 65.14/9.55 fact_82_card__mono, fact_83_card__mono, fact_84_card__mono, fact_85_card__mono,
% 65.14/9.55 fact_86_card__seteq, fact_87_card__seteq, fact_88_card__seteq,
% 65.14/9.55 fact_89_card__seteq, fact_8_finite__Collect__subsets, fact_90_card__seteq,
% 65.14/9.55 fact_91_card__seteq, fact_92_card__insert__le, fact_93_card__insert__le,
% 65.14/9.55 fact_94_card__insert__le, fact_95_card__insert__le, fact_96_card__insert__le,
% 65.14/9.55 fact_97_card__insert__le, fact_98_card__insert__if, fact_99_card__insert__if,
% 65.14/9.55 fact_9_finite__Collect__subsets,
% 65.14/9.55 gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a,
% 65.14/9.55 gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname,
% 65.14/9.55 gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool,
% 65.14/9.55 gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_,
% 65.14/9.55 gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool,
% 65.14/9.55 gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool,
% 65.14/9.55 gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo,
% 65.14/9.55 gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t,
% 65.14/9.55 gsy_c_Finite__Set_Ofinite_000t__a, gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,
% 65.14/9.55 gsy_c_HOL_Oundefined_000t__a, gsy_c_HOL_Oundefined_000tc__Com__Opname,
% 65.14/9.55 gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.55 gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 65.14/9.55 gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,
% 65.14/9.55 gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 65.14/9.55 gsy_c_Set_OCollect_000t__a, gsy_c_Set_OCollect_000tc__Com__Opname,
% 65.14/9.55 gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.55 gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_Set_Oimage_000t__a_000t__a, gsy_c_Set_Oimage_000t__a_000tc__Com__Opname,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__,
% 65.14/9.56 gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003,
% 65.14/9.56 gsy_c_Set_Oinsert_000t__a, gsy_c_Set_Oinsert_000tc__Com__Opname,
% 65.14/9.56 gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000t__a_000tc__HOL__Obool,
% 65.14/9.56 gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000tc__Com__Opname_000t__a,
% 65.14/9.56 gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,
% 65.14/9.56 gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,
% 65.14/9.56 gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,
% 65.14/9.56 gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,
% 65.14/9.56 gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,
% 65.14/9.56 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,
% 65.14/9.56 gsy_v_G, gsy_v_P, gsy_v_pn,
% 65.14/9.56 help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,
% 65.14/9.56 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010,
% 65.14/9.56 help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,
% 65.14/9.56 help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,
% 65.14/9.56 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,
% 65.14/9.56 help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 65.14/9.56 help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 65.14/9.56 help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 65.14/9.56 help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_,
% 65.14/9.56 help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,
% 65.14/9.56 help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,
% 65.14/9.56 help_fNot_1_1_U, help_fNot_2_1_U, help_fconj_1_1_U, help_fconj_2_1_U,
% 65.14/9.56 help_fconj_3_1_U, help_fdisj_1_1_U, help_fdisj_2_1_U, help_fdisj_3_1_U,
% 65.14/9.56 help_fequal_1_1_fequal_000t__a_T, help_fequal_1_1_fequal_000tc__Com__Opname_T,
% 65.14/9.56 help_fequal_1_1_fequal_000tc__Nat__Onat_T,
% 65.14/9.56 help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,
% 65.14/9.56 help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 65.14/9.56 help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,
% 65.14/9.56 help_fequal_2_1_fequal_000t__a_T, help_fequal_2_1_fequal_000tc__Com__Opname_T,
% 65.14/9.56 help_fequal_2_1_fequal_000tc__Nat__Onat_T,
% 65.14/9.56 help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,
% 65.14/9.56 help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 65.14/9.56 help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,
% 65.14/9.56 help_fimplies_1_1_U, help_fimplies_2_1_U, help_fimplies_3_1_U
% 65.14/9.56
% 65.14/9.56 Those formulas are unsatisfiable:
% 65.14/9.56 ---------------------------------
% 65.14/9.56
% 65.14/9.56 Begin of proof
% 65.14/9.56 |
% 65.14/9.56 | ALPHA: (gsy_v_U) implies:
% 65.14/9.56 | (1) is_fun_pname_bool(u)
% 65.14/9.56 |
% 65.14/9.56 | ALPHA: (fact_102_card__insert__if) implies:
% 65.14/9.56 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 65.14/9.56 | (hAPP_f1664156314l_bool(v2, v1) = v3) | ~
