TSTP Solution File: SWW473+5 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:50:19 EDT 2023
% Result : Theorem 42.65s 6.59s
% Output : Proof 101.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 20:22:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.70 ________ _____
% 0.19/0.70 ___ __ \_________(_)________________________________
% 0.19/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.70
% 0.19/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.70 (2023-06-19)
% 0.19/0.70
% 0.19/0.70 (c) Philipp Rümmer, 2009-2023
% 0.19/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.70 Amanda Stjerna.
% 0.19/0.70 Free software under BSD-3-Clause.
% 0.19/0.70
% 0.19/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.70
% 0.19/0.70 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.72 Running up to 7 provers in parallel.
% 0.19/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 8.21/1.98 Prover 1: Preprocessing ...
% 8.21/2.01 Prover 4: Preprocessing ...
% 8.93/2.03 Prover 3: Preprocessing ...
% 8.93/2.03 Prover 5: Preprocessing ...
% 8.93/2.03 Prover 2: Preprocessing ...
% 8.93/2.04 Prover 6: Preprocessing ...
% 8.93/2.04 Prover 0: Preprocessing ...
% 23.06/3.95 Prover 1: Warning: ignoring some quantifiers
% 23.14/3.96 Prover 3: Warning: ignoring some quantifiers
% 23.54/4.03 Prover 6: Proving ...
% 23.85/4.10 Prover 3: Constructing countermodel ...
% 23.85/4.13 Prover 1: Constructing countermodel ...
% 24.90/4.26 Prover 4: Warning: ignoring some quantifiers
% 25.68/4.40 Prover 0: Proving ...
% 26.42/4.43 Prover 4: Constructing countermodel ...
% 28.32/4.66 Prover 5: Proving ...
% 34.33/5.48 Prover 2: Proving ...
% 42.65/6.58 Prover 3: proved (5848ms)
% 42.65/6.58
% 42.65/6.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.65/6.59
% 42.65/6.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 42.65/6.61 Prover 5: stopped
% 42.65/6.62 Prover 0: stopped
% 42.65/6.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 42.65/6.62 Prover 2: stopped
% 42.65/6.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 42.65/6.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 44.63/6.85 Prover 6: stopped
% 44.99/6.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 45.96/7.11 Prover 10: Preprocessing ...
% 45.96/7.13 Prover 7: Preprocessing ...
% 47.64/7.22 Prover 11: Preprocessing ...
% 47.64/7.23 Prover 8: Preprocessing ...
% 48.11/7.33 Prover 13: Preprocessing ...
% 52.77/7.92 Prover 8: Warning: ignoring some quantifiers
% 53.47/7.98 Prover 8: Constructing countermodel ...
% 55.08/8.19 Prover 10: Warning: ignoring some quantifiers
% 55.72/8.28 Prover 10: Constructing countermodel ...
% 55.98/8.35 Prover 7: Warning: ignoring some quantifiers
% 55.98/8.38 Prover 7: Constructing countermodel ...
% 56.49/8.47 Prover 11: Warning: ignoring some quantifiers
% 56.49/8.52 Prover 11: Constructing countermodel ...
% 56.49/8.52 Prover 13: Warning: ignoring some quantifiers
% 57.72/8.58 Prover 13: Constructing countermodel ...
% 99.90/14.12 Prover 10: Found proof (size 381)
% 99.90/14.13 Prover 10: proved (7500ms)
% 99.90/14.13 Prover 11: stopped
% 99.90/14.13 Prover 4: stopped
% 99.90/14.13 Prover 7: stopped
% 99.90/14.14 Prover 1: stopped
% 100.45/14.17 Prover 8: stopped
% 100.56/14.19 Prover 13: stopped
% 100.56/14.19
% 100.56/14.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 100.56/14.19
% 101.18/14.33 % SZS output start Proof for theBenchmark
% 101.18/14.33 Assumptions after simplification:
% 101.18/14.33 ---------------------------------
% 101.18/14.33
% 101.18/14.33 (conj_0)
% 101.18/14.36 $i(u) & $i(pname) & $i(bool) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 101.18/14.36 (hAPP(v0, bool, v1, u) = v2 & finite_finite(pname) = v1 & fun(pname, bool) =
% 101.18/14.36 v0 & $i(v2) & $i(v1) & $i(v0) & hBOOL(v2))
% 101.18/14.36
% 101.18/14.36 (conj_1)
% 101.18/14.36 $i(mgt_call) & $i(u) & $i(pname) & $i(g) & $i(x_a) & $i(bool) & ? [v0: $i] :
% 101.18/14.36 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 101.18/14.36 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : (hAPP(v5, v6,
% 101.18/14.36 v7, mgt_call) = v8 & hAPP(v4, v0, v8, u) = v9 & hAPP(v0, v1, v2, g) = v3 &
% 101.18/14.36 hAPP(v0, bool, v3, v9) = v10 & image(pname, x_a) = v7 & ord_less_eq(v0) = v2
% 101.18/14.36 & fun(v4, v0) = v6 & fun(v0, bool) = v1 & fun(pname, x_a) = v5 & fun(pname,
% 101.18/14.36 bool) = v4 & fun(x_a, bool) = v0 & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 101.18/14.36 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v10))
% 101.18/14.37
% 101.18/14.37 (conj_2)
% 101.18/14.37 $i(na) & $i(mgt_call) & $i(u) & $i(pname) & $i(x_a) & $i(suc) & $i(nat) &
% 101.18/14.37 $i(bool) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 101.18/14.37 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 101.18/14.37 [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : (hAPP(v7, v8, v9,
% 101.18/14.37 mgt_call) = v10 & hAPP(v6, v4, v10, u) = v11 & hAPP(v4, nat, v5, v11) =
% 101.18/14.37 v12 & hAPP(nat, v0, v1, v2) = v3 & hAPP(nat, nat, suc, na) = v2 & hAPP(nat,
% 101.18/14.37 bool, v3, v12) = v13 & image(pname, x_a) = v9 & ord_less_eq(nat) = v1 &
% 101.18/14.37 finite_card(x_a) = v5 & fun(v6, v4) = v8 & fun(pname, x_a) = v7 & fun(pname,
% 101.18/14.37 bool) = v6 & fun(x_a, bool) = v4 & fun(nat, bool) = v0 & $i(v13) & $i(v12)
% 101.18/14.37 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 101.18/14.37 $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v13))
% 101.18/14.37
% 101.18/14.37 (conj_3)
% 101.42/14.37 $i(na) & $i(mgt_call) & $i(u) & $i(pname) & $i(g) & $i(x_a) & $i(suc) &
% 101.42/14.37 $i(nat) & $i(bool) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 101.42/14.37 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 101.42/14.37 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : (hAPP(v6,
% 101.42/14.37 v7, v8, mgt_call) = v9 & hAPP(v5, v0, v9, u) = v10 & hAPP(v0, nat, v1,
% 101.42/14.37 v10) = v11 & hAPP(v0, nat, v1, g) = v2 & hAPP(nat, v3, v4, v11) = v12 &
% 101.42/14.37 hAPP(nat, nat, v12, v13) = v2 & hAPP(nat, nat, suc, na) = v13 & image(pname,
% 101.42/14.37 x_a) = v8 & minus_minus(nat) = v4 & finite_card(x_a) = v1 & fun(v5, v0) =
% 101.42/14.37 v7 & fun(pname, x_a) = v6 & fun(pname, bool) = v5 & fun(x_a, bool) = v0 &
% 101.42/14.37 fun(nat, nat) = v3 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8)
% 101.42/14.37 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 101.42/14.37
% 101.42/14.37 (conj_4)
% 101.42/14.38 $i(pn) & $i(u) & $i(pname) & $i(bool) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 101.42/14.38 $i] : ? [v3: $i] : ? [v4: $i] : (member(pname) = v2 & hAPP(v0, bool, v3,
% 101.42/14.38 u) = v4 & hAPP(pname, v1, v2, pn) = v3 & fun(v0, bool) = v1 & fun(pname,
% 101.42/14.38 bool) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v4))
% 101.42/14.38
% 101.42/14.38 (conj_5)
% 101.42/14.38 $i(pn) & $i(mgt_call) & $i(pname) & $i(g) & $i(x_a) & $i(bool) & ? [v0: $i] :
% 101.42/14.38 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 101.42/14.38 (member(x_a) = v2 & hAPP(v0, bool, v4, g) = v5 & hAPP(pname, x_a, mgt_call,
% 101.42/14.38 pn) = v3 & hAPP(x_a, v1, v2, v3) = v4 & fun(v0, bool) = v1 & fun(x_a,
% 101.42/14.38 bool) = v0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 101.42/14.38 hBOOL(v5))
% 101.42/14.38
% 101.42/14.38 (conj_6)
% 101.42/14.38 $i(pn) & $i(mgt_call) & $i(u) & $i(pname) & $i(g) & $i(x_a) & $i(bool) & ?
% 101.42/14.38 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 101.42/14.38 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 101.42/14.38 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 101.42/14.38 (hAPP(v10, v11, v12, mgt_call) = v13 & hAPP(v9, v0, v13, u) = v14 & hAPP(v0,
% 101.42/14.38 v1, v2, v7) = v8 & hAPP(v0, v0, v6, g) = v7 & hAPP(v0, bool, v8, v14) =
% 101.42/14.38 v15 & hAPP(pname, x_a, mgt_call, pn) = v5 & hAPP(x_a, v3, v4, v5) = v6 &
% 101.42/14.38 insert(x_a) = v4 & image(pname, x_a) = v12 & ord_less_eq(v0) = v2 & fun(v9,
% 101.42/14.38 v0) = v11 & fun(v0, v0) = v3 & fun(v0, bool) = v1 & fun(pname, x_a) = v10
% 101.42/14.38 & fun(pname, bool) = v9 & fun(x_a, bool) = v0 & $i(v15) & $i(v14) & $i(v13)
% 101.42/14.38 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 101.42/14.38 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v15))
% 101.42/14.38
% 101.42/14.38 (fact_0_assms_I1_J)
% 101.42/14.39 $i(p) & $i(x_a) & $i(bool) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 101.42/14.39 (ord_less_eq(v0) = v2 & fun(v0, bool) = v1 & fun(x_a, bool) = v0 & $i(v2) &
% 101.42/14.39 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 101.42/14.39 ~ (hAPP(v0, v1, v2, v3) = v5) | ~ (hAPP(v0, bool, v5, v4) = v6) | ~
% 101.42/14.39 $i(v4) | ~ $i(v3) | ~ hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : (hAPP(v0,
% 101.42/14.39 v1, p, v4) = v7 & hAPP(v0, bool, v7, v3) = v8 & $i(v8) & $i(v7) &
% 101.42/14.39 hBOOL(v8))))
% 101.42/14.39
% 101.42/14.39 (fact_28_finite__subset)
% 101.42/14.39 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.39 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v1) = v6) |
% 101.42/14.39 ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (ord_less_eq(v3) = v5) | ~ (fun(v3,
% 101.42/14.39 bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 101.42/14.39 $i(v0) | ~ hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 101.42/14.39 (finite_finite(v0) = v8 & $i(v8) & ((hAPP(v3, bool, v8, v2) = v9 & $i(v9) &
% 101.42/14.39 ~ hBOOL(v9)) | (hAPP(v3, bool, v8, v1) = v10 & $i(v10) &
% 101.42/14.39 hBOOL(v10)))))
% 101.42/14.39
% 101.42/14.39 (fact_29_rev__finite__subset)
% 101.42/14.39 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.39 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v1) = v6) |
% 101.42/14.39 ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (ord_less_eq(v3) = v5) | ~ (fun(v3,
% 101.42/14.39 bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 101.42/14.39 $i(v0) | ~ hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 101.42/14.39 (finite_finite(v0) = v8 & $i(v8) & ((hAPP(v3, bool, v8, v2) = v9 & $i(v9) &
% 101.42/14.39 ~ hBOOL(v9)) | (hAPP(v3, bool, v8, v1) = v10 & $i(v10) &
% 101.42/14.39 hBOOL(v10)))))
% 101.42/14.39
% 101.42/14.39 (fact_46_finite__surj)
% 101.42/14.39 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.39 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 101.42/14.39 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : !
% 101.42/14.39 [v15: $i] : ( ~ (hAPP(v10, v11, v12, v3) = v13) | ~ (hAPP(v6, v7, v8, v2) =
% 101.42/14.39 v9) | ~ (hAPP(v6, bool, v9, v14) = v15) | ~ (hAPP(v5, v6, v13, v4) =
% 101.42/14.39 v14) | ~ (image(v1, v0) = v12) | ~ (ord_less_eq(v6) = v8) | ~ (fun(v6,
% 101.42/14.39 bool) = v7) | ~ (fun(v5, v6) = v11) | ~ (fun(v1, v0) = v10) | ~
% 101.42/14.39 (fun(v1, bool) = v5) | ~ (fun(v0, bool) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 101.42/14.39 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v15) | ? [v16: $i] : ? [v17: $i]
% 101.42/14.39 : ? [v18: $i] : ? [v19: $i] : ((hAPP(v6, bool, v18, v2) = v19 &
% 101.42/14.39 finite_finite(v0) = v18 & $i(v19) & $i(v18) & hBOOL(v19)) | (hAPP(v5,
% 101.42/14.39 bool, v16, v4) = v17 & finite_finite(v1) = v16 & $i(v17) & $i(v16) &
% 101.42/14.39 ~ hBOOL(v17))))
% 101.42/14.39
% 101.42/14.39 (fact_47_finite__subset__image)
% 101.42/14.40 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.40 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 101.42/14.40 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : !
% 101.42/14.40 [v15: $i] : ( ~ (hAPP(v10, v11, v12, v2) = v13) | ~ (hAPP(v9, v5, v13, v3) =
% 101.42/14.40 v14) | ~ (hAPP(v5, v6, v7, v4) = v8) | ~ (hAPP(v5, bool, v8, v14) = v15)
% 101.42/14.40 | ~ (image(v0, v1) = v12) | ~ (ord_less_eq(v5) = v7) | ~ (fun(v9, v5) =
% 101.42/14.40 v11) | ~ (fun(v5, bool) = v6) | ~ (fun(v1, bool) = v5) | ~ (fun(v0, v1)
% 101.42/14.40 = v10) | ~ (fun(v0, bool) = v9) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 101.42/14.40 $i(v1) | ~ $i(v0) | ~ hBOOL(v15) | ? [v16: $i] : ? [v17: $i] : ? [v18:
% 101.42/14.40 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23:
% 101.42/14.40 $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ($i(v22) & ((v26 = v21
% 101.42/14.40 & hAPP(v9, v18, v19, v22) = v23 & hAPP(v9, v5, v13, v22) = v21 &
% 101.42/14.40 hAPP(v9, bool, v23, v3) = v24 & hAPP(v9, bool, v20, v22) = v25 &
% 101.42/14.40 ord_less_eq(v9) = v19 & finite_finite(v0) = v20 & fun(v9, bool) = v18
% 101.42/14.40 & ti(v5, v4) = v21 & $i(v25) & $i(v24) & $i(v23) & $i(v21) & $i(v20) &
% 101.42/14.40 $i(v19) & $i(v18) & hBOOL(v25) & hBOOL(v24)) | (hAPP(v5, bool, v16,
% 101.42/14.40 v4) = v17 & finite_finite(v1) = v16 & $i(v17) & $i(v16) & ~
% 101.42/14.40 hBOOL(v17)))))
% 101.42/14.40
% 101.42/14.40 (fact_67_equalityD1)
% 101.42/14.40 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.40 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v1) = v6) |
% 101.42/14.40 ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (ord_less_eq(v3) = v5) | ~ (fun(v3,
% 101.42/14.40 bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 101.42/14.40 $i(v0) | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = v8) & ti(v3, v2)
% 101.42/14.40 = v9 & ti(v3, v1) = v8 & $i(v9) & $i(v8)))
% 101.42/14.40
% 101.42/14.40 (fact_68_equalityD2)
% 101.42/14.40 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.40 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v2) = v6) |
% 101.42/14.40 ~ (hAPP(v3, bool, v6, v1) = v7) | ~ (ord_less_eq(v3) = v5) | ~ (fun(v3,
% 101.42/14.40 bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 101.42/14.40 $i(v0) | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = v8) & ti(v3, v2)
% 101.42/14.40 = v9 & ti(v3, v1) = v8 & $i(v9) & $i(v8)))
% 101.42/14.40
% 101.42/14.40 (fact_73_equalityE)
% 101.42/14.40 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.40 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v1) = v6) |
% 101.42/14.40 ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (ord_less_eq(v3) = v5) | ~ (fun(v3,
% 101.42/14.40 bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 101.42/14.40 $i(v0) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v9
% 101.42/14.40 = v8) & ti(v3, v2) = v9 & ti(v3, v1) = v8 & $i(v9) & $i(v8)) |
% 101.42/14.40 (hAPP(v3, v4, v5, v2) = v10 & hAPP(v3, bool, v10, v1) = v11 & $i(v11) &
% 101.42/14.40 $i(v10) & hBOOL(v11) & hBOOL(v7))))
% 101.42/14.40
% 101.42/14.40 (fact_74_ext)
% 101.42/14.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 101.42/14.40 $i] : ! [v6: $i] : (v6 = v5 | ~ (fun(v0, v1) = v4) | ~ (ti(v4, v3) = v6)
% 101.42/14.40 | ~ (ti(v4, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 101.42/14.40 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = v8) & hAPP(v0, v1, v3, v7)
% 101.42/14.40 = v9 & hAPP(v0, v1, v2, v7) = v8 & $i(v9) & $i(v8) & $i(v7)))
% 101.42/14.40
% 101.42/14.40 (fact_77_image__iff)
% 101.42/14.41 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.41 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 101.42/14.41 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : !
% 101.42/14.41 [v15: $i] : ( ~ (member(v0) = v8) | ~ (hAPP(v10, v11, v12, v3) = v13) | ~
% 101.42/14.41 (hAPP(v6, bool, v9, v14) = v15) | ~ (hAPP(v5, v6, v13, v4) = v14) | ~
% 101.42/14.41 (hAPP(v0, v7, v8, v2) = v9) | ~ (image(v1, v0) = v12) | ~ (fun(v6, bool) =
% 101.42/14.41 v7) | ~ (fun(v5, v6) = v11) | ~ (fun(v1, v0) = v10) | ~ (fun(v1, bool)
% 101.42/14.41 = v5) | ~ (fun(v0, bool) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 101.42/14.41 $i(v1) | ~ $i(v0) | hBOOL(v15) | ? [v16: $i] : ? [v17: $i] : ? [v18: $i]
% 101.42/14.41 : (member(v1) = v17 & fun(v5, bool) = v16 & ti(v0, v2) = v18 & $i(v18) &
% 101.42/14.41 $i(v17) & $i(v16) & ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~
% 101.42/14.41 (hAPP(v5, bool, v20, v4) = v21) | ~ (hAPP(v1, v16, v17, v19) = v20) |
% 101.42/14.41 ~ $i(v19) | ~ hBOOL(v21) | ? [v22: $i] : ( ~ (v22 = v18) & hAPP(v1,
% 101.42/14.41 v0, v3, v19) = v22 & $i(v22))))) & ! [v0: $i] : ! [v1: $i] : !
% 101.42/14.41 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 101.42/14.41 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : !
% 101.42/14.41 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ( ~ (member(v0) = v7) | ~
% 101.42/14.41 (hAPP(v10, v11, v12, v3) = v13) | ~ (hAPP(v9, v5, v13, v4) = v14) | ~
% 101.42/14.41 (hAPP(v5, bool, v8, v14) = v15) | ~ (hAPP(v0, v6, v7, v2) = v8) | ~
% 101.42/14.41 (image(v1, v0) = v12) | ~ (fun(v9, v5) = v11) | ~ (fun(v5, bool) = v6) |
% 101.42/14.41 ~ (fun(v1, v0) = v10) | ~ (fun(v1, bool) = v9) | ~ (fun(v0, bool) = v5) |
% 101.42/14.41 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v15) |
% 101.42/14.41 ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ?
% 101.42/14.41 [v21: $i] : (member(v1) = v17 & hAPP(v9, bool, v20, v4) = v21 & hAPP(v1,
% 101.42/14.41 v16, v17, v19) = v20 & hAPP(v1, v0, v3, v19) = v18 & fun(v9, bool) = v16
% 101.42/14.41 & ti(v0, v2) = v18 & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) &
% 101.42/14.41 $i(v16) & hBOOL(v21)))
% 101.42/14.41
% 101.42/14.41 (fact_78_imageI)
% 101.42/14.41 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.41 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 101.42/14.41 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : !
% 101.42/14.41 [v15: $i] : ! [v16: $i] : ( ~ (member(v0) = v8) | ~ (hAPP(v11, v12, v13, v2)
% 101.42/14.41 = v14) | ~ (hAPP(v6, bool, v10, v15) = v16) | ~ (hAPP(v5, v6, v14, v4) =
% 101.42/14.41 v15) | ~ (hAPP(v1, v0, v2, v3) = v9) | ~ (hAPP(v0, v7, v8, v9) = v10) |
% 101.42/14.41 ~ (image(v1, v0) = v13) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, v6) = v12) |
% 101.42/14.41 ~ (fun(v1, v0) = v11) | ~ (fun(v1, bool) = v5) | ~ (fun(v0, bool) = v6) |
% 101.42/14.41 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v16) | ?
% 101.42/14.41 [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : (member(v1) = v18 &
% 101.42/14.41 hAPP(v5, bool, v19, v4) = v20 & hAPP(v1, v17, v18, v3) = v19 & fun(v5,
% 101.42/14.41 bool) = v17 & $i(v20) & $i(v19) & $i(v18) & $i(v17) & ~ hBOOL(v20)))
% 101.42/14.41
% 101.42/14.41 (fact_84_insert__subset)
% 101.42/14.41 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.41 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 101.42/14.41 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ (hAPP(v4, v5, v6, v10) = v11) |
% 101.42/14.41 ~ (hAPP(v4, v4, v9, v2) = v10) | ~ (hAPP(v4, bool, v11, v3) = v12) | ~
% 101.42/14.41 (hAPP(v0, v7, v8, v1) = v9) | ~ (insert(v0) = v8) | ~ (ord_less_eq(v4) =
% 101.42/14.41 v6) | ~ (fun(v4, v4) = v7) | ~ (fun(v4, bool) = v5) | ~ (fun(v0, bool)
% 101.42/14.41 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v12) | ?
% 101.42/14.41 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] :
% 101.42/14.41 (member(v0) = v13 & hAPP(v4, v5, v6, v2) = v16 & hAPP(v4, bool, v16, v3) =
% 101.42/14.41 v17 & hAPP(v4, bool, v14, v3) = v15 & hAPP(v0, v5, v13, v1) = v14 &
% 101.42/14.41 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & hBOOL(v17) &
% 101.42/14.41 hBOOL(v15))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 101.42/14.41 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 101.42/14.41 : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ (hAPP(v4, v5, v6, v10) =
% 101.42/14.41 v11) | ~ (hAPP(v4, v4, v9, v2) = v10) | ~ (hAPP(v4, bool, v11, v3) =
% 101.42/14.41 v12) | ~ (hAPP(v0, v7, v8, v1) = v9) | ~ (insert(v0) = v8) | ~
% 101.42/14.41 (ord_less_eq(v4) = v6) | ~ (fun(v4, v4) = v7) | ~ (fun(v4, bool) = v5) |
% 101.42/14.41 ~ (fun(v0, bool) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 101.42/14.41 hBOOL(v12) | ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ?
% 101.42/14.41 [v17: $i] : ((member(v0) = v13 & hAPP(v4, bool, v14, v3) = v15 & hAPP(v0,
% 101.42/14.41 v5, v13, v1) = v14 & $i(v15) & $i(v14) & $i(v13) & ~ hBOOL(v15)) |
% 101.42/14.41 (hAPP(v4, v5, v6, v2) = v16 & hAPP(v4, bool, v16, v3) = v17 & $i(v17) &
% 101.42/14.41 $i(v16) & ~ hBOOL(v17))))
% 101.42/14.41
% 101.42/14.41 (fact_90_subset__image__iff)
% 101.42/14.42 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.42 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 101.42/14.42 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : !
% 101.42/14.42 [v15: $i] : ( ~ (hAPP(v10, v11, v12, v3) = v13) | ~ (hAPP(v9, v5, v13, v4) =
% 101.42/14.42 v14) | ~ (hAPP(v5, v6, v7, v2) = v8) | ~ (hAPP(v5, bool, v8, v14) = v15)
% 101.42/14.42 | ~ (image(v1, v0) = v12) | ~ (ord_less_eq(v5) = v7) | ~ (fun(v9, v5) =
% 101.42/14.42 v11) | ~ (fun(v5, bool) = v6) | ~ (fun(v1, v0) = v10) | ~ (fun(v1,
% 101.42/14.42 bool) = v9) | ~ (fun(v0, bool) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 101.42/14.42 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v15) | ? [v16: $i] : ? [v17: $i]
% 101.42/14.42 : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : (hAPP(v9, v16,
% 101.42/14.42 v17, v19) = v20 & hAPP(v9, v5, v13, v19) = v18 & hAPP(v9, bool, v20, v4)
% 101.42/14.42 = v21 & ord_less_eq(v9) = v17 & fun(v9, bool) = v16 & ti(v5, v2) = v18 &
% 101.42/14.42 $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & hBOOL(v21))) &
% 101.42/14.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 101.42/14.42 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 101.42/14.42 ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ( ~
% 101.42/14.42 (hAPP(v7, v8, v9, v3) = v10) | ~ (hAPP(v6, v11, v12, v2) = v13) | ~
% 101.42/14.42 (hAPP(v6, bool, v13, v14) = v15) | ~ (hAPP(v5, v6, v10, v4) = v14) | ~
% 101.42/14.42 (image(v1, v0) = v9) | ~ (ord_less_eq(v6) = v12) | ~ (fun(v6, bool) = v11)
% 101.42/14.42 | ~ (fun(v5, v6) = v8) | ~ (fun(v1, v0) = v7) | ~ (fun(v1, bool) = v5) |
% 101.42/14.42 ~ (fun(v0, bool) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 101.42/14.42 $i(v0) | hBOOL(v15) | ? [v16: $i] : ? [v17: $i] : ? [v18: $i] :
% 101.42/14.42 (ord_less_eq(v5) = v17 & fun(v5, bool) = v16 & ti(v6, v2) = v18 & $i(v18) &
% 101.42/14.42 $i(v17) & $i(v16) & ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~
% 101.42/14.42 (hAPP(v5, v16, v17, v19) = v20) | ~ (hAPP(v5, bool, v20, v4) = v21) |
% 101.42/14.42 ~ $i(v19) | ~ hBOOL(v21) | ? [v22: $i] : ( ~ (v22 = v18) & hAPP(v5,
% 101.42/14.42 v6, v10, v19) = v22 & $i(v22)))))
% 101.42/14.42
% 101.42/14.42 (fact_93_subsetI)
% 101.42/14.42 $i(bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.42 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v2) = v6) |
% 101.42/14.42 ~ (hAPP(v3, bool, v6, v1) = v7) | ~ (ord_less_eq(v3) = v5) | ~ (fun(v3,
% 101.42/14.42 bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 101.42/14.42 $i(v0) | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i]
% 101.42/14.42 : ? [v12: $i] : (member(v0) = v8 & hAPP(v3, bool, v10, v2) = v11 & hAPP(v3,
% 101.42/14.42 bool, v10, v1) = v12 & hAPP(v0, v4, v8, v9) = v10 & $i(v12) & $i(v11) &
% 101.42/14.42 $i(v10) & $i(v9) & $i(v8) & hBOOL(v11) & ~ hBOOL(v12)))
% 101.42/14.42
% 101.42/14.42 (tsy_c_hAPP_res)
% 101.42/14.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 101.42/14.42 $i] : (v5 = v4 | ~ (hAPP(v1, v0, v2, v3) = v4) | ~ (ti(v0, v4) = v5) | ~
% 101.42/14.42 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 101.42/14.42
% 101.42/14.42 (tsy_v_G_res)
% 101.42/14.42 $i(g) & $i(x_a) & $i(bool) & ? [v0: $i] : (fun(x_a, bool) = v0 & ti(v0, g) =
% 101.42/14.42 g & $i(v0))
% 101.42/14.42
% 101.42/14.42 (tsy_v_P_res)
% 101.42/14.42 $i(p) & $i(x_a) & $i(bool) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 101.42/14.42 (fun(v0, v1) = v2 & fun(v0, bool) = v1 & fun(x_a, bool) = v0 & ti(v2, p) = p &
% 101.42/14.42 $i(v2) & $i(v1) & $i(v0))
% 101.42/14.42
% 101.42/14.42 (tsy_v_U_res)
% 101.42/14.42 $i(u) & $i(pname) & $i(bool) & ? [v0: $i] : (fun(pname, bool) = v0 & ti(v0,
% 101.42/14.42 u) = u & $i(v0))
% 101.42/14.42
% 101.42/14.42 (tsy_v_mgt__call_res)
% 101.42/14.42 $i(mgt_call) & $i(pname) & $i(x_a) & ? [v0: $i] : (fun(pname, x_a) = v0 &
% 101.42/14.42 ti(v0, mgt_call) = mgt_call & $i(v0))
% 101.42/14.42
% 101.42/14.42 (function-axioms)
% 101.42/14.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 101.42/14.43 $i] : (v1 = v0 | ~ (hAPP(v5, v4, v3, v2) = v1) | ~ (hAPP(v5, v4, v3, v2) =
% 101.42/14.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 101.42/14.43 : (v1 = v0 | ~ (combs(v4, v3, v2) = v1) | ~ (combs(v4, v3, v2) = v0)) & !
% 101.42/14.43 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 101.42/14.43 ~ (combc(v4, v3, v2) = v1) | ~ (combc(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 101.42/14.43 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (combb(v4,
% 101.42/14.43 v3, v2) = v1) | ~ (combb(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 101.42/14.43 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~
% 101.42/14.43 (image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 101.42/14.43 $i] : (v1 = v0 | ~ (fun(v3, v2) = v1) | ~ (fun(v3, v2) = v0)) & ! [v0:
% 101.42/14.43 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ti(v3, v2) =
% 101.42/14.43 v1) | ~ (ti(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 101.42/14.43 (v1 = v0 | ~ (member(v2) = v1) | ~ (member(v2) = v0)) & ! [v0: $i] : !
% 101.42/14.43 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (fequal(v2) = v1) | ~ (fequal(v2) =
% 101.42/14.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (insert(v2)
% 101.42/14.43 = v1) | ~ (insert(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 101.42/14.43 (v1 = v0 | ~ (collect(v2) = v1) | ~ (collect(v2) = v0)) & ! [v0: $i] : !