% 65.14/9.56 | (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~ $i(v1) | ~
% 65.14/9.56 | $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 65.14/9.56 | [v8: $i] : ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v4 &
% 65.14/9.56 | $i(v4) & ~ hBOOL(v4)) | (( ~ hBOOL(v3) | (v7 = v6 &
% 65.14/9.56 | hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 65.14/9.56 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v6 &
% 65.14/9.56 | insert_pname(v0, v1) = v5 & $i(v6) & $i(v5))) & (hBOOL(v3) |
% 65.14/9.56 | (v8 = v6 & hAPP_nat_nat(suc, v7) = v6 &
% 65.14/9.56 | hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 65.14/9.56 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v7 &
% 65.14/9.56 | insert_pname(v0, v1) = v5 & $i(v7) & $i(v6) & $i(v5))))))
% 65.14/9.56 |
% 65.14/9.56 | ALPHA: (fact_103_card__insert__if) implies:
% 65.14/9.56 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 65.14/9.56 | (hAPP_fun_a_bool_bool(v2, v1) = v3) | ~
% 65.14/9.56 | (hAPP_a85458249l_bool(member_a, v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 65.14/9.56 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 65.14/9.56 | ((hAPP_fun_a_bool_bool(finite_finite_a, v1) = v4 & $i(v4) & ~
% 65.14/9.56 | hBOOL(v4)) | (( ~ hBOOL(v3) | (v7 = v6 &
% 65.14/9.56 | hAPP_fun_a_bool_nat(finite_card_a, v5) = v6 &
% 65.14/9.56 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v6 & insert_a(v0,
% 65.14/9.56 | v1) = v5 & $i(v6) & $i(v5))) & (hBOOL(v3) | (v8 = v6 &
% 65.14/9.56 | hAPP_nat_nat(suc, v7) = v6 &
% 65.14/9.56 | hAPP_fun_a_bool_nat(finite_card_a, v5) = v6 &
% 65.14/9.56 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v7 & insert_a(v0,
% 65.14/9.56 | v1) = v5 & $i(v7) & $i(v6) & $i(v5))))))
% 65.14/9.56 |
% 65.14/9.56 | ALPHA: (fact_169_finite__surj) implies:
% 65.14/9.56 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 65.14/9.56 | ! [v5: $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v0) =
% 65.14/9.56 | v3) | ~ (hAPP_fun_a_bool_bool(v3, v4) = v5) | ~
% 65.14/9.56 | (image_pname_a(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 65.14/9.56 | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] :
% 65.14/9.56 | ((hAPP_f1664156314l_bool(finite_finite_pname, v2) = v6 & $i(v6) & ~
% 65.14/9.56 | hBOOL(v6)) | (hAPP_fun_a_bool_bool(finite_finite_a, v0) = v7 &
% 65.14/9.56 | $i(v7) & hBOOL(v7))))
% 65.14/9.56 |
% 65.14/9.56 | ALPHA: (fact_223_insert__absorb) implies:
% 65.14/9.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 65.14/9.57 | (hAPP_f1664156314l_bool(v2, v1) = v3) | ~
% 65.14/9.57 | (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~ $i(v1) | ~
% 65.14/9.57 | $i(v0) | ~ hBOOL(v3) | ~ is_fun_pname_bool(v1) | insert_pname(v0,
% 65.14/9.57 | v1) = v1)
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (fact_262_rev__image__eqI) implies:
% 65.14/9.57 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 65.14/9.57 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 65.14/9.57 | (hAPP_f1664156314l_bool(v4, v3) = v5) | ~ (hAPP_fun_a_bool_bool(v6,
% 65.14/9.57 | v7) = v8) | ~ (hAPP_p338031245l_bool(member_pname, v2) = v4) |
% 65.14/9.57 | ~ (hAPP_a85458249l_bool(member_a, v0) = v6) | ~ (image_pname_a(v1,
% 65.14/9.57 | v3) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 65.14/9.57 | hBOOL(v5) | hBOOL(v8) | ? [v9: $i] : ( ~ (v9 = v0) &
% 65.14/9.57 | hAPP_pname_a(v1, v2) = v9 & $i(v9)))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (fact_274_insert__subset) implies:
% 65.14/9.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 65.14/9.57 | ! [v5: $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) =
% 65.14/9.57 | v4) | ~ (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ (insert_a(v0, v1)
% 65.14/9.57 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v5) | ? [v6: $i]
% 65.14/9.57 | : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 65.14/9.57 | ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v8 &
% 65.14/9.57 | hAPP_fun_a_bool_bool(v8, v2) = v9 & $i(v9) & $i(v8) & ~
% 65.14/9.57 | hBOOL(v9)) | (hAPP_fun_a_bool_bool(v6, v2) = v7 &
% 65.14/9.57 | hAPP_a85458249l_bool(member_a, v0) = v6 & $i(v7) & $i(v6) & ~
% 65.14/9.57 | hBOOL(v7))))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (fact_290_subsetI) implies:
% 65.14/9.57 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 65.14/9.57 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2) | ~
% 65.14/9.57 | (hAPP_fun_a_bool_bool(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 65.14/9.57 | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 65.14/9.57 | (hAPP_fun_a_bool_bool(v5, v1) = v6 & hAPP_fun_a_bool_bool(v5, v0) =
% 65.14/9.57 | v7 & hAPP_a85458249l_bool(member_a, v4) = v5 & $i(v7) & $i(v6) &
% 65.14/9.57 | $i(v5) & $i(v4) & hBOOL(v6) & is_a(v4) & ~ hBOOL(v7)))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (conj_0) implies:
% 65.14/9.57 | (9) ? [v0: $i] : (hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 &
% 65.14/9.57 | $i(v0) & hBOOL(v0))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (conj_1) implies:
% 65.14/9.57 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 65.14/9.57 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v0 &
% 65.14/9.57 | hAPP_fun_a_bool_bool(v0, v1) = v2 & image_pname_a(mgt_call, u) = v1
% 65.14/9.57 | & $i(v2) & $i(v1) & $i(v0) & hBOOL(v2))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (conj_2) implies:
% 65.14/9.57 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 65.14/9.57 | (hAPP_nat_nat(suc, na) = v0 & hAPP_fun_a_bool_nat(finite_card_a, v2) =
% 65.14/9.57 | v3 & hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 &
% 65.14/9.57 | hAPP_nat_bool(v1, v3) = v4 & image_pname_a(mgt_call, u) = v2 &
% 65.14/9.57 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v4))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (conj_3) implies:
% 65.14/9.57 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 65.14/9.57 | (minus_minus_nat(v2) = v3 & hAPP_nat_nat(v3, v4) = v0 &
% 65.14/9.57 | hAPP_nat_nat(suc, na) = v4 & hAPP_fun_a_bool_nat(finite_card_a, v1)
% 65.14/9.57 | = v2 & hAPP_fun_a_bool_nat(finite_card_a, g) = v0 &
% 65.14/9.57 | image_pname_a(mgt_call, u) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 65.14/9.57 | & $i(v0))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (conj_4) implies:
% 65.14/9.57 | (13) ? [v0: $i] : ? [v1: $i] : (hAPP_f1664156314l_bool(v0, u) = v1 &
% 65.14/9.57 | hAPP_p338031245l_bool(member_pname, pn) = v0 & $i(v1) & $i(v0) &
% 65.14/9.57 | hBOOL(v1))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (conj_5) implies:
% 65.14/9.57 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_fun_a_bool_bool(v1, g)
% 65.14/9.57 | = v2 & hAPP_pname_a(mgt_call, pn) = v0 &
% 65.14/9.57 | hAPP_a85458249l_bool(member_a, v0) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 65.14/9.57 | ~ hBOOL(v2))
% 65.14/9.57 |
% 65.14/9.57 | ALPHA: (conj_6) implies:
% 65.14/9.58 | (15) $i(g)
% 65.14/9.58 | (16) $i(u)
% 65.14/9.58 | (17) $i(pn)
% 65.14/9.58 | (18) $i(mgt_call)
% 65.14/9.58 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 65.14/9.58 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2 &
% 65.14/9.58 | hAPP_fun_a_bool_bool(v2, v3) = v4 & hAPP_pname_a(mgt_call, pn) = v0
% 65.14/9.58 | & insert_a(v0, g) = v1 & image_pname_a(mgt_call, u) = v3 & $i(v4) &
% 65.14/9.58 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v4))
% 65.14/9.58 |
% 65.14/9.58 | ALPHA: (function-axioms) implies:
% 65.14/9.58 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.58 | (image_pname_a(v3, v2) = v1) | ~ (image_pname_a(v3, v2) = v0))
% 65.14/9.58 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.58 | (insert_pname(v3, v2) = v1) | ~ (insert_pname(v3, v2) = v0))
% 65.14/9.58 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.58 | (hAPP_a85458249l_bool(v3, v2) = v1) | ~ (hAPP_a85458249l_bool(v3,
% 65.14/9.58 | v2) = v0))
% 65.14/9.58 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.58 | (hAPP_pname_a(v3, v2) = v1) | ~ (hAPP_pname_a(v3, v2) = v0))
% 65.14/9.58 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.58 | (hAPP_fun_a_bool_bool(v3, v2) = v1) | ~ (hAPP_fun_a_bool_bool(v3,
% 65.14/9.58 | v2) = v0))
% 65.14/9.58 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.58 | (hAPP_f1631501043l_bool(v3, v2) = v1) | ~
% 65.14/9.58 | (hAPP_f1631501043l_bool(v3, v2) = v0))
% 65.14/9.58 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.14/9.58 | (hAPP_f1664156314l_bool(v3, v2) = v1) | ~
% 65.14/9.58 | (hAPP_f1664156314l_bool(v3, v2) = v0))
% 65.14/9.58 |
% 65.56/9.58 | DELTA: instantiating (9) with fresh symbol all_407_0 gives:
% 65.56/9.58 | (27) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_407_0 &
% 65.56/9.58 | $i(all_407_0) & hBOOL(all_407_0)
% 65.56/9.58 |
% 65.56/9.58 | ALPHA: (27) implies:
% 65.56/9.58 | (28) hBOOL(all_407_0)
% 65.56/9.58 | (29) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_407_0
% 65.56/9.58 |
% 65.56/9.58 | DELTA: instantiating (13) with fresh symbols all_411_0, all_411_1 gives:
% 65.56/9.58 | (30) hAPP_f1664156314l_bool(all_411_1, u) = all_411_0 &
% 65.56/9.58 | hAPP_p338031245l_bool(member_pname, pn) = all_411_1 & $i(all_411_0) &
% 65.56/9.58 | $i(all_411_1) & hBOOL(all_411_0)
% 65.56/9.58 |
% 65.56/9.58 | ALPHA: (30) implies:
% 65.56/9.58 | (31) hBOOL(all_411_0)
% 65.56/9.58 | (32) hAPP_p338031245l_bool(member_pname, pn) = all_411_1
% 65.56/9.58 | (33) hAPP_f1664156314l_bool(all_411_1, u) = all_411_0
% 65.56/9.58 |
% 65.56/9.58 | DELTA: instantiating (10) with fresh symbols all_417_0, all_417_1, all_417_2
% 65.56/9.58 | gives:
% 65.56/9.58 | (34) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_417_2 &
% 65.56/9.58 | hAPP_fun_a_bool_bool(all_417_2, all_417_1) = all_417_0 &
% 65.56/9.58 | image_pname_a(mgt_call, u) = all_417_1 & $i(all_417_0) & $i(all_417_1)
% 65.56/9.58 | & $i(all_417_2) & hBOOL(all_417_0)
% 65.56/9.58 |
% 65.56/9.58 | ALPHA: (34) implies:
% 65.56/9.58 | (35) hBOOL(all_417_0)
% 65.56/9.58 | (36) image_pname_a(mgt_call, u) = all_417_1
% 65.56/9.58 | (37) hAPP_fun_a_bool_bool(all_417_2, all_417_1) = all_417_0
% 65.56/9.58 | (38) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_417_2
% 65.56/9.58 |
% 65.56/9.58 | DELTA: instantiating (14) with fresh symbols all_421_0, all_421_1, all_421_2
% 65.56/9.58 | gives:
% 65.56/9.58 | (39) hAPP_fun_a_bool_bool(all_421_1, g) = all_421_0 &
% 65.56/9.58 | hAPP_pname_a(mgt_call, pn) = all_421_2 &
% 65.56/9.58 | hAPP_a85458249l_bool(member_a, all_421_2) = all_421_1 & $i(all_421_0)
% 65.56/9.58 | & $i(all_421_1) & $i(all_421_2) & ~ hBOOL(all_421_0)
% 65.56/9.58 |
% 65.56/9.58 | ALPHA: (39) implies:
% 65.56/9.58 | (40) ~ hBOOL(all_421_0)
% 65.56/9.58 | (41) hAPP_a85458249l_bool(member_a, all_421_2) = all_421_1
% 65.56/9.58 | (42) hAPP_pname_a(mgt_call, pn) = all_421_2
% 65.56/9.59 | (43) hAPP_fun_a_bool_bool(all_421_1, g) = all_421_0
% 65.56/9.59 |
% 65.56/9.59 | DELTA: instantiating (12) with fresh symbols all_431_0, all_431_1, all_431_2,
% 65.56/9.59 | all_431_3, all_431_4 gives:
% 65.56/9.59 | (44) minus_minus_nat(all_431_2) = all_431_1 & hAPP_nat_nat(all_431_1,
% 65.56/9.59 | all_431_0) = all_431_4 & hAPP_nat_nat(suc, na) = all_431_0 &
% 65.56/9.59 | hAPP_fun_a_bool_nat(finite_card_a, all_431_3) = all_431_2 &
% 65.56/9.59 | hAPP_fun_a_bool_nat(finite_card_a, g) = all_431_4 &
% 65.56/9.59 | image_pname_a(mgt_call, u) = all_431_3 & $i(all_431_0) & $i(all_431_1)
% 65.56/9.59 | & $i(all_431_2) & $i(all_431_3) & $i(all_431_4)
% 65.56/9.59 |
% 65.56/9.59 | ALPHA: (44) implies:
% 65.56/9.59 | (45) $i(all_431_3)
% 65.56/9.59 | (46) image_pname_a(mgt_call, u) = all_431_3
% 65.56/9.59 |
% 65.56/9.59 | DELTA: instantiating (19) with fresh symbols all_433_0, all_433_1, all_433_2,
% 65.56/9.59 | all_433_3, all_433_4 gives:
% 65.56/9.59 | (47) hAPP_f1631501043l_bool(ord_le1311769555a_bool, all_433_3) = all_433_2
% 65.56/9.59 | & hAPP_fun_a_bool_bool(all_433_2, all_433_1) = all_433_0 &
% 65.56/9.59 | hAPP_pname_a(mgt_call, pn) = all_433_4 & insert_a(all_433_4, g) =
% 65.56/9.59 | all_433_3 & image_pname_a(mgt_call, u) = all_433_1 & $i(all_433_0) &
% 65.56/9.59 | $i(all_433_1) & $i(all_433_2) & $i(all_433_3) & $i(all_433_4) & ~
% 65.56/9.59 | hBOOL(all_433_0)
% 65.56/9.59 |
% 65.56/9.59 | ALPHA: (47) implies:
% 65.56/9.59 | (48) ~ hBOOL(all_433_0)
% 65.56/9.59 | (49) $i(all_433_4)
% 65.56/9.59 | (50) $i(all_433_3)
% 65.56/9.59 | (51) image_pname_a(mgt_call, u) = all_433_1
% 65.56/9.59 | (52) insert_a(all_433_4, g) = all_433_3
% 65.56/9.59 | (53) hAPP_pname_a(mgt_call, pn) = all_433_4
% 65.56/9.59 | (54) hAPP_fun_a_bool_bool(all_433_2, all_433_1) = all_433_0
% 65.56/9.59 | (55) hAPP_f1631501043l_bool(ord_le1311769555a_bool, all_433_3) = all_433_2
% 65.56/9.59 |
% 65.56/9.59 | DELTA: instantiating (11) with fresh symbols all_435_0, all_435_1, all_435_2,
% 65.56/9.59 | all_435_3, all_435_4 gives:
% 65.56/9.59 | (56) hAPP_nat_nat(suc, na) = all_435_4 & hAPP_fun_a_bool_nat(finite_card_a,
% 65.56/9.59 | all_435_2) = all_435_1 & hAPP_n1699378549t_bool(ord_less_eq_nat,
% 65.56/9.59 | all_435_4) = all_435_3 & hAPP_nat_bool(all_435_3, all_435_1) =
% 65.56/9.59 | all_435_0 & image_pname_a(mgt_call, u) = all_435_2 & $i(all_435_0) &
% 65.56/9.59 | $i(all_435_1) & $i(all_435_2) & $i(all_435_3) & $i(all_435_4) &
% 65.56/9.59 | hBOOL(all_435_0)
% 65.56/9.59 |
% 65.56/9.59 | ALPHA: (56) implies:
% 65.56/9.59 | (57) image_pname_a(mgt_call, u) = all_435_2
% 65.56/9.59 |
% 65.56/9.59 | GROUND_INST: instantiating (20) with all_433_1, all_435_2, u, mgt_call,
% 65.56/9.59 | simplifying with (51), (57) gives:
% 65.56/9.59 | (58) all_435_2 = all_433_1
% 65.56/9.59 |
% 65.56/9.59 | GROUND_INST: instantiating (20) with all_431_3, all_435_2, u, mgt_call,
% 65.56/9.59 | simplifying with (46), (57) gives:
% 65.56/9.59 | (59) all_435_2 = all_431_3
% 65.56/9.59 |
% 65.56/9.59 | GROUND_INST: instantiating (20) with all_417_1, all_435_2, u, mgt_call,
% 65.56/9.59 | simplifying with (36), (57) gives:
% 65.56/9.59 | (60) all_435_2 = all_417_1
% 65.56/9.59 |
% 65.56/9.59 | GROUND_INST: instantiating (23) with all_421_2, all_433_4, pn, mgt_call,
% 65.56/9.59 | simplifying with (42), (53) gives:
% 65.56/9.59 | (61) all_433_4 = all_421_2
% 65.56/9.59 |
% 65.56/9.59 | COMBINE_EQS: (58), (60) imply:
% 65.56/9.59 | (62) all_433_1 = all_417_1
% 65.56/9.59 |
% 65.56/9.59 | COMBINE_EQS: (58), (59) imply:
% 65.56/9.59 | (63) all_433_1 = all_431_3
% 65.56/9.59 |
% 65.56/9.59 | COMBINE_EQS: (62), (63) imply:
% 65.56/9.59 | (64) all_431_3 = all_417_1
% 65.56/9.59 |
% 65.56/9.59 | SIMP: (64) implies:
% 65.56/9.59 | (65) all_431_3 = all_417_1
% 65.56/9.59 |
% 65.56/9.59 | REDUCE: (54), (62) imply:
% 65.56/9.59 | (66) hAPP_fun_a_bool_bool(all_433_2, all_417_1) = all_433_0
% 65.56/9.59 |
% 65.56/9.59 | REDUCE: (52), (61) imply:
% 65.56/9.59 | (67) insert_a(all_421_2, g) = all_433_3
% 65.56/9.59 |
% 65.56/9.59 | REDUCE: (49), (61) imply:
% 65.56/9.59 | (68) $i(all_421_2)
% 65.56/9.59 |
% 65.56/9.59 | REDUCE: (45), (65) imply:
% 65.56/9.59 | (69) $i(all_417_1)
% 65.56/9.59 |
% 65.56/9.59 | GROUND_INST: instantiating (3) with all_421_2, g, all_421_1, all_421_0,
% 65.56/9.59 | simplifying with (15), (41), (43), (68) gives:
% 65.56/9.59 | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 65.56/9.59 | ((hAPP_fun_a_bool_bool(finite_finite_a, g) = v0 & $i(v0) & ~
% 65.56/9.59 | hBOOL(v0)) | (( ~ hBOOL(all_421_0) | (v3 = v2 &
% 65.56/9.59 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 65.56/9.59 | hAPP_fun_a_bool_nat(finite_card_a, g) = v2 &
% 65.56/9.59 | insert_a(all_421_2, g) = v1 & $i(v2) & $i(v1))) &
% 65.56/9.59 | (hBOOL(all_421_0) | (v4 = v2 & hAPP_nat_nat(suc, v3) = v2 &
% 65.56/9.59 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 65.56/9.59 | hAPP_fun_a_bool_nat(finite_card_a, g) = v3 &
% 65.56/9.59 | insert_a(all_421_2, g) = v1 & $i(v3) & $i(v2) & $i(v1)))))
% 65.56/9.59 |
% 65.56/9.60 | GROUND_INST: instantiating (4) with g, mgt_call, u, all_417_2, all_417_1,
% 65.56/9.60 | all_417_0, simplifying with (15), (16), (18), (35), (36), (37),
% 65.56/9.60 | (38) gives:
% 65.56/9.60 | (71) ? [v0: $i] : ? [v1: $i] :
% 65.56/9.60 | ((hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 & $i(v0) & ~
% 65.56/9.60 | hBOOL(v0)) | (hAPP_fun_a_bool_bool(finite_finite_a, g) = v1 &
% 65.56/9.60 | $i(v1) & hBOOL(v1)))
% 65.56/9.60 |
% 65.56/9.60 | GROUND_INST: instantiating (7) with all_421_2, g, all_417_1, all_433_3,
% 65.56/9.60 | all_433_2, all_433_0, simplifying with (15), (48), (55), (66),
% 65.56/9.60 | (67), (68), (69) gives:
% 65.56/9.60 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 65.56/9.60 | ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v2 &
% 65.56/9.60 | hAPP_fun_a_bool_bool(v2, all_417_1) = v3 & $i(v3) & $i(v2) & ~
% 65.56/9.60 | hBOOL(v3)) | (hAPP_fun_a_bool_bool(v0, all_417_1) = v1 &
% 65.56/9.60 | hAPP_a85458249l_bool(member_a, all_421_2) = v0 & $i(v1) & $i(v0) &
% 65.56/9.60 | ~ hBOOL(v1)))
% 65.56/9.60 |
% 65.64/9.60 | GROUND_INST: instantiating (8) with all_417_1, all_433_3, all_433_2,
% 65.64/9.60 | all_433_0, simplifying with (48), (50), (55), (66), (69) gives:
% 65.64/9.60 | (73) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 65.64/9.60 | (hAPP_fun_a_bool_bool(v1, all_433_3) = v2 & hAPP_fun_a_bool_bool(v1,
% 65.64/9.60 | all_417_1) = v3 & hAPP_a85458249l_bool(member_a, v0) = v1 & $i(v3)
% 65.64/9.60 | & $i(v2) & $i(v1) & $i(v0) & hBOOL(v2) & is_a(v0) & ~ hBOOL(v3))
% 65.64/9.60 |
% 65.64/9.60 | GROUND_INST: instantiating (5) with pn, u, all_411_1, all_411_0, simplifying
% 65.64/9.60 | with (1), (16), (17), (31), (32), (33) gives:
% 65.64/9.60 | (74) insert_pname(pn, u) = u
% 65.64/9.60 |
% 65.64/9.60 | GROUND_INST: instantiating (2) with pn, u, all_411_1, all_411_0, simplifying
% 65.64/9.60 | with (16), (17), (32), (33) gives:
% 65.64/9.60 | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 65.64/9.60 | ((hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 & $i(v0) & ~
% 65.64/9.60 | hBOOL(v0)) | (( ~ hBOOL(all_411_0) | (v3 = v2 &
% 65.64/9.60 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v2 &
% 65.64/9.60 | hAPP_f921600141ol_nat(finite_card_pname, u) = v2 &
% 65.64/9.60 | insert_pname(pn, u) = v1 & $i(v2) & $i(v1))) &
% 65.64/9.60 | (hBOOL(all_411_0) | (v4 = v2 & hAPP_nat_nat(suc, v3) = v2 &
% 65.64/9.60 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v2 &
% 65.64/9.60 | hAPP_f921600141ol_nat(finite_card_pname, u) = v3 &
% 65.64/9.60 | insert_pname(pn, u) = v1 & $i(v3) & $i(v2) & $i(v1)))))
% 65.64/9.60 |
% 65.64/9.60 | DELTA: instantiating (71) with fresh symbols all_550_0, all_550_1 gives:
% 65.64/9.60 | (76) (hAPP_f1664156314l_bool(finite_finite_pname, u) = all_550_1 &
% 65.64/9.60 | $i(all_550_1) & ~ hBOOL(all_550_1)) |
% 65.64/9.60 | (hAPP_fun_a_bool_bool(finite_finite_a, g) = all_550_0 & $i(all_550_0)
% 65.64/9.60 | & hBOOL(all_550_0))
% 65.64/9.60 |
% 65.64/9.60 | DELTA: instantiating (73) with fresh symbols all_556_0, all_556_1, all_556_2,
% 65.64/9.60 | all_556_3 gives:
% 65.64/9.60 | (77) hAPP_fun_a_bool_bool(all_556_2, all_433_3) = all_556_1 &
% 65.64/9.60 | hAPP_fun_a_bool_bool(all_556_2, all_417_1) = all_556_0 &
% 65.64/9.60 | hAPP_a85458249l_bool(member_a, all_556_3) = all_556_2 & $i(all_556_0)
% 65.64/9.60 | & $i(all_556_1) & $i(all_556_2) & $i(all_556_3) & hBOOL(all_556_1) &
% 65.64/9.60 | is_a(all_556_3) & ~ hBOOL(all_556_0)
% 65.64/9.60 |
% 65.64/9.60 | ALPHA: (77) implies:
% 65.64/9.60 | (78) ~ hBOOL(all_556_0)
% 65.64/9.60 | (79) $i(all_556_3)
% 65.64/9.60 | (80) hAPP_a85458249l_bool(member_a, all_556_3) = all_556_2