% 101.42/14.43 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (ord_less_eq(v2) = v1) | ~
% 101.42/14.43 (ord_less_eq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 101.42/14.43 | ~ (undefined(v2) = v1) | ~ (undefined(v2) = v0)) & ! [v0: $i] : ! [v1:
% 101.42/14.43 $i] : ! [v2: $i] : (v1 = v0 | ~ (minus_minus(v2) = v1) | ~
% 101.42/14.43 (minus_minus(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 101.42/14.43 | ~ (finite_finite(v2) = v1) | ~ (finite_finite(v2) = v0)) & ! [v0: $i] :
% 101.42/14.43 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (finite_card(v2) = v1) | ~
% 101.42/14.43 (finite_card(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 101.42/14.43 | ~ (combi(v2) = v1) | ~ (combi(v2) = v0))
% 101.42/14.43
% 101.42/14.43 Further assumptions not needed in the proof:
% 101.42/14.43 --------------------------------------------
% 101.42/14.43 arity_HOL_Obool___Finite__Set_Ofinite, arity_HOL_Obool___Orderings_Oorder,
% 101.42/14.43 arity_HOL_Obool___Orderings_Opreorder, arity_Nat_Onat___Orderings_Oorder,
% 101.42/14.43 arity_Nat_Onat___Orderings_Opreorder, arity_fun___Finite__Set_Ofinite,
% 101.42/14.43 arity_fun___Orderings_Oorder, arity_fun___Orderings_Opreorder,
% 101.42/14.43 fact_10_finite__Collect__conjI, fact_11_Suc__diff__le,
% 101.42/14.43 fact_12_finite__Collect__le__nat, fact_13_card__Collect__le__nat,
% 101.42/14.43 fact_14_finite__code, fact_15_finite, fact_16_Suc__inject, fact_17_nat_Oinject,
% 101.42/14.43 fact_18_Suc__n__not__n, fact_19_n__not__Suc__n, fact_1_finite__Collect__subsets,
% 101.42/14.43 fact_20_le__antisym, fact_21_le__trans, fact_22_eq__imp__le,
% 101.42/14.43 fact_23_nat__le__linear, fact_24_le__refl, fact_25_diff__commute,
% 101.42/14.43 fact_26_finite__Collect__disjI, fact_27_finite__insert, fact_2_finite__imageI,
% 101.42/14.43 fact_30_Suc__leD, fact_31_le__SucE, fact_32_le__SucI, fact_33_Suc__le__mono,
% 101.42/14.43 fact_34_le__Suc__eq, fact_35_not__less__eq__eq, fact_36_Suc__n__not__le__n,
% 101.42/14.43 fact_37_Suc__diff__diff, fact_38_diff__Suc__Suc, fact_39_le__diff__iff,
% 101.42/14.43 fact_3_finite_OinsertI, fact_40_Nat_Odiff__diff__eq, fact_41_eq__diff__iff,
% 101.42/14.43 fact_42_diff__diff__cancel, fact_43_diff__le__mono, fact_44_diff__le__mono2,
% 101.42/14.43 fact_45_diff__le__self, fact_48_lift__Suc__mono__le,
% 101.42/14.43 fact_49_pigeonhole__infinite, fact_4_card__image__le, fact_50_image__eqI,
% 101.42/14.43 fact_51_equalityI, fact_52_subsetD, fact_53_insertCI, fact_54_insertE,
% 101.42/14.43 fact_55_insertI1, fact_56_insert__compr, fact_57_insert__Collect,
% 101.42/14.43 fact_58_insert__absorb2, fact_59_insert__commute, fact_5_card__mono,
% 101.42/14.43 fact_60_insert__iff, fact_61_insert__code, fact_62_insert__ident,
% 101.42/14.43 fact_63_insertI2, fact_64_insert__absorb, fact_65_subset__refl,
% 101.42/14.43 fact_66_set__eq__subset, fact_69_in__mono, fact_6_card__seteq,
% 101.42/14.43 fact_70_set__rev__mp, fact_71_set__mp, fact_72_subset__trans, fact_75_mem__def,
% 101.42/14.43 fact_76_Collect__def, fact_79_rev__image__eqI, fact_7_card__insert__le,
% 101.42/14.43 fact_80_insert__compr__raw, fact_81_image__image, fact_82_image__ident,
% 101.42/14.43 fact_83_subset__insertI, fact_85_subset__insert, fact_86_subset__insertI2,
% 101.42/14.43 fact_87_insert__mono, fact_88_image__insert, fact_89_insert__image,
% 101.42/14.43 fact_8_card__insert__if, fact_91_image__mono, fact_92_imageE,
% 101.42/14.43 fact_94_zero__induct__lemma, fact_95_Suc__le__D, fact_96_image__subsetI,
% 101.42/14.43 fact_97_order__refl, fact_98_finite__nat__set__iff__bounded__le,
% 101.42/14.43 fact_9_card__insert__disjoint, help_COMBB_1_1_U, help_COMBC_1_1_U,
% 101.42/14.43 help_COMBI_1_1_U, help_COMBS_1_1_U, help_fNot_1_1_U, help_fNot_2_1_U,
% 101.42/14.43 help_fconj_1_1_U, help_fconj_2_1_U, help_fconj_3_1_U, help_fdisj_1_1_U,
% 101.42/14.43 help_fdisj_2_1_U, help_fdisj_3_1_U, help_fequal_1_1_T, help_fequal_2_1_T,
% 101.42/14.43 help_fimplies_1_1_U, help_fimplies_2_1_U, help_fimplies_3_1_U, help_ti_idem,
% 101.42/14.43 tsy_c_COMBB_res, tsy_c_COMBC_res, tsy_c_COMBI_res, tsy_c_COMBS_res,
% 101.42/14.43 tsy_c_Finite__Set_Ocard_res, tsy_c_Finite__Set_Ofinite_res,
% 101.42/14.43 tsy_c_Groups_Ominus__class_Ominus_res, tsy_c_HOL_Oundefined_res,
% 101.42/14.43 tsy_c_Nat_OSuc_res, tsy_c_Orderings_Oord__class_Oless__eq_res,
% 101.42/14.43 tsy_c_Set_OCollect_res, tsy_c_Set_Oimage_res, tsy_c_Set_Oinsert_res,
% 101.42/14.43 tsy_c_fNot_res, tsy_c_fconj_res, tsy_c_fdisj_res, tsy_c_fequal_res,
% 101.42/14.43 tsy_c_fimplies_res, tsy_c_hAPP_arg1, tsy_c_hAPP_arg2, tsy_c_hBOOL_arg1,
% 101.42/14.43 tsy_c_member_res, tsy_v_na_res, tsy_v_pn_res
% 101.42/14.43
% 101.42/14.43 Those formulas are unsatisfiable:
% 101.42/14.43 ---------------------------------
% 101.42/14.43
% 101.42/14.43 Begin of proof
% 101.42/14.43 |
% 101.42/14.43 | ALPHA: (tsy_v_G_res) implies:
% 101.42/14.43 | (1) ? [v0: $i] : (fun(x_a, bool) = v0 & ti(v0, g) = g & $i(v0))
% 101.42/14.43 |
% 101.42/14.43 | ALPHA: (tsy_v_P_res) implies:
% 101.42/14.43 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (fun(v0, v1) = v2 & fun(v0,
% 101.42/14.43 | bool) = v1 & fun(x_a, bool) = v0 & ti(v2, p) = p & $i(v2) & $i(v1)
% 101.42/14.43 | & $i(v0))
% 101.42/14.43 |
% 101.42/14.43 | ALPHA: (tsy_v_U_res) implies:
% 101.42/14.44 | (3) ? [v0: $i] : (fun(pname, bool) = v0 & ti(v0, u) = u & $i(v0))
% 101.42/14.44 |
% 101.42/14.44 | ALPHA: (tsy_v_mgt__call_res) implies:
% 101.42/14.44 | (4) ? [v0: $i] : (fun(pname, x_a) = v0 & ti(v0, mgt_call) = mgt_call &
% 101.42/14.44 | $i(v0))
% 101.42/14.44 |
% 101.42/14.44 | ALPHA: (fact_0_assms_I1_J) implies:
% 101.42/14.44 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ord_less_eq(v0) = v2 &
% 101.42/14.44 | fun(v0, bool) = v1 & fun(x_a, bool) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 101.42/14.44 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v0,
% 101.42/14.44 | v1, v2, v3) = v5) | ~ (hAPP(v0, bool, v5, v4) = v6) | ~
% 101.42/14.44 | $i(v4) | ~ $i(v3) | ~ hBOOL(v6) | ? [v7: $i] : ? [v8: $i] :
% 101.42/14.44 | (hAPP(v0, v1, p, v4) = v7 & hAPP(v0, bool, v7, v3) = v8 & $i(v8) &
% 101.42/14.44 | $i(v7) & hBOOL(v8))))
% 101.42/14.44 |
% 101.42/14.44 | ALPHA: (fact_29_rev__finite__subset) implies:
% 101.42/14.44 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.42/14.44 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v1) =
% 101.42/14.44 | v6) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (ord_less_eq(v3) = v5)
% 101.42/14.44 | | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~
% 101.42/14.44 | $i(v1) | ~ $i(v0) | ~ hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ?
% 101.42/14.44 | [v10: $i] : (finite_finite(v0) = v8 & $i(v8) & ((hAPP(v3, bool, v8,
% 101.42/14.44 | v2) = v9 & $i(v9) & ~ hBOOL(v9)) | (hAPP(v3, bool, v8, v1) =
% 101.42/14.44 | v10 & $i(v10) & hBOOL(v10)))))
% 101.42/14.44 |
% 101.42/14.44 | ALPHA: (fact_46_finite__surj) implies:
% 101.42/14.44 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.42/14.44 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 101.42/14.44 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] :
% 101.42/14.44 | ! [v15: $i] : ( ~ (hAPP(v10, v11, v12, v3) = v13) | ~ (hAPP(v6, v7,
% 101.42/14.44 | v8, v2) = v9) | ~ (hAPP(v6, bool, v9, v14) = v15) | ~ (hAPP(v5,
% 101.42/14.44 | v6, v13, v4) = v14) | ~ (image(v1, v0) = v12) | ~
% 101.42/14.44 | (ord_less_eq(v6) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, v6) =
% 101.42/14.44 | v11) | ~ (fun(v1, v0) = v10) | ~ (fun(v1, bool) = v5) | ~
% 101.42/14.44 | (fun(v0, bool) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 101.42/14.44 | | ~ $i(v0) | ~ hBOOL(v15) | ? [v16: $i] : ? [v17: $i] : ? [v18:
% 101.42/14.44 | $i] : ? [v19: $i] : ((hAPP(v6, bool, v18, v2) = v19 &
% 101.42/14.44 | finite_finite(v0) = v18 & $i(v19) & $i(v18) & hBOOL(v19)) |
% 101.42/14.44 | (hAPP(v5, bool, v16, v4) = v17 & finite_finite(v1) = v16 & $i(v17)
% 101.42/14.44 | & $i(v16) & ~ hBOOL(v17))))
% 101.42/14.44 |
% 101.42/14.44 | ALPHA: (fact_47_finite__subset__image) implies:
% 101.42/14.44 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.42/14.44 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 101.42/14.44 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] :
% 101.42/14.44 | ! [v15: $i] : ( ~ (hAPP(v10, v11, v12, v2) = v13) | ~ (hAPP(v9, v5,
% 101.42/14.44 | v13, v3) = v14) | ~ (hAPP(v5, v6, v7, v4) = v8) | ~ (hAPP(v5,
% 101.42/14.44 | bool, v8, v14) = v15) | ~ (image(v0, v1) = v12) | ~
% 101.42/14.44 | (ord_less_eq(v5) = v7) | ~ (fun(v9, v5) = v11) | ~ (fun(v5, bool) =
% 101.42/14.44 | v6) | ~ (fun(v1, bool) = v5) | ~ (fun(v0, v1) = v10) | ~
% 101.42/14.44 | (fun(v0, bool) = v9) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 101.42/14.44 | | ~ $i(v0) | ~ hBOOL(v15) | ? [v16: $i] : ? [v17: $i] : ? [v18:
% 101.42/14.44 | $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] :
% 101.42/14.44 | ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ($i(v22) &
% 101.42/14.44 | ((v26 = v21 & hAPP(v9, v18, v19, v22) = v23 & hAPP(v9, v5, v13,
% 101.42/14.44 | v22) = v21 & hAPP(v9, bool, v23, v3) = v24 & hAPP(v9, bool,
% 101.42/14.44 | v20, v22) = v25 & ord_less_eq(v9) = v19 & finite_finite(v0) =
% 101.42/14.44 | v20 & fun(v9, bool) = v18 & ti(v5, v4) = v21 & $i(v25) &
% 101.42/14.44 | $i(v24) & $i(v23) & $i(v21) & $i(v20) & $i(v19) & $i(v18) &
% 101.42/14.44 | hBOOL(v25) & hBOOL(v24)) | (hAPP(v5, bool, v16, v4) = v17 &
% 101.42/14.44 | finite_finite(v1) = v16 & $i(v17) & $i(v16) & ~ hBOOL(v17)))))
% 101.42/14.44 |
% 101.42/14.44 | ALPHA: (fact_67_equalityD1) implies:
% 101.42/14.45 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.42/14.45 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v1) =
% 101.42/14.45 | v6) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (ord_less_eq(v3) = v5)
% 101.42/14.45 | | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~
% 101.42/14.45 | $i(v1) | ~ $i(v0) | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ( ~ (v9
% 101.42/14.45 | = v8) & ti(v3, v2) = v9 & ti(v3, v1) = v8 & $i(v9) & $i(v8)))
% 101.42/14.45 |
% 101.42/14.45 | ALPHA: (fact_68_equalityD2) implies:
% 101.42/14.45 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.42/14.45 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v2) =
% 101.42/14.45 | v6) | ~ (hAPP(v3, bool, v6, v1) = v7) | ~ (ord_less_eq(v3) = v5)
% 101.42/14.45 | | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~
% 101.42/14.45 | $i(v1) | ~ $i(v0) | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ( ~ (v9
% 101.42/14.45 | = v8) & ti(v3, v2) = v9 & ti(v3, v1) = v8 & $i(v9) & $i(v8)))
% 101.42/14.45 |
% 101.42/14.45 | ALPHA: (fact_73_equalityE) implies:
% 101.42/14.45 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.42/14.45 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v1) =
% 101.42/14.45 | v6) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (ord_less_eq(v3) = v5)
% 101.42/14.45 | | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~
% 101.42/14.45 | $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 101.42/14.45 | [v11: $i] : (( ~ (v9 = v8) & ti(v3, v2) = v9 & ti(v3, v1) = v8 &
% 101.42/14.45 | $i(v9) & $i(v8)) | (hAPP(v3, v4, v5, v2) = v10 & hAPP(v3, bool,
% 101.42/14.45 | v10, v1) = v11 & $i(v11) & $i(v10) & hBOOL(v11) & hBOOL(v7))))
% 101.42/14.45 |
% 101.42/14.45 | ALPHA: (fact_77_image__iff) implies:
% 101.79/14.45 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.79/14.45 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 101.79/14.45 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14:
% 101.79/14.45 | $i] : ! [v15: $i] : ( ~ (member(v0) = v8) | ~ (hAPP(v10, v11, v12,
% 101.79/14.45 | v3) = v13) | ~ (hAPP(v6, bool, v9, v14) = v15) | ~ (hAPP(v5,
% 101.79/14.45 | v6, v13, v4) = v14) | ~ (hAPP(v0, v7, v8, v2) = v9) | ~
% 101.79/14.45 | (image(v1, v0) = v12) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, v6) =
% 101.79/14.45 | v11) | ~ (fun(v1, v0) = v10) | ~ (fun(v1, bool) = v5) | ~
% 101.79/14.45 | (fun(v0, bool) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 101.79/14.45 | | ~ $i(v0) | hBOOL(v15) | ? [v16: $i] : ? [v17: $i] : ? [v18:
% 101.79/14.45 | $i] : (member(v1) = v17 & fun(v5, bool) = v16 & ti(v0, v2) = v18 &
% 101.79/14.45 | $i(v18) & $i(v17) & $i(v16) & ! [v19: $i] : ! [v20: $i] : !
% 101.79/14.45 | [v21: $i] : ( ~ (hAPP(v5, bool, v20, v4) = v21) | ~ (hAPP(v1,
% 101.79/14.45 | v16, v17, v19) = v20) | ~ $i(v19) | ~ hBOOL(v21) | ?
% 101.79/14.45 | [v22: $i] : ( ~ (v22 = v18) & hAPP(v1, v0, v3, v19) = v22 &
% 101.79/14.45 | $i(v22)))))
% 101.79/14.45 |
% 101.79/14.45 | ALPHA: (fact_78_imageI) implies:
% 101.79/14.46 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.79/14.46 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 101.79/14.46 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14:
% 101.79/14.46 | $i] : ! [v15: $i] : ! [v16: $i] : ( ~ (member(v0) = v8) | ~
% 101.79/14.46 | (hAPP(v11, v12, v13, v2) = v14) | ~ (hAPP(v6, bool, v10, v15) =
% 101.79/14.46 | v16) | ~ (hAPP(v5, v6, v14, v4) = v15) | ~ (hAPP(v1, v0, v2, v3)
% 101.79/14.46 | = v9) | ~ (hAPP(v0, v7, v8, v9) = v10) | ~ (image(v1, v0) = v13)
% 101.79/14.46 | | ~ (fun(v6, bool) = v7) | ~ (fun(v5, v6) = v12) | ~ (fun(v1, v0)
% 101.79/14.46 | = v11) | ~ (fun(v1, bool) = v5) | ~ (fun(v0, bool) = v6) | ~
% 101.79/14.46 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v16)
% 101.79/14.46 | | ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] :
% 101.79/14.46 | (member(v1) = v18 & hAPP(v5, bool, v19, v4) = v20 & hAPP(v1, v17,
% 101.79/14.46 | v18, v3) = v19 & fun(v5, bool) = v17 & $i(v20) & $i(v19) &
% 101.79/14.46 | $i(v18) & $i(v17) & ~ hBOOL(v20)))
% 101.79/14.46 |
% 101.79/14.46 | ALPHA: (fact_84_insert__subset) implies:
% 101.79/14.46 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.79/14.46 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 101.79/14.46 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ (hAPP(v4, v5, v6, v10)
% 101.79/14.46 | = v11) | ~ (hAPP(v4, v4, v9, v2) = v10) | ~ (hAPP(v4, bool, v11,
% 101.79/14.46 | v3) = v12) | ~ (hAPP(v0, v7, v8, v1) = v9) | ~ (insert(v0) =
% 101.79/14.46 | v8) | ~ (ord_less_eq(v4) = v6) | ~ (fun(v4, v4) = v7) | ~
% 101.79/14.46 | (fun(v4, bool) = v5) | ~ (fun(v0, bool) = v4) | ~ $i(v3) | ~
% 101.79/14.46 | $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v12) | ? [v13: $i] : ?
% 101.79/14.46 | [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] :
% 101.79/14.46 | ((member(v0) = v13 & hAPP(v4, bool, v14, v3) = v15 & hAPP(v0, v5,
% 101.79/14.46 | v13, v1) = v14 & $i(v15) & $i(v14) & $i(v13) & ~ hBOOL(v15))
% 101.79/14.46 | | (hAPP(v4, v5, v6, v2) = v16 & hAPP(v4, bool, v16, v3) = v17 &
% 101.79/14.46 | $i(v17) & $i(v16) & ~ hBOOL(v17))))
% 101.79/14.46 |
% 101.79/14.46 | ALPHA: (fact_90_subset__image__iff) implies:
% 101.79/14.46 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.79/14.46 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 101.79/14.46 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14:
% 101.79/14.46 | $i] : ! [v15: $i] : ( ~ (hAPP(v7, v8, v9, v3) = v10) | ~ (hAPP(v6,
% 101.79/14.46 | v11, v12, v2) = v13) | ~ (hAPP(v6, bool, v13, v14) = v15) | ~
% 101.79/14.46 | (hAPP(v5, v6, v10, v4) = v14) | ~ (image(v1, v0) = v9) | ~
% 101.79/14.46 | (ord_less_eq(v6) = v12) | ~ (fun(v6, bool) = v11) | ~ (fun(v5, v6)
% 101.79/14.46 | = v8) | ~ (fun(v1, v0) = v7) | ~ (fun(v1, bool) = v5) | ~
% 101.79/14.46 | (fun(v0, bool) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 101.79/14.46 | | ~ $i(v0) | hBOOL(v15) | ? [v16: $i] : ? [v17: $i] : ? [v18:
% 101.79/14.46 | $i] : (ord_less_eq(v5) = v17 & fun(v5, bool) = v16 & ti(v6, v2) =
% 101.79/14.46 | v18 & $i(v18) & $i(v17) & $i(v16) & ! [v19: $i] : ! [v20: $i] :
% 101.79/14.46 | ! [v21: $i] : ( ~ (hAPP(v5, v16, v17, v19) = v20) | ~ (hAPP(v5,
% 101.79/14.46 | bool, v20, v4) = v21) | ~ $i(v19) | ~ hBOOL(v21) | ?
% 101.79/14.46 | [v22: $i] : ( ~ (v22 = v18) & hAPP(v5, v6, v10, v19) = v22 &
% 101.79/14.46 | $i(v22)))))
% 101.79/14.46 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.79/14.46 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 101.79/14.46 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14:
% 101.79/14.46 | $i] : ! [v15: $i] : ( ~ (hAPP(v10, v11, v12, v3) = v13) | ~
% 101.79/14.46 | (hAPP(v9, v5, v13, v4) = v14) | ~ (hAPP(v5, v6, v7, v2) = v8) | ~
% 101.79/14.46 | (hAPP(v5, bool, v8, v14) = v15) | ~ (image(v1, v0) = v12) | ~
% 101.79/14.46 | (ord_less_eq(v5) = v7) | ~ (fun(v9, v5) = v11) | ~ (fun(v5, bool)
% 101.79/14.46 | = v6) | ~ (fun(v1, v0) = v10) | ~ (fun(v1, bool) = v9) | ~
% 101.79/14.46 | (fun(v0, bool) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 101.79/14.46 | | ~ $i(v0) | ~ hBOOL(v15) | ? [v16: $i] : ? [v17: $i] : ? [v18:
% 101.79/14.46 | $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : (hAPP(v9, v16,
% 101.79/14.46 | v17, v19) = v20 & hAPP(v9, v5, v13, v19) = v18 & hAPP(v9, bool,
% 101.79/14.46 | v20, v4) = v21 & ord_less_eq(v9) = v17 & fun(v9, bool) = v16 &
% 101.79/14.46 | ti(v5, v2) = v18 & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17)
% 101.79/14.46 | & $i(v16) & hBOOL(v21)))
% 101.79/14.46 |
% 101.79/14.46 | ALPHA: (fact_93_subsetI) implies:
% 101.79/14.47 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.79/14.47 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v4, v5, v2) =
% 101.79/14.47 | v6) | ~ (hAPP(v3, bool, v6, v1) = v7) | ~ (ord_less_eq(v3) = v5)
% 101.79/14.47 | | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ~ $i(v2) | ~
% 101.79/14.47 | $i(v1) | ~ $i(v0) | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ?
% 101.79/14.47 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : (member(v0) = v8 &
% 101.79/14.47 | hAPP(v3, bool, v10, v2) = v11 & hAPP(v3, bool, v10, v1) = v12 &
% 101.79/14.47 | hAPP(v0, v4, v8, v9) = v10 & $i(v12) & $i(v11) & $i(v10) & $i(v9)
% 101.79/14.47 | & $i(v8) & hBOOL(v11) & ~ hBOOL(v12)))
% 101.79/14.47 |
% 101.79/14.47 | ALPHA: (conj_0) implies:
% 101.79/14.47 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP(v0, bool, v1, u) = v2
% 101.79/14.47 | & finite_finite(pname) = v1 & fun(pname, bool) = v0 & $i(v2) &
% 101.79/14.47 | $i(v1) & $i(v0) & hBOOL(v2))
% 101.79/14.47 |
% 101.79/14.47 | ALPHA: (conj_1) implies:
% 101.79/14.47 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.47 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 101.79/14.47 | ? [v10: $i] : (hAPP(v5, v6, v7, mgt_call) = v8 & hAPP(v4, v0, v8, u) =
% 101.79/14.47 | v9 & hAPP(v0, v1, v2, g) = v3 & hAPP(v0, bool, v3, v9) = v10 &
% 101.79/14.47 | image(pname, x_a) = v7 & ord_less_eq(v0) = v2 & fun(v4, v0) = v6 &
% 101.79/14.47 | fun(v0, bool) = v1 & fun(pname, x_a) = v5 & fun(pname, bool) = v4 &
% 101.79/14.47 | fun(x_a, bool) = v0 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 101.79/14.47 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v10))
% 101.79/14.47 |
% 101.79/14.47 | ALPHA: (conj_2) implies:
% 101.79/14.47 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.47 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 101.79/14.47 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : (hAPP(v7,
% 101.79/14.47 | v8, v9, mgt_call) = v10 & hAPP(v6, v4, v10, u) = v11 & hAPP(v4,
% 101.79/14.47 | nat, v5, v11) = v12 & hAPP(nat, v0, v1, v2) = v3 & hAPP(nat, nat,
% 101.79/14.47 | suc, na) = v2 & hAPP(nat, bool, v3, v12) = v13 & image(pname, x_a)
% 101.79/14.47 | = v9 & ord_less_eq(nat) = v1 & finite_card(x_a) = v5 & fun(v6, v4) =
% 101.79/14.47 | v8 & fun(pname, x_a) = v7 & fun(pname, bool) = v6 & fun(x_a, bool) =
% 101.79/14.47 | v4 & fun(nat, bool) = v0 & $i(v13) & $i(v12) & $i(v11) & $i(v10) &
% 101.79/14.47 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 101.79/14.47 | $i(v2) & $i(v1) & $i(v0) & hBOOL(v13))
% 101.79/14.47 |
% 101.79/14.47 | ALPHA: (conj_3) implies:
% 101.79/14.47 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.47 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 101.79/14.47 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : (hAPP(v6,
% 101.79/14.47 | v7, v8, mgt_call) = v9 & hAPP(v5, v0, v9, u) = v10 & hAPP(v0, nat,
% 101.79/14.47 | v1, v10) = v11 & hAPP(v0, nat, v1, g) = v2 & hAPP(nat, v3, v4,
% 101.79/14.47 | v11) = v12 & hAPP(nat, nat, v12, v13) = v2 & hAPP(nat, nat, suc,
% 101.79/14.47 | na) = v13 & image(pname, x_a) = v8 & minus_minus(nat) = v4 &
% 101.79/14.47 | finite_card(x_a) = v1 & fun(v5, v0) = v7 & fun(pname, x_a) = v6 &
% 101.79/14.47 | fun(pname, bool) = v5 & fun(x_a, bool) = v0 & fun(nat, nat) = v3 &
% 101.79/14.47 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 101.79/14.47 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 101.79/14.47 |
% 101.79/14.47 | ALPHA: (conj_4) implies:
% 101.79/14.47 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.47 | (member(pname) = v2 & hAPP(v0, bool, v3, u) = v4 & hAPP(pname, v1, v2,
% 101.79/14.47 | pn) = v3 & fun(v0, bool) = v1 & fun(pname, bool) = v0 & $i(v4) &
% 101.79/14.47 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v4))
% 101.79/14.47 |
% 101.79/14.47 | ALPHA: (conj_5) implies:
% 101.79/14.47 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.47 | ? [v5: $i] : (member(x_a) = v2 & hAPP(v0, bool, v4, g) = v5 &
% 101.79/14.47 | hAPP(pname, x_a, mgt_call, pn) = v3 & hAPP(x_a, v1, v2, v3) = v4 &
% 101.79/14.47 | fun(v0, bool) = v1 & fun(x_a, bool) = v0 & $i(v5) & $i(v4) & $i(v3)
% 101.79/14.47 | & $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v5))
% 101.79/14.47 |
% 101.79/14.47 | ALPHA: (conj_6) implies:
% 101.79/14.47 | (24) $i(bool)
% 101.79/14.47 | (25) $i(x_a)
% 101.79/14.47 | (26) $i(g)
% 101.79/14.47 | (27) $i(pname)
% 101.79/14.47 | (28) $i(u)
% 101.79/14.47 | (29) $i(mgt_call)
% 101.79/14.47 | (30) $i(pn)
% 101.79/14.48 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.48 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 101.79/14.48 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 101.79/14.48 | $i] : ? [v15: $i] : (hAPP(v10, v11, v12, mgt_call) = v13 & hAPP(v9,
% 101.79/14.48 | v0, v13, u) = v14 & hAPP(v0, v1, v2, v7) = v8 & hAPP(v0, v0, v6,
% 101.79/14.48 | g) = v7 & hAPP(v0, bool, v8, v14) = v15 & hAPP(pname, x_a,
% 101.79/14.48 | mgt_call, pn) = v5 & hAPP(x_a, v3, v4, v5) = v6 & insert(x_a) = v4
% 101.79/14.48 | & image(pname, x_a) = v12 & ord_less_eq(v0) = v2 & fun(v9, v0) = v11
% 101.79/14.48 | & fun(v0, v0) = v3 & fun(v0, bool) = v1 & fun(pname, x_a) = v10 &
% 101.79/14.48 | fun(pname, bool) = v9 & fun(x_a, bool) = v0 & $i(v15) & $i(v14) &
% 101.79/14.48 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 101.79/14.48 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 101.79/14.48 | hBOOL(v15))
% 101.79/14.48 |
% 101.79/14.48 | ALPHA: (function-axioms) implies:
% 101.79/14.48 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 101.79/14.48 | (finite_finite(v2) = v1) | ~ (finite_finite(v2) = v0))
% 101.79/14.48 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 101.79/14.48 | (ord_less_eq(v2) = v1) | ~ (ord_less_eq(v2) = v0))
% 101.79/14.48 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (member(v2) =
% 101.79/14.48 | v1) | ~ (member(v2) = v0))
% 101.79/14.48 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 101.79/14.48 | (ti(v3, v2) = v1) | ~ (ti(v3, v2) = v0))
% 101.79/14.48 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 101.79/14.48 | (fun(v3, v2) = v1) | ~ (fun(v3, v2) = v0))
% 101.79/14.48 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 101.79/14.48 | (image(v3, v2) = v1) | ~ (image(v3, v2) = v0))
% 101.79/14.48 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 101.79/14.48 | ! [v5: $i] : (v1 = v0 | ~ (hAPP(v5, v4, v3, v2) = v1) | ~ (hAPP(v5,
% 101.79/14.48 | v4, v3, v2) = v0))
% 101.79/14.48 |
% 101.79/14.48 | DELTA: instantiating (3) with fresh symbol all_92_0 gives:
% 101.79/14.48 | (39) fun(pname, bool) = all_92_0 & ti(all_92_0, u) = u & $i(all_92_0)
% 101.79/14.48 |
% 101.79/14.48 | ALPHA: (39) implies:
% 101.79/14.48 | (40) fun(pname, bool) = all_92_0
% 101.79/14.48 |
% 101.79/14.48 | DELTA: instantiating (1) with fresh symbol all_94_0 gives:
% 101.79/14.48 | (41) fun(x_a, bool) = all_94_0 & ti(all_94_0, g) = g & $i(all_94_0)
% 101.79/14.48 |
% 101.79/14.48 | ALPHA: (41) implies:
% 101.79/14.48 | (42) ti(all_94_0, g) = g
% 101.79/14.48 | (43) fun(x_a, bool) = all_94_0
% 101.79/14.48 |
% 101.79/14.48 | DELTA: instantiating (4) with fresh symbol all_96_0 gives:
% 101.79/14.48 | (44) fun(pname, x_a) = all_96_0 & ti(all_96_0, mgt_call) = mgt_call &
% 101.79/14.48 | $i(all_96_0)
% 101.79/14.48 |
% 101.79/14.48 | ALPHA: (44) implies:
% 101.79/14.48 | (45) fun(pname, x_a) = all_96_0
% 101.79/14.48 |
% 101.79/14.48 | DELTA: instantiating (2) with fresh symbols all_108_0, all_108_1, all_108_2
% 101.79/14.48 | gives:
% 101.79/14.48 | (46) fun(all_108_2, all_108_1) = all_108_0 & fun(all_108_2, bool) =
% 101.79/14.48 | all_108_1 & fun(x_a, bool) = all_108_2 & ti(all_108_0, p) = p &
% 101.79/14.48 | $i(all_108_0) & $i(all_108_1) & $i(all_108_2)
% 101.79/14.48 |
% 101.79/14.48 | ALPHA: (46) implies:
% 101.79/14.48 | (47) $i(all_108_2)
% 101.79/14.48 | (48) fun(x_a, bool) = all_108_2
% 101.79/14.48 | (49) fun(all_108_2, bool) = all_108_1
% 101.79/14.48 |
% 101.79/14.48 | DELTA: instantiating (18) with fresh symbols all_112_0, all_112_1, all_112_2
% 101.79/14.48 | gives:
% 101.79/14.48 | (50) hAPP(all_112_2, bool, all_112_1, u) = all_112_0 & finite_finite(pname)
% 101.79/14.48 | = all_112_1 & fun(pname, bool) = all_112_2 & $i(all_112_0) &
% 101.79/14.48 | $i(all_112_1) & $i(all_112_2) & hBOOL(all_112_0)
% 101.79/14.48 |
% 101.79/14.48 | ALPHA: (50) implies:
% 101.79/14.48 | (51) hBOOL(all_112_0)
% 101.79/14.48 | (52) $i(all_112_2)
% 101.79/14.48 | (53) fun(pname, bool) = all_112_2
% 101.79/14.48 | (54) finite_finite(pname) = all_112_1
% 101.79/14.48 | (55) hAPP(all_112_2, bool, all_112_1, u) = all_112_0
% 101.79/14.48 |
% 101.79/14.48 | DELTA: instantiating (22) with fresh symbols all_150_0, all_150_1, all_150_2,
% 101.79/14.48 | all_150_3, all_150_4 gives:
% 101.79/14.48 | (56) member(pname) = all_150_2 & hAPP(all_150_4, bool, all_150_1, u) =
% 101.79/14.48 | all_150_0 & hAPP(pname, all_150_3, all_150_2, pn) = all_150_1 &
% 101.79/14.48 | fun(all_150_4, bool) = all_150_3 & fun(pname, bool) = all_150_4 &
% 101.79/14.48 | $i(all_150_0) & $i(all_150_1) & $i(all_150_2) & $i(all_150_3) &
% 101.79/14.48 | $i(all_150_4) & hBOOL(all_150_0)
% 101.79/14.48 |
% 101.79/14.48 | ALPHA: (56) implies:
% 101.79/14.48 | (57) hBOOL(all_150_0)
% 101.79/14.48 | (58) fun(pname, bool) = all_150_4
% 101.79/14.48 | (59) fun(all_150_4, bool) = all_150_3
% 101.79/14.48 | (60) hAPP(pname, all_150_3, all_150_2, pn) = all_150_1
% 101.79/14.48 | (61) hAPP(all_150_4, bool, all_150_1, u) = all_150_0
% 101.79/14.48 | (62) member(pname) = all_150_2
% 101.79/14.48 |
% 101.79/14.48 | DELTA: instantiating (23) with fresh symbols all_155_0, all_155_1, all_155_2,
% 101.79/14.48 | all_155_3, all_155_4, all_155_5 gives:
% 101.79/14.48 | (63) member(x_a) = all_155_3 & hAPP(all_155_5, bool, all_155_1, g) =
% 101.79/14.48 | all_155_0 & hAPP(pname, x_a, mgt_call, pn) = all_155_2 & hAPP(x_a,
% 101.79/14.48 | all_155_4, all_155_3, all_155_2) = all_155_1 & fun(all_155_5, bool)
% 101.79/14.48 | = all_155_4 & fun(x_a, bool) = all_155_5 & $i(all_155_0) &
% 101.79/14.48 | $i(all_155_1) & $i(all_155_2) & $i(all_155_3) & $i(all_155_4) &
% 101.79/14.48 | $i(all_155_5) & ~ hBOOL(all_155_0)
% 101.79/14.48 |
% 101.79/14.48 | ALPHA: (63) implies:
% 101.79/14.48 | (64) ~ hBOOL(all_155_0)
% 101.79/14.48 | (65) fun(x_a, bool) = all_155_5
% 101.79/14.48 | (66) fun(all_155_5, bool) = all_155_4
% 101.79/14.48 | (67) hAPP(x_a, all_155_4, all_155_3, all_155_2) = all_155_1
% 101.79/14.48 | (68) hAPP(pname, x_a, mgt_call, pn) = all_155_2
% 101.79/14.48 | (69) hAPP(all_155_5, bool, all_155_1, g) = all_155_0
% 101.79/14.48 | (70) member(x_a) = all_155_3
% 101.79/14.48 |
% 101.79/14.48 | DELTA: instantiating (5) with fresh symbols all_178_0, all_178_1, all_178_2
% 101.79/14.48 | gives:
% 101.79/14.49 | (71) ord_less_eq(all_178_2) = all_178_0 & fun(all_178_2, bool) = all_178_1
% 101.79/14.49 | & fun(x_a, bool) = all_178_2 & $i(all_178_0) & $i(all_178_1) &
% 101.79/14.49 | $i(all_178_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 101.79/14.49 | : ( ~ (hAPP(all_178_2, all_178_1, all_178_0, v0) = v2) | ~
% 101.79/14.49 | (hAPP(all_178_2, bool, v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 101.79/14.49 | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : (hAPP(all_178_2, all_178_1,
% 101.79/14.49 | p, v1) = v4 & hAPP(all_178_2, bool, v4, v0) = v5 & $i(v5) &
% 101.79/14.49 | $i(v4) & hBOOL(v5)))
% 101.79/14.49 |
% 101.79/14.49 | ALPHA: (71) implies:
% 101.79/14.49 | (72) fun(x_a, bool) = all_178_2
% 101.79/14.49 | (73) fun(all_178_2, bool) = all_178_1
% 101.79/14.49 | (74) ord_less_eq(all_178_2) = all_178_0
% 101.79/14.49 |
% 101.79/14.49 | DELTA: instantiating (19) with fresh symbols all_202_0, all_202_1, all_202_2,
% 101.79/14.49 | all_202_3, all_202_4, all_202_5, all_202_6, all_202_7, all_202_8,
% 101.79/14.49 | all_202_9, all_202_10 gives:
% 101.79/14.49 | (75) hAPP(all_202_5, all_202_4, all_202_3, mgt_call) = all_202_2 &
% 101.79/14.49 | hAPP(all_202_6, all_202_10, all_202_2, u) = all_202_1 &
% 101.79/14.49 | hAPP(all_202_10, all_202_9, all_202_8, g) = all_202_7 &
% 101.79/14.49 | hAPP(all_202_10, bool, all_202_7, all_202_1) = all_202_0 &