% 65.64/9.60 | (81) hAPP_fun_a_bool_bool(all_556_2, all_417_1) = all_556_0
% 65.64/9.60 |
% 65.64/9.60 | DELTA: instantiating (72) with fresh symbols all_558_0, all_558_1, all_558_2,
% 65.64/9.60 | all_558_3 gives:
% 65.64/9.60 | (82) (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_558_1 &
% 65.64/9.60 | hAPP_fun_a_bool_bool(all_558_1, all_417_1) = all_558_0 &
% 65.64/9.60 | $i(all_558_0) & $i(all_558_1) & ~ hBOOL(all_558_0)) |
% 65.64/9.60 | (hAPP_fun_a_bool_bool(all_558_3, all_417_1) = all_558_2 &
% 65.64/9.60 | hAPP_a85458249l_bool(member_a, all_421_2) = all_558_3 &
% 65.64/9.60 | $i(all_558_2) & $i(all_558_3) & ~ hBOOL(all_558_2))
% 65.64/9.60 |
% 65.64/9.60 | DELTA: instantiating (70) with fresh symbols all_562_0, all_562_1, all_562_2,
% 65.64/9.60 | all_562_3, all_562_4 gives:
% 65.64/9.60 | (83) (hAPP_fun_a_bool_bool(finite_finite_a, g) = all_562_4 & $i(all_562_4)
% 65.64/9.60 | & ~ hBOOL(all_562_4)) | (( ~ hBOOL(all_421_0) | (all_562_1 =
% 65.64/9.60 | all_562_2 & hAPP_fun_a_bool_nat(finite_card_a, all_562_3) =
% 65.64/9.60 | all_562_2 & hAPP_fun_a_bool_nat(finite_card_a, g) = all_562_2 &
% 65.64/9.60 | insert_a(all_421_2, g) = all_562_3 & $i(all_562_2) &
% 65.64/9.60 | $i(all_562_3))) & (hBOOL(all_421_0) | (all_562_0 = all_562_2 &
% 65.64/9.60 | hAPP_nat_nat(suc, all_562_1) = all_562_2 &
% 65.64/9.60 | hAPP_fun_a_bool_nat(finite_card_a, all_562_3) = all_562_2 &
% 65.64/9.60 | hAPP_fun_a_bool_nat(finite_card_a, g) = all_562_1 &
% 65.64/9.60 | insert_a(all_421_2, g) = all_562_3 & $i(all_562_1) &
% 65.64/9.60 | $i(all_562_2) & $i(all_562_3))))
% 65.64/9.60 |
% 65.64/9.60 | DELTA: instantiating (75) with fresh symbols all_563_0, all_563_1, all_563_2,
% 65.64/9.60 | all_563_3, all_563_4 gives:
% 65.64/9.60 | (84) (hAPP_f1664156314l_bool(finite_finite_pname, u) = all_563_4 &
% 65.64/9.60 | $i(all_563_4) & ~ hBOOL(all_563_4)) | (( ~ hBOOL(all_411_0) |
% 65.64/9.60 | (all_563_1 = all_563_2 & hAPP_f921600141ol_nat(finite_card_pname,
% 65.64/9.60 | all_563_3) = all_563_2 &
% 65.64/9.60 | hAPP_f921600141ol_nat(finite_card_pname, u) = all_563_2 &
% 65.64/9.60 | insert_pname(pn, u) = all_563_3 & $i(all_563_2) &
% 65.64/9.60 | $i(all_563_3))) & (hBOOL(all_411_0) | (all_563_0 = all_563_2 &
% 65.64/9.60 | hAPP_nat_nat(suc, all_563_1) = all_563_2 &
% 65.64/9.60 | hAPP_f921600141ol_nat(finite_card_pname, all_563_3) = all_563_2
% 65.64/9.60 | & hAPP_f921600141ol_nat(finite_card_pname, u) = all_563_1 &
% 65.64/9.60 | insert_pname(pn, u) = all_563_3 & $i(all_563_1) & $i(all_563_2)
% 65.64/9.60 | & $i(all_563_3))))
% 65.64/9.60 |
% 65.64/9.60 | BETA: splitting (84) gives:
% 65.64/9.60 |
% 65.64/9.60 | Case 1:
% 65.64/9.60 | |
% 65.64/9.60 | | (85) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_563_4 &
% 65.64/9.60 | | $i(all_563_4) & ~ hBOOL(all_563_4)
% 65.64/9.60 | |
% 65.64/9.60 | | ALPHA: (85) implies:
% 65.64/9.60 | | (86) ~ hBOOL(all_563_4)
% 65.64/9.60 | | (87) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_563_4
% 65.64/9.60 | |
% 65.64/9.60 | | GROUND_INST: instantiating (26) with all_407_0, all_563_4, u,
% 65.64/9.60 | | finite_finite_pname, simplifying with (29), (87) gives:
% 65.64/9.61 | | (88) all_563_4 = all_407_0
% 65.64/9.61 | |
% 65.64/9.61 | | REDUCE: (86), (88) imply:
% 65.64/9.61 | | (89) ~ hBOOL(all_407_0)
% 65.64/9.61 | |
% 65.64/9.61 | | PRED_UNIFY: (28), (89) imply:
% 65.64/9.61 | | (90) $false
% 65.64/9.61 | |
% 65.64/9.61 | | CLOSE: (90) is inconsistent.
% 65.64/9.61 | |
% 65.64/9.61 | Case 2:
% 65.64/9.61 | |
% 65.64/9.61 | | (91) ( ~ hBOOL(all_411_0) | (all_563_1 = all_563_2 &
% 65.64/9.61 | | hAPP_f921600141ol_nat(finite_card_pname, all_563_3) = all_563_2
% 65.64/9.61 | | & hAPP_f921600141ol_nat(finite_card_pname, u) = all_563_2 &
% 65.64/9.61 | | insert_pname(pn, u) = all_563_3 & $i(all_563_2) &
% 65.64/9.61 | | $i(all_563_3))) & (hBOOL(all_411_0) | (all_563_0 = all_563_2 &
% 65.64/9.61 | | hAPP_nat_nat(suc, all_563_1) = all_563_2 &
% 65.64/9.61 | | hAPP_f921600141ol_nat(finite_card_pname, all_563_3) = all_563_2
% 65.64/9.61 | | & hAPP_f921600141ol_nat(finite_card_pname, u) = all_563_1 &
% 65.64/9.61 | | insert_pname(pn, u) = all_563_3 & $i(all_563_1) & $i(all_563_2)
% 65.64/9.61 | | & $i(all_563_3)))
% 65.64/9.61 | |
% 65.64/9.61 | | ALPHA: (91) implies:
% 65.64/9.61 | | (92) ~ hBOOL(all_411_0) | (all_563_1 = all_563_2 &
% 65.64/9.61 | | hAPP_f921600141ol_nat(finite_card_pname, all_563_3) = all_563_2 &
% 65.64/9.61 | | hAPP_f921600141ol_nat(finite_card_pname, u) = all_563_2 &
% 65.64/9.61 | | insert_pname(pn, u) = all_563_3 & $i(all_563_2) & $i(all_563_3))
% 65.64/9.61 | |
% 65.64/9.61 | | BETA: splitting (92) gives:
% 65.64/9.61 | |
% 65.64/9.61 | | Case 1:
% 65.64/9.61 | | |
% 65.64/9.61 | | | (93) ~ hBOOL(all_411_0)
% 65.64/9.61 | | |
% 65.64/9.61 | | | PRED_UNIFY: (31), (93) imply:
% 65.64/9.61 | | | (94) $false
% 65.64/9.61 | | |
% 65.64/9.61 | | | CLOSE: (94) is inconsistent.