% 101.79/14.49 | image(pname, x_a) = all_202_3 & ord_less_eq(all_202_10) = all_202_8 &
% 101.79/14.49 | fun(all_202_6, all_202_10) = all_202_4 & fun(all_202_10, bool) =
% 101.79/14.49 | all_202_9 & fun(pname, x_a) = all_202_5 & fun(pname, bool) = all_202_6
% 101.79/14.49 | & fun(x_a, bool) = all_202_10 & $i(all_202_0) & $i(all_202_1) &
% 101.79/14.49 | $i(all_202_2) & $i(all_202_3) & $i(all_202_4) & $i(all_202_5) &
% 101.79/14.49 | $i(all_202_6) & $i(all_202_7) & $i(all_202_8) & $i(all_202_9) &
% 101.79/14.49 | $i(all_202_10) & hBOOL(all_202_0)
% 101.79/14.49 |
% 101.79/14.49 | ALPHA: (75) implies:
% 101.79/14.49 | (76) hBOOL(all_202_0)
% 101.79/14.49 | (77) fun(x_a, bool) = all_202_10
% 101.79/14.49 | (78) fun(pname, bool) = all_202_6
% 101.79/14.49 | (79) fun(pname, x_a) = all_202_5
% 101.79/14.49 | (80) fun(all_202_10, bool) = all_202_9
% 101.79/14.49 | (81) fun(all_202_6, all_202_10) = all_202_4
% 101.79/14.49 | (82) ord_less_eq(all_202_10) = all_202_8
% 101.79/14.49 | (83) image(pname, x_a) = all_202_3
% 101.79/14.49 | (84) hAPP(all_202_10, bool, all_202_7, all_202_1) = all_202_0
% 101.79/14.49 | (85) hAPP(all_202_10, all_202_9, all_202_8, g) = all_202_7
% 101.79/14.49 | (86) hAPP(all_202_6, all_202_10, all_202_2, u) = all_202_1
% 101.79/14.49 | (87) hAPP(all_202_5, all_202_4, all_202_3, mgt_call) = all_202_2
% 101.79/14.49 |
% 101.79/14.49 | DELTA: instantiating (21) with fresh symbols all_234_0, all_234_1, all_234_2,
% 101.79/14.49 | all_234_3, all_234_4, all_234_5, all_234_6, all_234_7, all_234_8,
% 101.79/14.49 | all_234_9, all_234_10, all_234_11, all_234_12, all_234_13 gives:
% 101.79/14.49 | (88) hAPP(all_234_7, all_234_6, all_234_5, mgt_call) = all_234_4 &
% 101.79/14.49 | hAPP(all_234_8, all_234_13, all_234_4, u) = all_234_3 &
% 101.79/14.49 | hAPP(all_234_13, nat, all_234_12, all_234_3) = all_234_2 &
% 101.79/14.49 | hAPP(all_234_13, nat, all_234_12, g) = all_234_11 & hAPP(nat,
% 101.79/14.49 | all_234_10, all_234_9, all_234_2) = all_234_1 & hAPP(nat, nat,
% 101.79/14.49 | all_234_1, all_234_0) = all_234_11 & hAPP(nat, nat, suc, na) =
% 101.79/14.49 | all_234_0 & image(pname, x_a) = all_234_5 & minus_minus(nat) =
% 101.79/14.49 | all_234_9 & finite_card(x_a) = all_234_12 & fun(all_234_8, all_234_13)
% 101.79/14.49 | = all_234_6 & fun(pname, x_a) = all_234_7 & fun(pname, bool) =
% 101.79/14.49 | all_234_8 & fun(x_a, bool) = all_234_13 & fun(nat, nat) = all_234_10 &
% 101.79/14.49 | $i(all_234_0) & $i(all_234_1) & $i(all_234_2) & $i(all_234_3) &
% 101.79/14.49 | $i(all_234_4) & $i(all_234_5) & $i(all_234_6) & $i(all_234_7) &
% 101.79/14.49 | $i(all_234_8) & $i(all_234_9) & $i(all_234_10) & $i(all_234_11) &
% 101.79/14.49 | $i(all_234_12) & $i(all_234_13)
% 101.79/14.49 |
% 101.79/14.49 | ALPHA: (88) implies:
% 101.79/14.49 | (89) $i(all_234_4)
% 101.79/14.49 | (90) $i(all_234_3)
% 101.79/14.49 | (91) fun(x_a, bool) = all_234_13
% 101.79/14.49 | (92) fun(pname, bool) = all_234_8
% 101.79/14.49 | (93) fun(pname, x_a) = all_234_7
% 101.79/14.49 | (94) fun(all_234_8, all_234_13) = all_234_6
% 101.79/14.49 | (95) image(pname, x_a) = all_234_5
% 101.79/14.49 | (96) hAPP(all_234_8, all_234_13, all_234_4, u) = all_234_3
% 101.79/14.49 | (97) hAPP(all_234_7, all_234_6, all_234_5, mgt_call) = all_234_4
% 101.79/14.49 |
% 101.79/14.49 | DELTA: instantiating (20) with fresh symbols all_239_0, all_239_1, all_239_2,
% 101.79/14.49 | all_239_3, all_239_4, all_239_5, all_239_6, all_239_7, all_239_8,
% 101.79/14.49 | all_239_9, all_239_10, all_239_11, all_239_12, all_239_13 gives:
% 101.79/14.49 | (98) hAPP(all_239_6, all_239_5, all_239_4, mgt_call) = all_239_3 &
% 101.79/14.49 | hAPP(all_239_7, all_239_9, all_239_3, u) = all_239_2 & hAPP(all_239_9,
% 101.79/14.49 | nat, all_239_8, all_239_2) = all_239_1 & hAPP(nat, all_239_13,
% 101.79/14.49 | all_239_12, all_239_11) = all_239_10 & hAPP(nat, nat, suc, na) =
% 101.79/14.49 | all_239_11 & hAPP(nat, bool, all_239_10, all_239_1) = all_239_0 &
% 101.79/14.49 | image(pname, x_a) = all_239_4 & ord_less_eq(nat) = all_239_12 &
% 101.79/14.49 | finite_card(x_a) = all_239_8 & fun(all_239_7, all_239_9) = all_239_5 &
% 101.79/14.49 | fun(pname, x_a) = all_239_6 & fun(pname, bool) = all_239_7 & fun(x_a,
% 101.79/14.49 | bool) = all_239_9 & fun(nat, bool) = all_239_13 & $i(all_239_0) &
% 101.79/14.49 | $i(all_239_1) & $i(all_239_2) & $i(all_239_3) & $i(all_239_4) &
% 101.79/14.49 | $i(all_239_5) & $i(all_239_6) & $i(all_239_7) & $i(all_239_8) &
% 101.79/14.49 | $i(all_239_9) & $i(all_239_10) & $i(all_239_11) & $i(all_239_12) &
% 101.79/14.49 | $i(all_239_13) & hBOOL(all_239_0)
% 101.79/14.49 |
% 101.79/14.49 | ALPHA: (98) implies:
% 101.79/14.49 | (99) fun(x_a, bool) = all_239_9
% 101.79/14.49 | (100) fun(pname, bool) = all_239_7
% 101.79/14.49 | (101) fun(pname, x_a) = all_239_6
% 101.79/14.49 | (102) fun(all_239_7, all_239_9) = all_239_5
% 101.79/14.49 | (103) image(pname, x_a) = all_239_4
% 101.79/14.49 | (104) hAPP(all_239_7, all_239_9, all_239_3, u) = all_239_2
% 101.79/14.49 | (105) hAPP(all_239_6, all_239_5, all_239_4, mgt_call) = all_239_3
% 101.79/14.49 |
% 101.79/14.49 | DELTA: instantiating (31) with fresh symbols all_247_0, all_247_1, all_247_2,
% 101.79/14.49 | all_247_3, all_247_4, all_247_5, all_247_6, all_247_7, all_247_8,
% 101.79/14.49 | all_247_9, all_247_10, all_247_11, all_247_12, all_247_13, all_247_14,
% 101.79/14.49 | all_247_15 gives:
% 101.79/14.49 | (106) hAPP(all_247_5, all_247_4, all_247_3, mgt_call) = all_247_2 &
% 101.79/14.49 | hAPP(all_247_6, all_247_15, all_247_2, u) = all_247_1 &
% 101.79/14.49 | hAPP(all_247_15, all_247_14, all_247_13, all_247_8) = all_247_7 &
% 101.79/14.49 | hAPP(all_247_15, all_247_15, all_247_9, g) = all_247_8 &
% 101.79/14.49 | hAPP(all_247_15, bool, all_247_7, all_247_1) = all_247_0 &
% 101.79/14.49 | hAPP(pname, x_a, mgt_call, pn) = all_247_10 & hAPP(x_a, all_247_12,
% 101.79/14.49 | all_247_11, all_247_10) = all_247_9 & insert(x_a) = all_247_11 &
% 101.79/14.49 | image(pname, x_a) = all_247_3 & ord_less_eq(all_247_15) = all_247_13
% 101.79/14.49 | & fun(all_247_6, all_247_15) = all_247_4 & fun(all_247_15,
% 101.79/14.49 | all_247_15) = all_247_12 & fun(all_247_15, bool) = all_247_14 &
% 101.79/14.49 | fun(pname, x_a) = all_247_5 & fun(pname, bool) = all_247_6 & fun(x_a,
% 101.79/14.49 | bool) = all_247_15 & $i(all_247_0) & $i(all_247_1) & $i(all_247_2)
% 101.79/14.49 | & $i(all_247_3) & $i(all_247_4) & $i(all_247_5) & $i(all_247_6) &
% 101.79/14.49 | $i(all_247_7) & $i(all_247_8) & $i(all_247_9) & $i(all_247_10) &
% 101.79/14.49 | $i(all_247_11) & $i(all_247_12) & $i(all_247_13) & $i(all_247_14) &
% 101.79/14.49 | $i(all_247_15) & ~ hBOOL(all_247_0)
% 101.79/14.49 |
% 101.79/14.49 | ALPHA: (106) implies:
% 101.79/14.49 | (107) ~ hBOOL(all_247_0)
% 101.79/14.49 | (108) $i(all_247_10)
% 101.79/14.49 | (109) $i(all_247_9)
% 101.79/14.49 | (110) $i(all_247_8)
% 101.79/14.49 | (111) fun(x_a, bool) = all_247_15
% 101.79/14.49 | (112) fun(pname, bool) = all_247_6
% 101.79/14.49 | (113) fun(pname, x_a) = all_247_5
% 101.79/14.49 | (114) fun(all_247_15, bool) = all_247_14
% 101.79/14.49 | (115) fun(all_247_15, all_247_15) = all_247_12
% 101.79/14.49 | (116) fun(all_247_6, all_247_15) = all_247_4
% 101.79/14.49 | (117) ord_less_eq(all_247_15) = all_247_13
% 101.79/14.49 | (118) image(pname, x_a) = all_247_3
% 101.79/14.49 | (119) insert(x_a) = all_247_11
% 101.79/14.49 | (120) hAPP(x_a, all_247_12, all_247_11, all_247_10) = all_247_9
% 101.79/14.49 | (121) hAPP(pname, x_a, mgt_call, pn) = all_247_10
% 101.79/14.49 | (122) hAPP(all_247_15, bool, all_247_7, all_247_1) = all_247_0
% 101.79/14.49 | (123) hAPP(all_247_15, all_247_15, all_247_9, g) = all_247_8
% 101.79/14.49 | (124) hAPP(all_247_15, all_247_14, all_247_13, all_247_8) = all_247_7
% 101.79/14.49 | (125) hAPP(all_247_6, all_247_15, all_247_2, u) = all_247_1
% 101.79/14.49 | (126) hAPP(all_247_5, all_247_4, all_247_3, mgt_call) = all_247_2
% 101.79/14.49 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_108_2, all_155_5, bool, x_a,
% 101.79/14.50 | simplifying with (48), (65) gives:
% 101.79/14.50 | (127) all_155_5 = all_108_2
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_155_5, all_178_2, bool, x_a,
% 101.79/14.50 | simplifying with (65), (72) gives:
% 101.79/14.50 | (128) all_178_2 = all_155_5
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_178_2, all_202_10, bool, x_a,
% 101.79/14.50 | simplifying with (72), (77) gives:
% 101.79/14.50 | (129) all_202_10 = all_178_2
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_202_10, all_234_13, bool, x_a,
% 101.79/14.50 | simplifying with (77), (91) gives:
% 101.79/14.50 | (130) all_234_13 = all_202_10
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_234_13, all_239_9, bool, x_a,
% 101.79/14.50 | simplifying with (91), (99) gives:
% 101.79/14.50 | (131) all_239_9 = all_234_13
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_239_9, all_247_15, bool, x_a,
% 101.79/14.50 | simplifying with (99), (111) gives:
% 101.79/14.50 | (132) all_247_15 = all_239_9
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_94_0, all_247_15, bool, x_a,
% 101.79/14.50 | simplifying with (43), (111) gives:
% 101.79/14.50 | (133) all_247_15 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_92_0, all_202_6, bool, pname,
% 101.79/14.50 | simplifying with (40), (78) gives:
% 101.79/14.50 | (134) all_202_6 = all_92_0
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_202_6, all_239_7, bool, pname,
% 101.79/14.50 | simplifying with (78), (100) gives:
% 101.79/14.50 | (135) all_239_7 = all_202_6
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_112_2, all_239_7, bool, pname,
% 101.79/14.50 | simplifying with (53), (100) gives:
% 101.79/14.50 | (136) all_239_7 = all_112_2
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_234_8, all_247_6, bool, pname,
% 101.79/14.50 | simplifying with (92), (112) gives:
% 101.79/14.50 | (137) all_247_6 = all_234_8
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_202_6, all_247_6, bool, pname,
% 101.79/14.50 | simplifying with (78), (112) gives:
% 101.79/14.50 | (138) all_247_6 = all_202_6
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_150_4, all_247_6, bool, pname,
% 101.79/14.50 | simplifying with (58), (112) gives:
% 101.79/14.50 | (139) all_247_6 = all_150_4
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_202_5, all_234_7, x_a, pname,
% 101.79/14.50 | simplifying with (79), (93) gives:
% 101.79/14.50 | (140) all_234_7 = all_202_5
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_239_6, all_247_5, x_a, pname,
% 101.79/14.50 | simplifying with (101), (113) gives:
% 101.79/14.50 | (141) all_247_5 = all_239_6
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_234_7, all_247_5, x_a, pname,
% 101.79/14.50 | simplifying with (93), (113) gives:
% 101.79/14.50 | (142) all_247_5 = all_234_7
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (36) with all_96_0, all_247_5, x_a, pname,
% 101.79/14.50 | simplifying with (45), (113) gives:
% 101.79/14.50 | (143) all_247_5 = all_96_0
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (37) with all_202_3, all_239_4, x_a, pname,
% 101.79/14.50 | simplifying with (83), (103) gives:
% 101.79/14.50 | (144) all_239_4 = all_202_3
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (37) with all_239_4, all_247_3, x_a, pname,
% 101.79/14.50 | simplifying with (103), (118) gives:
% 101.79/14.50 | (145) all_247_3 = all_239_4
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (37) with all_234_5, all_247_3, x_a, pname,
% 101.79/14.50 | simplifying with (95), (118) gives:
% 101.79/14.50 | (146) all_247_3 = all_234_5
% 101.79/14.50 |
% 101.79/14.50 | GROUND_INST: instantiating (38) with all_155_2, all_247_10, pn, mgt_call, x_a,
% 101.79/14.50 | pname, simplifying with (68), (121) gives:
% 101.79/14.50 | (147) all_247_10 = all_155_2
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (145), (146) imply:
% 101.79/14.50 | (148) all_239_4 = all_234_5
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (148) implies:
% 101.79/14.50 | (149) all_239_4 = all_234_5
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (141), (142) imply:
% 101.79/14.50 | (150) all_239_6 = all_234_7
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (141), (143) imply:
% 101.79/14.50 | (151) all_239_6 = all_96_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (137), (138) imply:
% 101.79/14.50 | (152) all_234_8 = all_202_6
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (137), (139) imply:
% 101.79/14.50 | (153) all_234_8 = all_150_4
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (132), (133) imply:
% 101.79/14.50 | (154) all_239_9 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (154) implies:
% 101.79/14.50 | (155) all_239_9 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (144), (149) imply:
% 101.79/14.50 | (156) all_234_5 = all_202_3
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (156) implies:
% 101.79/14.50 | (157) all_234_5 = all_202_3
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (150), (151) imply:
% 101.79/14.50 | (158) all_234_7 = all_96_0
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (158) implies:
% 101.79/14.50 | (159) all_234_7 = all_96_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (135), (136) imply:
% 101.79/14.50 | (160) all_202_6 = all_112_2
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (160) implies:
% 101.79/14.50 | (161) all_202_6 = all_112_2
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (131), (155) imply:
% 101.79/14.50 | (162) all_234_13 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (162) implies:
% 101.79/14.50 | (163) all_234_13 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (140), (159) imply:
% 101.79/14.50 | (164) all_202_5 = all_96_0
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (164) implies:
% 101.79/14.50 | (165) all_202_5 = all_96_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (152), (153) imply:
% 101.79/14.50 | (166) all_202_6 = all_150_4
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (166) implies:
% 101.79/14.50 | (167) all_202_6 = all_150_4
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (130), (163) imply:
% 101.79/14.50 | (168) all_202_10 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (168) implies:
% 101.79/14.50 | (169) all_202_10 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (134), (167) imply:
% 101.79/14.50 | (170) all_150_4 = all_92_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (161), (167) imply:
% 101.79/14.50 | (171) all_150_4 = all_112_2
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (129), (169) imply:
% 101.79/14.50 | (172) all_178_2 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (172) implies:
% 101.79/14.50 | (173) all_178_2 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (128), (173) imply:
% 101.79/14.50 | (174) all_155_5 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (174) implies:
% 101.79/14.50 | (175) all_155_5 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | COMBINE_EQS: (127), (175) imply:
% 101.79/14.50 | (176) all_108_2 = all_94_0
% 101.79/14.50 |
% 101.79/14.50 | SIMP: (176) implies:
% 101.79/14.51 | (177) all_108_2 = all_94_0
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (170), (171) imply:
% 101.79/14.51 | (178) all_112_2 = all_92_0
% 101.79/14.51 |
% 101.79/14.51 | SIMP: (178) implies:
% 101.79/14.51 | (179) all_112_2 = all_92_0
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (153), (170) imply:
% 101.79/14.51 | (180) all_234_8 = all_92_0
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (136), (179) imply:
% 101.79/14.51 | (181) all_239_7 = all_92_0
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (137), (180) imply:
% 101.79/14.51 | (182) all_247_6 = all_92_0
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (146), (157) imply:
% 101.79/14.51 | (183) all_247_3 = all_202_3
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (126), (143), (183) imply:
% 101.79/14.51 | (184) hAPP(all_96_0, all_247_4, all_202_3, mgt_call) = all_247_2
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (125), (133), (182) imply:
% 101.79/14.51 | (185) hAPP(all_92_0, all_94_0, all_247_2, u) = all_247_1
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (124), (133) imply:
% 101.79/14.51 | (186) hAPP(all_94_0, all_247_14, all_247_13, all_247_8) = all_247_7
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (123), (133) imply:
% 101.79/14.51 | (187) hAPP(all_94_0, all_94_0, all_247_9, g) = all_247_8
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (122), (133) imply:
% 101.79/14.51 | (188) hAPP(all_94_0, bool, all_247_7, all_247_1) = all_247_0
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (105), (144), (151) imply:
% 101.79/14.51 | (189) hAPP(all_96_0, all_239_5, all_202_3, mgt_call) = all_239_3
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (104), (155), (181) imply:
% 101.79/14.51 | (190) hAPP(all_92_0, all_94_0, all_239_3, u) = all_239_2
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (97), (157), (159) imply:
% 101.79/14.51 | (191) hAPP(all_96_0, all_234_6, all_202_3, mgt_call) = all_234_4
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (96), (163), (180) imply:
% 101.79/14.51 | (192) hAPP(all_92_0, all_94_0, all_234_4, u) = all_234_3
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (87), (165) imply:
% 101.79/14.51 | (193) hAPP(all_96_0, all_202_4, all_202_3, mgt_call) = all_202_2
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (86), (134), (169) imply:
% 101.79/14.51 | (194) hAPP(all_92_0, all_94_0, all_202_2, u) = all_202_1
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (85), (169) imply:
% 101.79/14.51 | (195) hAPP(all_94_0, all_202_9, all_202_8, g) = all_202_7
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (84), (169) imply:
% 101.79/14.51 | (196) hAPP(all_94_0, bool, all_202_7, all_202_1) = all_202_0
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (69), (175) imply:
% 101.79/14.51 | (197) hAPP(all_94_0, bool, all_155_1, g) = all_155_0
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (61), (170) imply:
% 101.79/14.51 | (198) hAPP(all_92_0, bool, all_150_1, u) = all_150_0
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (55), (179) imply:
% 101.79/14.51 | (199) hAPP(all_92_0, bool, all_112_1, u) = all_112_0
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (120), (147) imply:
% 101.79/14.51 | (200) hAPP(x_a, all_247_12, all_247_11, all_155_2) = all_247_9
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (117), (133) imply:
% 101.79/14.51 | (201) ord_less_eq(all_94_0) = all_247_13
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (82), (169) imply:
% 101.79/14.51 | (202) ord_less_eq(all_94_0) = all_202_8
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (74), (173) imply:
% 101.79/14.51 | (203) ord_less_eq(all_94_0) = all_178_0
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (116), (133), (182) imply:
% 101.79/14.51 | (204) fun(all_92_0, all_94_0) = all_247_4
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (115), (133) imply:
% 101.79/14.51 | (205) fun(all_94_0, all_94_0) = all_247_12
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (114), (133) imply:
% 101.79/14.51 | (206) fun(all_94_0, bool) = all_247_14
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (102), (155), (181) imply:
% 101.79/14.51 | (207) fun(all_92_0, all_94_0) = all_239_5
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (94), (163), (180) imply:
% 101.79/14.51 | (208) fun(all_92_0, all_94_0) = all_234_6
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (81), (134), (169) imply:
% 101.79/14.51 | (209) fun(all_92_0, all_94_0) = all_202_4
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (80), (169) imply:
% 101.79/14.51 | (210) fun(all_94_0, bool) = all_202_9
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (73), (173) imply:
% 101.79/14.51 | (211) fun(all_94_0, bool) = all_178_1
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (66), (175) imply:
% 101.79/14.51 | (212) fun(all_94_0, bool) = all_155_4
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (59), (170) imply:
% 101.79/14.51 | (213) fun(all_92_0, bool) = all_150_3
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (49), (177) imply:
% 101.79/14.51 | (214) fun(all_94_0, bool) = all_108_1
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (108), (147) imply:
% 101.79/14.51 | (215) $i(all_155_2)
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (52), (179) imply:
% 101.79/14.51 | (216) $i(all_92_0)
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (47), (177) imply:
% 101.79/14.51 | (217) $i(all_94_0)
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (36) with all_234_6, all_239_5, all_94_0, all_92_0,
% 101.79/14.51 | simplifying with (207), (208) gives:
% 101.79/14.51 | (218) all_239_5 = all_234_6
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (36) with all_239_5, all_247_4, all_94_0, all_92_0,
% 101.79/14.51 | simplifying with (204), (207) gives:
% 101.79/14.51 | (219) all_247_4 = all_239_5
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (36) with all_202_4, all_247_4, all_94_0, all_92_0,
% 101.79/14.51 | simplifying with (204), (209) gives:
% 101.79/14.51 | (220) all_247_4 = all_202_4
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (36) with all_155_4, all_202_9, bool, all_94_0,
% 101.79/14.51 | simplifying with (210), (212) gives:
% 101.79/14.51 | (221) all_202_9 = all_155_4
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (36) with all_108_1, all_202_9, bool, all_94_0,
% 101.79/14.51 | simplifying with (210), (214) gives:
% 101.79/14.51 | (222) all_202_9 = all_108_1
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (36) with all_202_9, all_247_14, bool, all_94_0,
% 101.79/14.51 | simplifying with (206), (210) gives:
% 101.79/14.51 | (223) all_247_14 = all_202_9
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (36) with all_178_1, all_247_14, bool, all_94_0,
% 101.79/14.51 | simplifying with (206), (211) gives:
% 101.79/14.51 | (224) all_247_14 = all_178_1
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (33) with all_202_8, all_247_13, all_94_0,
% 101.79/14.51 | simplifying with (201), (202) gives:
% 101.79/14.51 | (225) all_247_13 = all_202_8
% 101.79/14.51 |
% 101.79/14.51 | GROUND_INST: instantiating (33) with all_178_0, all_247_13, all_94_0,
% 101.79/14.51 | simplifying with (201), (203) gives:
% 101.79/14.51 | (226) all_247_13 = all_178_0
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (219), (220) imply:
% 101.79/14.51 | (227) all_239_5 = all_202_4
% 101.79/14.51 |
% 101.79/14.51 | SIMP: (227) implies:
% 101.79/14.51 | (228) all_239_5 = all_202_4
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (225), (226) imply:
% 101.79/14.51 | (229) all_202_8 = all_178_0
% 101.79/14.51 |
% 101.79/14.51 | SIMP: (229) implies:
% 101.79/14.51 | (230) all_202_8 = all_178_0
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (223), (224) imply:
% 101.79/14.51 | (231) all_202_9 = all_178_1
% 101.79/14.51 |
% 101.79/14.51 | SIMP: (231) implies:
% 101.79/14.51 | (232) all_202_9 = all_178_1
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (218), (228) imply:
% 101.79/14.51 | (233) all_234_6 = all_202_4
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (221), (232) imply:
% 101.79/14.51 | (234) all_178_1 = all_155_4
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (222), (232) imply:
% 101.79/14.51 | (235) all_178_1 = all_108_1
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (234), (235) imply:
% 101.79/14.51 | (236) all_155_4 = all_108_1
% 101.79/14.51 |
% 101.79/14.51 | COMBINE_EQS: (224), (235) imply:
% 101.79/14.51 | (237) all_247_14 = all_108_1
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (184), (220) imply:
% 101.79/14.51 | (238) hAPP(all_96_0, all_202_4, all_202_3, mgt_call) = all_247_2
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (189), (228) imply:
% 101.79/14.51 | (239) hAPP(all_96_0, all_202_4, all_202_3, mgt_call) = all_239_3
% 101.79/14.51 |
% 101.79/14.51 | REDUCE: (191), (233) imply:
% 101.79/14.52 | (240) hAPP(all_96_0, all_202_4, all_202_3, mgt_call) = all_234_4
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (186), (226), (237) imply:
% 101.79/14.52 | (241) hAPP(all_94_0, all_108_1, all_178_0, all_247_8) = all_247_7
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (195), (222), (230) imply:
% 101.79/14.52 | (242) hAPP(all_94_0, all_108_1, all_178_0, g) = all_202_7
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (67), (236) imply:
% 101.79/14.52 | (243) hAPP(x_a, all_108_1, all_155_3, all_155_2) = all_155_1
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (38) with all_202_2, all_239_3, mgt_call,
% 101.79/14.52 | all_202_3, all_202_4, all_96_0, simplifying with (193), (239)
% 101.79/14.52 | gives:
% 101.79/14.52 | (244) all_239_3 = all_202_2
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (38) with all_239_3, all_247_2, mgt_call,
% 101.79/14.52 | all_202_3, all_202_4, all_96_0, simplifying with (238), (239)
% 101.79/14.52 | gives:
% 101.79/14.52 | (245) all_247_2 = all_239_3
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (38) with all_234_4, all_247_2, mgt_call,
% 101.79/14.52 | all_202_3, all_202_4, all_96_0, simplifying with (238), (240)
% 101.79/14.52 | gives:
% 101.79/14.52 | (246) all_247_2 = all_234_4
% 101.79/14.52 |
% 101.79/14.52 | COMBINE_EQS: (245), (246) imply:
% 101.79/14.52 | (247) all_239_3 = all_234_4
% 101.79/14.52 |
% 101.79/14.52 | SIMP: (247) implies:
% 101.79/14.52 | (248) all_239_3 = all_234_4
% 101.79/14.52 |
% 101.79/14.52 | COMBINE_EQS: (244), (248) imply:
% 101.79/14.52 | (249) all_234_4 = all_202_2
% 101.79/14.52 |
% 101.79/14.52 | SIMP: (249) implies:
% 101.79/14.52 | (250) all_234_4 = all_202_2
% 101.79/14.52 |
% 101.79/14.52 | COMBINE_EQS: (246), (250) imply:
% 101.79/14.52 | (251) all_247_2 = all_202_2
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (185), (251) imply:
% 101.79/14.52 | (252) hAPP(all_92_0, all_94_0, all_202_2, u) = all_247_1
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (190), (244) imply:
% 101.79/14.52 | (253) hAPP(all_92_0, all_94_0, all_202_2, u) = all_239_2
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (192), (250) imply:
% 101.79/14.52 | (254) hAPP(all_92_0, all_94_0, all_202_2, u) = all_234_3
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (89), (250) imply:
% 101.79/14.52 | (255) $i(all_202_2)
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (38) with all_202_1, all_239_2, u, all_202_2,
% 101.79/14.52 | all_94_0, all_92_0, simplifying with (194), (253) gives:
% 101.79/14.52 | (256) all_239_2 = all_202_1
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (38) with all_239_2, all_247_1, u, all_202_2,
% 101.79/14.52 | all_94_0, all_92_0, simplifying with (252), (253) gives:
% 101.79/14.52 | (257) all_247_1 = all_239_2
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (38) with all_234_3, all_247_1, u, all_202_2,
% 101.79/14.52 | all_94_0, all_92_0, simplifying with (252), (254) gives:
% 101.79/14.52 | (258) all_247_1 = all_234_3
% 101.79/14.52 |