% 65.64/9.61 | | |
% 65.64/9.61 | | Case 2:
% 65.64/9.61 | | |
% 65.64/9.61 | | | (95) all_563_1 = all_563_2 & hAPP_f921600141ol_nat(finite_card_pname,
% 65.64/9.61 | | | all_563_3) = all_563_2 &
% 65.64/9.61 | | | hAPP_f921600141ol_nat(finite_card_pname, u) = all_563_2 &
% 65.64/9.61 | | | insert_pname(pn, u) = all_563_3 & $i(all_563_2) & $i(all_563_3)
% 65.64/9.61 | | |
% 65.64/9.61 | | | ALPHA: (95) implies:
% 65.64/9.61 | | | (96) $i(all_563_3)
% 65.64/9.61 | | | (97) insert_pname(pn, u) = all_563_3
% 65.64/9.61 | | |
% 65.64/9.61 | | | BETA: splitting (76) gives:
% 65.64/9.61 | | |
% 65.64/9.61 | | | Case 1:
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | (98) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_550_1 &
% 65.64/9.61 | | | | $i(all_550_1) & ~ hBOOL(all_550_1)
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | ALPHA: (98) implies:
% 65.64/9.61 | | | | (99) ~ hBOOL(all_550_1)
% 65.64/9.61 | | | | (100) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_550_1
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | GROUND_INST: instantiating (26) with all_407_0, all_550_1, u,
% 65.64/9.61 | | | | finite_finite_pname, simplifying with (29), (100) gives:
% 65.64/9.61 | | | | (101) all_550_1 = all_407_0
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | REDUCE: (99), (101) imply:
% 65.64/9.61 | | | | (102) ~ hBOOL(all_407_0)
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | PRED_UNIFY: (28), (102) imply:
% 65.64/9.61 | | | | (103) $false
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | CLOSE: (103) is inconsistent.
% 65.64/9.61 | | | |
% 65.64/9.61 | | | Case 2:
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | (104) hAPP_fun_a_bool_bool(finite_finite_a, g) = all_550_0 &
% 65.64/9.61 | | | | $i(all_550_0) & hBOOL(all_550_0)
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | ALPHA: (104) implies:
% 65.64/9.61 | | | | (105) hBOOL(all_550_0)
% 65.64/9.61 | | | | (106) hAPP_fun_a_bool_bool(finite_finite_a, g) = all_550_0
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | BETA: splitting (82) gives:
% 65.64/9.61 | | | |
% 65.64/9.61 | | | | Case 1:
% 65.64/9.61 | | | | |
% 65.64/9.61 | | | | | (107) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_558_1
% 65.64/9.61 | | | | | & hAPP_fun_a_bool_bool(all_558_1, all_417_1) = all_558_0 &
% 65.64/9.61 | | | | | $i(all_558_0) & $i(all_558_1) & ~ hBOOL(all_558_0)
% 65.64/9.61 | | | | |
% 65.64/9.61 | | | | | ALPHA: (107) implies:
% 65.64/9.61 | | | | | (108) ~ hBOOL(all_558_0)
% 65.64/9.61 | | | | | (109) hAPP_fun_a_bool_bool(all_558_1, all_417_1) = all_558_0
% 65.64/9.61 | | | | | (110) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_558_1
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | GROUND_INST: instantiating (25) with all_417_2, all_558_1, g,
% 65.71/9.61 | | | | | ord_le1311769555a_bool, simplifying with (38), (110)
% 65.71/9.61 | | | | | gives:
% 65.71/9.61 | | | | | (111) all_558_1 = all_417_2
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | REDUCE: (109), (111) imply:
% 65.71/9.61 | | | | | (112) hAPP_fun_a_bool_bool(all_417_2, all_417_1) = all_558_0
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | GROUND_INST: instantiating (24) with all_417_0, all_558_0, all_417_1,
% 65.71/9.61 | | | | | all_417_2, simplifying with (37), (112) gives:
% 65.71/9.61 | | | | | (113) all_558_0 = all_417_0
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | REDUCE: (108), (113) imply:
% 65.71/9.61 | | | | | (114) ~ hBOOL(all_417_0)
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | PRED_UNIFY: (35), (114) imply:
% 65.71/9.61 | | | | | (115) $false
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | CLOSE: (115) is inconsistent.
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | Case 2:
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | (116) hAPP_fun_a_bool_bool(all_558_3, all_417_1) = all_558_2 &
% 65.71/9.61 | | | | | hAPP_a85458249l_bool(member_a, all_421_2) = all_558_3 &
% 65.71/9.61 | | | | | $i(all_558_2) & $i(all_558_3) & ~ hBOOL(all_558_2)
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | ALPHA: (116) implies:
% 65.71/9.61 | | | | | (117) ~ hBOOL(all_558_2)
% 65.71/9.61 | | | | | (118) hAPP_a85458249l_bool(member_a, all_421_2) = all_558_3
% 65.71/9.61 | | | | | (119) hAPP_fun_a_bool_bool(all_558_3, all_417_1) = all_558_2
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | BETA: splitting (83) gives:
% 65.71/9.61 | | | | |
% 65.71/9.61 | | | | | Case 1:
% 65.71/9.61 | | | | | |
% 65.71/9.61 | | | | | | (120) hAPP_fun_a_bool_bool(finite_finite_a, g) = all_562_4 &
% 65.71/9.61 | | | | | | $i(all_562_4) & ~ hBOOL(all_562_4)
% 65.71/9.61 | | | | | |
% 65.71/9.61 | | | | | | ALPHA: (120) implies:
% 65.71/9.61 | | | | | | (121) ~ hBOOL(all_562_4)
% 65.71/9.61 | | | | | | (122) hAPP_fun_a_bool_bool(finite_finite_a, g) = all_562_4
% 65.71/9.61 | | | | | |
% 65.71/9.61 | | | | | | GROUND_INST: instantiating (24) with all_550_0, all_562_4, g,
% 65.71/9.61 | | | | | | finite_finite_a, simplifying with (106), (122) gives:
% 65.71/9.61 | | | | | | (123) all_562_4 = all_550_0
% 65.71/9.61 | | | | | |
% 65.71/9.61 | | | | | | REDUCE: (121), (123) imply:
% 65.71/9.61 | | | | | | (124) ~ hBOOL(all_550_0)
% 65.71/9.61 | | | | | |
% 65.71/9.61 | | | | | | PRED_UNIFY: (105), (124) imply:
% 65.71/9.61 | | | | | | (125) $false
% 65.71/9.61 | | | | | |
% 65.71/9.61 | | | | | | CLOSE: (125) is inconsistent.