% 101.79/14.52 | COMBINE_EQS: (257), (258) imply:
% 101.79/14.52 | (259) all_239_2 = all_234_3
% 101.79/14.52 |
% 101.79/14.52 | SIMP: (259) implies:
% 101.79/14.52 | (260) all_239_2 = all_234_3
% 101.79/14.52 |
% 101.79/14.52 | COMBINE_EQS: (256), (260) imply:
% 101.79/14.52 | (261) all_234_3 = all_202_1
% 101.79/14.52 |
% 101.79/14.52 | COMBINE_EQS: (258), (261) imply:
% 101.79/14.52 | (262) all_247_1 = all_202_1
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (188), (262) imply:
% 101.79/14.52 | (263) hAPP(all_94_0, bool, all_247_7, all_202_1) = all_247_0
% 101.79/14.52 |
% 101.79/14.52 | REDUCE: (90), (261) imply:
% 101.79/14.52 | (264) $i(all_202_1)
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (6) with x_a, g, all_202_1, all_94_0, all_108_1,
% 101.79/14.52 | all_178_0, all_202_7, all_202_0, simplifying with (25), (26),
% 101.79/14.52 | (43), (76), (196), (203), (214), (242), (264) gives:
% 101.79/14.52 | (265) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (finite_finite(x_a) = v0 &
% 101.79/14.52 | $i(v0) & ((hAPP(all_94_0, bool, v0, all_202_1) = v1 & $i(v1) & ~
% 101.79/14.52 | hBOOL(v1)) | (hAPP(all_94_0, bool, v0, g) = v2 & $i(v2) &
% 101.79/14.52 | hBOOL(v2))))
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (14) with x_a, all_155_2, g, all_202_1, all_94_0,
% 101.79/14.52 | all_108_1, all_178_0, all_247_12, all_247_11, all_247_9,
% 101.79/14.52 | all_247_8, all_247_7, all_247_0, simplifying with (25), (26),
% 101.79/14.52 | (43), (107), (119), (187), (200), (203), (205), (214), (215),
% 101.79/14.52 | (241), (263), (264) gives:
% 101.79/14.52 | (266) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.52 | ((member(x_a) = v0 & hAPP(all_94_0, bool, v1, all_202_1) = v2 &
% 101.79/14.52 | hAPP(x_a, all_108_1, v0, all_155_2) = v1 & $i(v2) & $i(v1) &
% 101.79/14.52 | $i(v0) & ~ hBOOL(v2)) | (hAPP(all_94_0, all_108_1, all_178_0, g)
% 101.79/14.52 | = v3 & hAPP(all_94_0, bool, v3, all_202_1) = v4 & $i(v4) & $i(v3)
% 101.79/14.52 | & ~ hBOOL(v4)))
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (17) with x_a, all_202_1, all_247_8, all_94_0,
% 101.79/14.52 | all_108_1, all_178_0, all_247_7, all_247_0, simplifying with
% 101.79/14.52 | (25), (43), (107), (110), (203), (214), (241), (263), (264)
% 101.79/14.52 | gives:
% 101.79/14.52 | (267) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.52 | (member(x_a) = v0 & hAPP(all_94_0, bool, v2, all_247_8) = v3 &
% 101.79/14.52 | hAPP(all_94_0, bool, v2, all_202_1) = v4 & hAPP(x_a, all_108_1, v0,
% 101.79/14.52 | v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v3)
% 101.79/14.52 | & ~ hBOOL(v4))
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (10) with x_a, all_202_1, all_247_8, all_94_0,
% 101.79/14.52 | all_108_1, all_178_0, all_247_7, all_247_0, simplifying with
% 101.79/14.52 | (25), (43), (107), (110), (203), (214), (241), (263), (264)
% 101.79/14.52 | gives:
% 101.79/14.52 | (268) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & ti(all_94_0, all_247_8) =
% 101.79/14.52 | v1 & ti(all_94_0, all_202_1) = v0 & $i(v1) & $i(v0))
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (9) with x_a, all_247_8, all_202_1, all_94_0,
% 101.79/14.52 | all_108_1, all_178_0, all_247_7, all_247_0, simplifying with
% 101.79/14.52 | (25), (43), (107), (110), (203), (214), (241), (263), (264)
% 101.79/14.52 | gives:
% 101.79/14.52 | (269) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & ti(all_94_0, all_247_8) =
% 101.79/14.52 | v0 & ti(all_94_0, all_202_1) = v1 & $i(v1) & $i(v0))
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (11) with x_a, all_247_8, all_202_1, all_94_0,
% 101.79/14.52 | all_108_1, all_178_0, all_247_7, all_247_0, simplifying with
% 101.79/14.52 | (25), (43), (110), (203), (214), (241), (263), (264) gives:
% 101.79/14.52 | (270) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (( ~ (v1 =
% 101.79/14.52 | v0) & ti(all_94_0, all_247_8) = v0 & ti(all_94_0, all_202_1) =
% 101.79/14.52 | v1 & $i(v1) & $i(v0)) | (hAPP(all_94_0, all_108_1, all_178_0,
% 101.79/14.52 | all_202_1) = v2 & hAPP(all_94_0, bool, v2, all_247_8) = v3 &
% 101.79/14.52 | $i(v3) & $i(v2) & hBOOL(v3) & hBOOL(all_247_0)))
% 101.79/14.52 |
% 101.79/14.52 | GROUND_INST: instantiating (15) with x_a, pname, all_247_8, mgt_call, u,
% 101.79/14.52 | all_92_0, all_94_0, all_96_0, all_202_4, all_202_3, all_202_2,
% 101.79/14.52 | all_108_1, all_178_0, all_247_7, all_202_1, all_247_0,
% 101.79/14.52 | simplifying with (25), (27), (28), (29), (40), (43), (45), (83),
% 101.79/14.52 | (107), (110), (193), (194), (203), (209), (214), (241), (263)
% 101.79/14.52 | gives:
% 101.79/14.53 | (271) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ord_less_eq(all_92_0) = v1
% 101.79/14.53 | & fun(all_92_0, bool) = v0 & ti(all_94_0, all_247_8) = v2 & $i(v2)
% 101.79/14.53 | & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 101.79/14.53 | (hAPP(all_92_0, v0, v1, v3) = v4) | ~ (hAPP(all_92_0, bool, v4,
% 101.79/14.53 | u) = v5) | ~ $i(v3) | ~ hBOOL(v5) | ? [v6: $i] : ( ~ (v6 =
% 101.79/14.53 | v2) & hAPP(all_92_0, all_94_0, all_202_2, v3) = v6 &
% 101.79/14.53 | $i(v6))))
% 101.79/14.53 |
% 101.79/14.53 | GROUND_INST: instantiating (7) with x_a, pname, g, mgt_call, u, all_92_0,
% 101.79/14.53 | all_94_0, all_108_1, all_178_0, all_202_7, all_96_0, all_202_4,
% 101.79/14.53 | all_202_3, all_202_2, all_202_1, all_202_0, simplifying with
% 101.79/14.53 | (25), (26), (27), (28), (29), (40), (43), (45), (76), (83),
% 101.79/14.53 | (193), (194), (196), (203), (209), (214), (242) gives:
% 101.79/14.53 | (272) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 101.79/14.53 | ((hAPP(all_94_0, bool, v2, g) = v3 & finite_finite(x_a) = v2 & $i(v3)
% 101.79/14.53 | & $i(v2) & hBOOL(v3)) | (hAPP(all_92_0, bool, v0, u) = v1 &
% 101.79/14.53 | finite_finite(pname) = v0 & $i(v1) & $i(v0) & ~ hBOOL(v1)))
% 101.79/14.53 |
% 101.79/14.53 | GROUND_INST: instantiating (16) with x_a, pname, g, mgt_call, u, all_94_0,
% 101.79/14.53 | all_108_1, all_178_0, all_202_7, all_92_0, all_96_0, all_202_4,
% 101.79/14.53 | all_202_3, all_202_2, all_202_1, all_202_0, simplifying with
% 101.79/14.53 | (25), (26), (27), (28), (29), (40), (43), (45), (76), (83),
% 101.79/14.53 | (193), (194), (196), (203), (209), (214), (242) gives:
% 101.79/14.53 | (273) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.53 | ? [v5: $i] : (hAPP(all_92_0, v0, v1, v3) = v4 & hAPP(all_92_0,
% 101.79/14.53 | all_94_0, all_202_2, v3) = v2 & hAPP(all_92_0, bool, v4, u) = v5
% 101.79/14.53 | & ord_less_eq(all_92_0) = v1 & fun(all_92_0, bool) = v0 &
% 101.79/14.53 | ti(all_94_0, g) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 101.79/14.53 | $i(v0) & hBOOL(v5))
% 101.79/14.53 |
% 101.79/14.53 | GROUND_INST: instantiating (8) with pname, x_a, mgt_call, u, g, all_94_0,
% 101.79/14.53 | all_108_1, all_178_0, all_202_7, all_92_0, all_96_0, all_202_4,
% 101.79/14.53 | all_202_3, all_202_2, all_202_1, all_202_0, simplifying with
% 101.79/14.53 | (25), (26), (27), (28), (29), (40), (43), (45), (76), (83),
% 101.79/14.53 | (193), (194), (196), (203), (209), (214), (242) gives:
% 101.79/14.53 | (274) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 101.79/14.53 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 101.79/14.53 | ? [v10: $i] : ($i(v6) & ((v10 = v5 & hAPP(all_92_0, v2, v3, v6) = v7
% 101.79/14.53 | & hAPP(all_92_0, all_94_0, all_202_2, v6) = v5 & hAPP(all_92_0,
% 101.79/14.53 | bool, v7, u) = v8 & hAPP(all_92_0, bool, v4, v6) = v9 &
% 101.79/14.53 | ord_less_eq(all_92_0) = v3 & finite_finite(pname) = v4 &
% 101.79/14.53 | fun(all_92_0, bool) = v2 & ti(all_94_0, g) = v5 & $i(v9) &
% 101.79/14.53 | $i(v8) & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & hBOOL(v9)
% 101.79/14.53 | & hBOOL(v8)) | (hAPP(all_94_0, bool, v0, g) = v1 &
% 101.79/14.53 | finite_finite(x_a) = v0 & $i(v1) & $i(v0) & ~ hBOOL(v1))))
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (269) with fresh symbols all_308_0, all_308_1 gives:
% 101.79/14.53 | (275) ~ (all_308_0 = all_308_1) & ti(all_94_0, all_247_8) = all_308_1 &
% 101.79/14.53 | ti(all_94_0, all_202_1) = all_308_0 & $i(all_308_0) & $i(all_308_1)
% 101.79/14.53 |
% 101.79/14.53 | ALPHA: (275) implies:
% 101.79/14.53 | (276) ti(all_94_0, all_202_1) = all_308_0
% 101.79/14.53 | (277) ti(all_94_0, all_247_8) = all_308_1
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (268) with fresh symbols all_310_0, all_310_1 gives:
% 101.79/14.53 | (278) ~ (all_310_0 = all_310_1) & ti(all_94_0, all_247_8) = all_310_0 &
% 101.79/14.53 | ti(all_94_0, all_202_1) = all_310_1 & $i(all_310_0) & $i(all_310_1)
% 101.79/14.53 |
% 101.79/14.53 | ALPHA: (278) implies:
% 101.79/14.53 | (279) ~ (all_310_0 = all_310_1)
% 101.79/14.53 | (280) ti(all_94_0, all_202_1) = all_310_1
% 101.79/14.53 | (281) ti(all_94_0, all_247_8) = all_310_0
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (265) with fresh symbols all_318_0, all_318_1, all_318_2
% 101.79/14.53 | gives:
% 101.79/14.53 | (282) finite_finite(x_a) = all_318_2 & $i(all_318_2) & ((hAPP(all_94_0,
% 101.79/14.53 | bool, all_318_2, all_202_1) = all_318_1 & $i(all_318_1) & ~
% 101.79/14.53 | hBOOL(all_318_1)) | (hAPP(all_94_0, bool, all_318_2, g) =
% 101.79/14.53 | all_318_0 & $i(all_318_0) & hBOOL(all_318_0)))
% 101.79/14.53 |
% 101.79/14.53 | ALPHA: (282) implies:
% 101.79/14.53 | (283) finite_finite(x_a) = all_318_2
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (272) with fresh symbols all_321_0, all_321_1, all_321_2,
% 101.79/14.53 | all_321_3 gives:
% 101.79/14.53 | (284) (hAPP(all_94_0, bool, all_321_1, g) = all_321_0 & finite_finite(x_a)
% 101.79/14.53 | = all_321_1 & $i(all_321_0) & $i(all_321_1) & hBOOL(all_321_0)) |
% 101.79/14.53 | (hAPP(all_92_0, bool, all_321_3, u) = all_321_2 &
% 101.79/14.53 | finite_finite(pname) = all_321_3 & $i(all_321_2) & $i(all_321_3) &
% 101.79/14.53 | ~ hBOOL(all_321_2))
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (270) with fresh symbols all_322_0, all_322_1, all_322_2,
% 101.79/14.53 | all_322_3 gives:
% 101.79/14.53 | (285) ( ~ (all_322_2 = all_322_3) & ti(all_94_0, all_247_8) = all_322_3 &
% 101.79/14.53 | ti(all_94_0, all_202_1) = all_322_2 & $i(all_322_2) &
% 101.79/14.53 | $i(all_322_3)) | (hAPP(all_94_0, all_108_1, all_178_0, all_202_1) =
% 101.79/14.53 | all_322_1 & hAPP(all_94_0, bool, all_322_1, all_247_8) = all_322_0
% 101.79/14.53 | & $i(all_322_0) & $i(all_322_1) & hBOOL(all_322_0) &
% 101.79/14.53 | hBOOL(all_247_0))
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (267) with fresh symbols all_323_0, all_323_1, all_323_2,
% 101.79/14.53 | all_323_3, all_323_4 gives:
% 101.79/14.53 | (286) member(x_a) = all_323_4 & hAPP(all_94_0, bool, all_323_2, all_247_8)
% 101.79/14.53 | = all_323_1 & hAPP(all_94_0, bool, all_323_2, all_202_1) = all_323_0
% 101.79/14.53 | & hAPP(x_a, all_108_1, all_323_4, all_323_3) = all_323_2 &
% 101.79/14.53 | $i(all_323_0) & $i(all_323_1) & $i(all_323_2) & $i(all_323_3) &
% 101.79/14.53 | $i(all_323_4) & hBOOL(all_323_1) & ~ hBOOL(all_323_0)
% 101.79/14.53 |
% 101.79/14.53 | ALPHA: (286) implies:
% 101.79/14.53 | (287) ~ hBOOL(all_323_0)
% 101.79/14.53 | (288) $i(all_323_3)
% 101.79/14.53 | (289) hAPP(x_a, all_108_1, all_323_4, all_323_3) = all_323_2
% 101.79/14.53 | (290) hAPP(all_94_0, bool, all_323_2, all_202_1) = all_323_0
% 101.79/14.53 | (291) member(x_a) = all_323_4
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (266) with fresh symbols all_327_0, all_327_1, all_327_2,
% 101.79/14.53 | all_327_3, all_327_4 gives:
% 101.79/14.53 | (292) (member(x_a) = all_327_4 & hAPP(all_94_0, bool, all_327_3, all_202_1)
% 101.79/14.53 | = all_327_2 & hAPP(x_a, all_108_1, all_327_4, all_155_2) =
% 101.79/14.53 | all_327_3 & $i(all_327_2) & $i(all_327_3) & $i(all_327_4) & ~
% 101.79/14.53 | hBOOL(all_327_2)) | (hAPP(all_94_0, all_108_1, all_178_0, g) =
% 101.79/14.53 | all_327_1 & hAPP(all_94_0, bool, all_327_1, all_202_1) = all_327_0
% 101.79/14.53 | & $i(all_327_0) & $i(all_327_1) & ~ hBOOL(all_327_0))
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (273) with fresh symbols all_328_0, all_328_1, all_328_2,
% 101.79/14.53 | all_328_3, all_328_4, all_328_5 gives:
% 101.79/14.53 | (293) hAPP(all_92_0, all_328_5, all_328_4, all_328_2) = all_328_1 &
% 101.79/14.53 | hAPP(all_92_0, all_94_0, all_202_2, all_328_2) = all_328_3 &
% 101.79/14.53 | hAPP(all_92_0, bool, all_328_1, u) = all_328_0 &
% 101.79/14.53 | ord_less_eq(all_92_0) = all_328_4 & fun(all_92_0, bool) = all_328_5 &
% 101.79/14.53 | ti(all_94_0, g) = all_328_3 & $i(all_328_0) & $i(all_328_1) &
% 101.79/14.53 | $i(all_328_2) & $i(all_328_3) & $i(all_328_4) & $i(all_328_5) &
% 101.79/14.53 | hBOOL(all_328_0)
% 101.79/14.53 |
% 101.79/14.53 | ALPHA: (293) implies:
% 101.79/14.53 | (294) $i(all_328_3)
% 101.79/14.53 | (295) $i(all_328_2)
% 101.79/14.53 | (296) ti(all_94_0, g) = all_328_3
% 101.79/14.53 | (297) fun(all_92_0, bool) = all_328_5
% 101.79/14.53 | (298) hAPP(all_92_0, all_94_0, all_202_2, all_328_2) = all_328_3
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (271) with fresh symbols all_330_0, all_330_1, all_330_2
% 101.79/14.53 | gives:
% 101.79/14.53 | (299) ord_less_eq(all_92_0) = all_330_1 & fun(all_92_0, bool) = all_330_2 &
% 101.79/14.53 | ti(all_94_0, all_247_8) = all_330_0 & $i(all_330_0) & $i(all_330_1) &
% 101.79/14.53 | $i(all_330_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 101.79/14.53 | (hAPP(all_92_0, all_330_2, all_330_1, v0) = v1) | ~
% 101.79/14.53 | (hAPP(all_92_0, bool, v1, u) = v2) | ~ $i(v0) | ~ hBOOL(v2) | ?