% 65.71/9.61 | | | | | |
% 65.71/9.61 | | | | | Case 2:
% 65.71/9.61 | | | | | |
% 65.71/9.62 | | | | | | (126) ( ~ hBOOL(all_421_0) | (all_562_1 = all_562_2 &
% 65.71/9.62 | | | | | | hAPP_fun_a_bool_nat(finite_card_a, all_562_3) =
% 65.71/9.62 | | | | | | all_562_2 & hAPP_fun_a_bool_nat(finite_card_a, g) =
% 65.71/9.62 | | | | | | all_562_2 & insert_a(all_421_2, g) = all_562_3 &
% 65.71/9.62 | | | | | | $i(all_562_2) & $i(all_562_3))) & (hBOOL(all_421_0) |
% 65.71/9.62 | | | | | | (all_562_0 = all_562_2 & hAPP_nat_nat(suc, all_562_1) =
% 65.71/9.62 | | | | | | all_562_2 & hAPP_fun_a_bool_nat(finite_card_a,
% 65.71/9.62 | | | | | | all_562_3) = all_562_2 &
% 65.71/9.62 | | | | | | hAPP_fun_a_bool_nat(finite_card_a, g) = all_562_1 &
% 65.71/9.62 | | | | | | insert_a(all_421_2, g) = all_562_3 & $i(all_562_1) &
% 65.71/9.62 | | | | | | $i(all_562_2) & $i(all_562_3)))
% 65.71/9.62 | | | | | |
% 65.71/9.62 | | | | | | ALPHA: (126) implies:
% 65.71/9.62 | | | | | | (127) hBOOL(all_421_0) | (all_562_0 = all_562_2 &
% 65.71/9.62 | | | | | | hAPP_nat_nat(suc, all_562_1) = all_562_2 &
% 65.71/9.62 | | | | | | hAPP_fun_a_bool_nat(finite_card_a, all_562_3) = all_562_2
% 65.71/9.62 | | | | | | & hAPP_fun_a_bool_nat(finite_card_a, g) = all_562_1 &
% 65.71/9.62 | | | | | | insert_a(all_421_2, g) = all_562_3 & $i(all_562_1) &
% 65.71/9.62 | | | | | | $i(all_562_2) & $i(all_562_3))
% 65.71/9.62 | | | | | |
% 65.71/9.62 | | | | | | BETA: splitting (127) gives:
% 65.71/9.62 | | | | | |
% 65.71/9.62 | | | | | | Case 1:
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | (128) hBOOL(all_421_0)
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | PRED_UNIFY: (40), (128) imply:
% 65.71/9.62 | | | | | | | (129) $false
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | CLOSE: (129) is inconsistent.
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | Case 2:
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | GROUND_INST: instantiating (21) with u, all_563_3, u, pn,
% 65.71/9.62 | | | | | | | simplifying with (74), (97) gives:
% 65.71/9.62 | | | | | | | (130) all_563_3 = u
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | GROUND_INST: instantiating (22) with all_421_1, all_558_3,
% 65.71/9.62 | | | | | | | all_421_2, member_a, simplifying with (41), (118)
% 65.71/9.62 | | | | | | | gives:
% 65.71/9.62 | | | | | | | (131) all_558_3 = all_421_1
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | REDUCE: (119), (131) imply:
% 65.71/9.62 | | | | | | | (132) hAPP_fun_a_bool_bool(all_421_1, all_417_1) = all_558_2
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | GROUND_INST: instantiating (6) with all_421_2, mgt_call, pn, u,
% 65.71/9.62 | | | | | | | all_411_1, all_411_0, all_421_1, all_417_1,
% 65.71/9.62 | | | | | | | all_558_2, simplifying with (16), (17), (18), (31),
% 65.71/9.62 | | | | | | | (32), (33), (36), (41), (68), (117), (132) gives:
% 65.71/9.62 | | | | | | | (133) ? [v0: any] : ( ~ (v0 = all_421_2) &
% 65.71/9.62 | | | | | | | hAPP_pname_a(mgt_call, pn) = v0 & $i(v0))
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | GROUND_INST: instantiating (6) with all_556_3, mgt_call, pn, u,
% 65.71/9.62 | | | | | | | all_411_1, all_411_0, all_556_2, all_417_1,
% 65.71/9.62 | | | | | | | all_556_0, simplifying with (16), (17), (18), (31),
% 65.71/9.62 | | | | | | | (32), (33), (36), (78), (79), (80), (81) gives:
% 65.71/9.62 | | | | | | | (134) ? [v0: any] : ( ~ (v0 = all_556_3) &
% 65.71/9.62 | | | | | | | hAPP_pname_a(mgt_call, pn) = v0 & $i(v0))
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | DELTA: instantiating (133) with fresh symbol all_620_0 gives:
% 65.71/9.62 | | | | | | | (135) ~ (all_620_0 = all_421_2) & hAPP_pname_a(mgt_call, pn) =
% 65.71/9.62 | | | | | | | all_620_0 & $i(all_620_0)
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | ALPHA: (135) implies:
% 65.71/9.62 | | | | | | | (136) ~ (all_620_0 = all_421_2)
% 65.71/9.62 | | | | | | | (137) hAPP_pname_a(mgt_call, pn) = all_620_0
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | DELTA: instantiating (134) with fresh symbol all_624_0 gives:
% 65.71/9.62 | | | | | | | (138) ~ (all_624_0 = all_556_3) & hAPP_pname_a(mgt_call, pn) =
% 65.71/9.62 | | | | | | | all_624_0 & $i(all_624_0)
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | ALPHA: (138) implies:
% 65.71/9.62 | | | | | | | (139) hAPP_pname_a(mgt_call, pn) = all_624_0
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | GROUND_INST: instantiating (23) with all_421_2, all_624_0, pn,
% 65.71/9.62 | | | | | | | mgt_call, simplifying with (42), (139) gives:
% 65.71/9.62 | | | | | | | (140) all_624_0 = all_421_2
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | GROUND_INST: instantiating (23) with all_620_0, all_624_0, pn,
% 65.71/9.62 | | | | | | | mgt_call, simplifying with (137), (139) gives:
% 65.71/9.62 | | | | | | | (141) all_624_0 = all_620_0
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | COMBINE_EQS: (140), (141) imply:
% 65.71/9.62 | | | | | | | (142) all_620_0 = all_421_2
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | REDUCE: (136), (142) imply:
% 65.71/9.62 | | | | | | | (143) $false
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | | CLOSE: (143) is inconsistent.
% 65.71/9.62 | | | | | | |
% 65.71/9.62 | | | | | | End of split
% 65.71/9.62 | | | | | |
% 65.71/9.62 | | | | | End of split
% 65.71/9.62 | | | | |
% 65.71/9.62 | | | | End of split
% 65.71/9.62 | | | |
% 65.71/9.62 | | | End of split
% 65.71/9.62 | | |
% 65.71/9.62 | | End of split
% 65.71/9.62 | |
% 65.71/9.62 | End of split
% 65.71/9.62 |
% 65.71/9.62 End of proof
% 65.71/9.62 % SZS output end Proof for theBenchmark
% 65.71/9.62
% 65.71/9.62 9001ms
%------------------------------------------------------------------------------