% 101.79/14.53 | [v3: any] : ( ~ (v3 = all_330_0) & hAPP(all_92_0, all_94_0,
% 101.79/14.53 | all_202_2, v0) = v3 & $i(v3)))
% 101.79/14.53 |
% 101.79/14.53 | ALPHA: (299) implies:
% 101.79/14.53 | (300) ti(all_94_0, all_247_8) = all_330_0
% 101.79/14.53 | (301) fun(all_92_0, bool) = all_330_2
% 101.79/14.53 |
% 101.79/14.53 | DELTA: instantiating (274) with fresh symbols all_333_0, all_333_1, all_333_2,
% 101.79/14.53 | all_333_3, all_333_4, all_333_5, all_333_6, all_333_7, all_333_8,
% 101.79/14.53 | all_333_9, all_333_10 gives:
% 101.79/14.54 | (302) $i(all_333_4) & ((all_333_0 = all_333_5 & hAPP(all_92_0, all_333_8,
% 101.79/14.54 | all_333_7, all_333_4) = all_333_3 & hAPP(all_92_0, all_94_0,
% 101.79/14.54 | all_202_2, all_333_4) = all_333_5 & hAPP(all_92_0, bool,
% 101.79/14.54 | all_333_3, u) = all_333_2 & hAPP(all_92_0, bool, all_333_6,
% 101.79/14.54 | all_333_4) = all_333_1 & ord_less_eq(all_92_0) = all_333_7 &
% 101.79/14.54 | finite_finite(pname) = all_333_6 & fun(all_92_0, bool) =
% 101.79/14.54 | all_333_8 & ti(all_94_0, g) = all_333_5 & $i(all_333_1) &
% 101.79/14.54 | $i(all_333_2) & $i(all_333_3) & $i(all_333_5) & $i(all_333_6) &
% 101.79/14.54 | $i(all_333_7) & $i(all_333_8) & hBOOL(all_333_1) &
% 101.79/14.54 | hBOOL(all_333_2)) | (hAPP(all_94_0, bool, all_333_10, g) =
% 101.79/14.54 | all_333_9 & finite_finite(x_a) = all_333_10 & $i(all_333_9) &
% 101.79/14.54 | $i(all_333_10) & ~ hBOOL(all_333_9)))
% 101.79/14.54 |
% 101.79/14.54 | ALPHA: (302) implies:
% 101.79/14.54 | (303) $i(all_333_4)
% 101.79/14.54 | (304) (all_333_0 = all_333_5 & hAPP(all_92_0, all_333_8, all_333_7,
% 101.79/14.54 | all_333_4) = all_333_3 & hAPP(all_92_0, all_94_0, all_202_2,
% 101.79/14.54 | all_333_4) = all_333_5 & hAPP(all_92_0, bool, all_333_3, u) =
% 101.79/14.54 | all_333_2 & hAPP(all_92_0, bool, all_333_6, all_333_4) = all_333_1
% 101.79/14.54 | & ord_less_eq(all_92_0) = all_333_7 & finite_finite(pname) =
% 101.79/14.54 | all_333_6 & fun(all_92_0, bool) = all_333_8 & ti(all_94_0, g) =
% 101.79/14.54 | all_333_5 & $i(all_333_1) & $i(all_333_2) & $i(all_333_3) &
% 101.79/14.54 | $i(all_333_5) & $i(all_333_6) & $i(all_333_7) & $i(all_333_8) &
% 101.79/14.54 | hBOOL(all_333_1) & hBOOL(all_333_2)) | (hAPP(all_94_0, bool,
% 101.79/14.54 | all_333_10, g) = all_333_9 & finite_finite(x_a) = all_333_10 &
% 101.79/14.54 | $i(all_333_9) & $i(all_333_10) & ~ hBOOL(all_333_9))
% 101.79/14.54 |
% 101.79/14.54 | BETA: splitting (292) gives:
% 101.79/14.54 |
% 101.79/14.54 | Case 1:
% 101.79/14.54 | |
% 101.79/14.54 | | (305) member(x_a) = all_327_4 & hAPP(all_94_0, bool, all_327_3,
% 101.79/14.54 | | all_202_1) = all_327_2 & hAPP(x_a, all_108_1, all_327_4,
% 101.79/14.54 | | all_155_2) = all_327_3 & $i(all_327_2) & $i(all_327_3) &
% 101.79/14.54 | | $i(all_327_4) & ~ hBOOL(all_327_2)
% 101.79/14.54 | |
% 101.79/14.54 | | ALPHA: (305) implies:
% 101.79/14.54 | | (306) ~ hBOOL(all_327_2)
% 101.79/14.54 | | (307) hAPP(x_a, all_108_1, all_327_4, all_155_2) = all_327_3
% 101.79/14.54 | | (308) hAPP(all_94_0, bool, all_327_3, all_202_1) = all_327_2
% 101.79/14.54 | | (309) member(x_a) = all_327_4
% 101.79/14.54 | |
% 101.79/14.54 | | BETA: splitting (284) gives:
% 101.79/14.54 | |
% 101.79/14.54 | | Case 1:
% 101.79/14.54 | | |
% 101.79/14.54 | | | (310) hAPP(all_94_0, bool, all_321_1, g) = all_321_0 &
% 101.79/14.54 | | | finite_finite(x_a) = all_321_1 & $i(all_321_0) & $i(all_321_1) &
% 101.79/14.54 | | | hBOOL(all_321_0)
% 101.79/14.54 | | |
% 101.79/14.54 | | | ALPHA: (310) implies:
% 101.79/14.54 | | | (311) hBOOL(all_321_0)
% 101.79/14.54 | | | (312) finite_finite(x_a) = all_321_1
% 101.79/14.54 | | | (313) hAPP(all_94_0, bool, all_321_1, g) = all_321_0
% 101.79/14.54 | | |
% 101.79/14.54 | | | BETA: splitting (304) gives:
% 101.79/14.54 | | |
% 101.79/14.54 | | | Case 1:
% 101.79/14.54 | | | |
% 101.79/14.54 | | | | (314) all_333_0 = all_333_5 & hAPP(all_92_0, all_333_8, all_333_7,
% 101.79/14.54 | | | | all_333_4) = all_333_3 & hAPP(all_92_0, all_94_0, all_202_2,
% 101.79/14.54 | | | | all_333_4) = all_333_5 & hAPP(all_92_0, bool, all_333_3, u) =
% 101.79/14.54 | | | | all_333_2 & hAPP(all_92_0, bool, all_333_6, all_333_4) =
% 101.79/14.54 | | | | all_333_1 & ord_less_eq(all_92_0) = all_333_7 &
% 101.79/14.54 | | | | finite_finite(pname) = all_333_6 & fun(all_92_0, bool) =
% 101.79/14.54 | | | | all_333_8 & ti(all_94_0, g) = all_333_5 & $i(all_333_1) &
% 101.79/14.54 | | | | $i(all_333_2) & $i(all_333_3) & $i(all_333_5) & $i(all_333_6) &
% 101.79/14.54 | | | | $i(all_333_7) & $i(all_333_8) & hBOOL(all_333_1) &
% 101.79/14.54 | | | | hBOOL(all_333_2)
% 101.79/14.54 | | | |
% 101.79/14.54 | | | | ALPHA: (314) implies:
% 101.79/14.54 | | | | (315) ti(all_94_0, g) = all_333_5
% 101.79/14.54 | | | | (316) fun(all_92_0, bool) = all_333_8
% 101.79/14.54 | | | | (317) hAPP(all_92_0, all_94_0, all_202_2, all_333_4) = all_333_5
% 101.79/14.54 | | | |
% 101.79/14.54 | | | | BETA: splitting (285) gives:
% 101.79/14.54 | | | |
% 101.79/14.54 | | | | Case 1:
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | (318) ~ (all_322_2 = all_322_3) & ti(all_94_0, all_247_8) =
% 101.79/14.54 | | | | | all_322_3 & ti(all_94_0, all_202_1) = all_322_2 &
% 101.79/14.54 | | | | | $i(all_322_2) & $i(all_322_3)
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | ALPHA: (318) implies:
% 101.79/14.54 | | | | | (319) ti(all_94_0, all_202_1) = all_322_2
% 101.79/14.54 | | | | | (320) ti(all_94_0, all_247_8) = all_322_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (35) with g, all_333_5, g, all_94_0,
% 101.79/14.54 | | | | | simplifying with (42), (315) gives:
% 101.79/14.54 | | | | | (321) all_333_5 = g
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (35) with all_328_3, all_333_5, g,
% 101.79/14.54 | | | | | all_94_0, simplifying with (296), (315) gives:
% 101.79/14.54 | | | | | (322) all_333_5 = all_328_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (35) with all_310_1, all_322_2, all_202_1,
% 101.79/14.54 | | | | | all_94_0, simplifying with (280), (319) gives:
% 101.79/14.54 | | | | | (323) all_322_2 = all_310_1
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (35) with all_308_0, all_322_2, all_202_1,
% 101.79/14.54 | | | | | all_94_0, simplifying with (276), (319) gives:
% 101.79/14.54 | | | | | (324) all_322_2 = all_308_0
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (35) with all_310_0, all_322_3, all_247_8,
% 101.79/14.54 | | | | | all_94_0, simplifying with (281), (320) gives:
% 101.79/14.54 | | | | | (325) all_322_3 = all_310_0
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (35) with all_322_3, all_330_0, all_247_8,
% 101.79/14.54 | | | | | all_94_0, simplifying with (300), (320) gives:
% 101.79/14.54 | | | | | (326) all_330_0 = all_322_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (35) with all_308_1, all_330_0, all_247_8,
% 101.79/14.54 | | | | | all_94_0, simplifying with (277), (300) gives:
% 101.79/14.54 | | | | | (327) all_330_0 = all_308_1
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (36) with all_328_5, all_330_2, bool,
% 101.79/14.54 | | | | | all_92_0, simplifying with (297), (301) gives:
% 101.79/14.54 | | | | | (328) all_330_2 = all_328_5
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (36) with all_150_3, all_333_8, bool,
% 101.79/14.54 | | | | | all_92_0, simplifying with (213), (316) gives:
% 101.79/14.54 | | | | | (329) all_333_8 = all_150_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (36) with all_330_2, all_333_8, bool,
% 101.79/14.54 | | | | | all_92_0, simplifying with (301), (316) gives:
% 101.79/14.54 | | | | | (330) all_333_8 = all_330_2
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (34) with all_155_3, all_327_4, x_a,
% 101.79/14.54 | | | | | simplifying with (70), (309) gives:
% 101.79/14.54 | | | | | (331) all_327_4 = all_155_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (34) with all_323_4, all_327_4, x_a,
% 101.79/14.54 | | | | | simplifying with (291), (309) gives:
% 101.79/14.54 | | | | | (332) all_327_4 = all_323_4
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | COMBINE_EQS: (321), (322) imply:
% 101.79/14.54 | | | | | (333) all_328_3 = g
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | SIMP: (333) implies:
% 101.79/14.54 | | | | | (334) all_328_3 = g
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | COMBINE_EQS: (329), (330) imply:
% 101.79/14.54 | | | | | (335) all_330_2 = all_150_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | SIMP: (335) implies:
% 101.79/14.54 | | | | | (336) all_330_2 = all_150_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | COMBINE_EQS: (326), (327) imply:
% 101.79/14.54 | | | | | (337) all_322_3 = all_308_1
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | SIMP: (337) implies:
% 101.79/14.54 | | | | | (338) all_322_3 = all_308_1
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | COMBINE_EQS: (328), (336) imply:
% 101.79/14.54 | | | | | (339) all_328_5 = all_150_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | SIMP: (339) implies:
% 101.79/14.54 | | | | | (340) all_328_5 = all_150_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | COMBINE_EQS: (331), (332) imply:
% 101.79/14.54 | | | | | (341) all_323_4 = all_155_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | COMBINE_EQS: (323), (324) imply:
% 101.79/14.54 | | | | | (342) all_310_1 = all_308_0
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | COMBINE_EQS: (325), (338) imply:
% 101.79/14.54 | | | | | (343) all_310_0 = all_308_1
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | SIMP: (343) implies:
% 101.79/14.54 | | | | | (344) all_310_0 = all_308_1
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | REDUCE: (279), (342), (344) imply:
% 101.79/14.54 | | | | | (345) ~ (all_308_0 = all_308_1)
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | SIMP: (345) implies:
% 101.79/14.54 | | | | | (346) ~ (all_308_0 = all_308_1)
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | REDUCE: (317), (321) imply:
% 101.79/14.54 | | | | | (347) hAPP(all_92_0, all_94_0, all_202_2, all_333_4) = g
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | REDUCE: (298), (334) imply:
% 101.79/14.54 | | | | | (348) hAPP(all_92_0, all_94_0, all_202_2, all_328_2) = g
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | REDUCE: (307), (331) imply:
% 101.79/14.54 | | | | | (349) hAPP(x_a, all_108_1, all_155_3, all_155_2) = all_327_3
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | REDUCE: (289), (341) imply:
% 101.79/14.54 | | | | | (350) hAPP(x_a, all_108_1, all_155_3, all_323_3) = all_323_2
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (38) with all_155_1, all_327_3, all_155_2,
% 101.79/14.54 | | | | | all_155_3, all_108_1, x_a, simplifying with (243), (349)
% 101.79/14.54 | | | | | gives:
% 101.79/14.54 | | | | | (351) all_327_3 = all_155_1
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | REDUCE: (308), (351) imply:
% 101.79/14.54 | | | | | (352) hAPP(all_94_0, bool, all_155_1, all_202_1) = all_327_2
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (tsy_c_hAPP_res) with all_94_0, all_92_0,
% 101.79/14.54 | | | | | all_202_2, u, all_202_1, all_308_0, simplifying with
% 101.79/14.54 | | | | | (28), (194), (216), (217), (255), (276) gives:
% 101.79/14.54 | | | | | (353) all_308_0 = all_202_1
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (fact_74_ext) with x_a, bool, all_247_8,
% 101.79/14.54 | | | | | all_202_1, all_94_0, all_308_1, all_308_0, simplifying
% 101.79/14.54 | | | | | with (24), (25), (43), (110), (264), (276), (277) gives:
% 101.79/14.54 | | | | | (354) all_308_0 = all_308_1 | ? [v0: $i] : ? [v1: $i] : ? [v2:
% 101.79/14.54 | | | | | $i] : ( ~ (v2 = v1) & hAPP(x_a, bool, all_247_8, v0) = v1 &
% 101.79/14.54 | | | | | hAPP(x_a, bool, all_202_1, v0) = v2 & $i(v2) & $i(v1) &
% 101.79/14.54 | | | | | $i(v0))
% 101.79/14.54 | | | | |
% 101.79/14.54 | | | | | GROUND_INST: instantiating (tsy_c_hAPP_res) with all_94_0, all_94_0,
% 101.79/14.54 | | | | | all_247_9, g, all_247_8, all_308_1, simplifying with
% 101.79/14.54 | | | | | (26), (109), (187), (217), (277) gives:
% 101.79/14.54 | | | | | (355) all_308_1 = all_247_8
% 101.79/14.54 | | | | |
% 101.79/14.55 | | | | | GROUND_INST: instantiating (13) with x_a, pname, mgt_call, pn,
% 101.79/14.55 | | | | | all_328_2, all_92_0, all_94_0, all_108_1, all_155_3,
% 101.79/14.55 | | | | | all_155_2, all_155_1, all_96_0, all_202_4, all_202_3,
% 101.79/14.55 | | | | | all_202_2, g, all_155_0, simplifying with (25), (27),
% 101.79/14.55 | | | | | (29), (30), (40), (43), (45), (64), (68), (70), (83),
% 101.79/14.55 | | | | | (193), (197), (209), (214), (243), (295), (348) gives:
% 101.79/14.55 | | | | | (356) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 101.79/14.55 | | | | | (member(pname) = v1 & hAPP(all_92_0, bool, v2, all_328_2) =
% 101.79/14.55 | | | | | v3 & hAPP(pname, v0, v1, pn) = v2 & fun(all_92_0, bool) =
% 101.79/14.55 | | | | | v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v3))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | GROUND_INST: instantiating (12) with x_a, pname, all_155_2, mgt_call,
% 101.79/14.55 | | | | | all_328_2, all_92_0, all_94_0, all_108_1, all_155_3,
% 101.79/14.55 | | | | | all_155_1, all_96_0, all_202_4, all_202_3, all_202_2, g,
% 101.79/14.55 | | | | | all_155_0, simplifying with (25), (27), (29), (40), (43),
% 101.79/14.55 | | | | | (45), (64), (70), (83), (193), (197), (209), (214),
% 101.79/14.55 | | | | | (215), (243), (295), (348) gives:
% 101.79/14.55 | | | | | (357) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (member(pname) = v1
% 101.79/14.55 | | | | | & fun(all_92_0, bool) = v0 & ti(x_a, all_155_2) = v2 &
% 101.79/14.55 | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : !
% 101.79/14.55 | | | | | [v5: $i] : ( ~ (hAPP(all_92_0, bool, v4, all_328_2) = v5) |
% 101.79/14.55 | | | | | ~ (hAPP(pname, v0, v1, v3) = v4) | ~ $i(v3) | ~
% 101.79/14.55 | | | | | hBOOL(v5) | ? [v6: $i] : ( ~ (v6 = v2) & hAPP(pname,
% 101.79/14.55 | | | | | x_a, mgt_call, v3) = v6 & $i(v6))))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | GROUND_INST: instantiating (13) with x_a, pname, mgt_call, pn,
% 101.79/14.55 | | | | | all_333_4, all_92_0, all_94_0, all_108_1, all_155_3,
% 101.79/14.55 | | | | | all_155_2, all_155_1, all_96_0, all_202_4, all_202_3,
% 101.79/14.55 | | | | | all_202_2, g, all_155_0, simplifying with (25), (27),
% 101.79/14.55 | | | | | (29), (30), (40), (43), (45), (64), (68), (70), (83),
% 101.79/14.55 | | | | | (193), (197), (209), (214), (243), (303), (347) gives:
% 101.79/14.55 | | | | | (358) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 101.79/14.55 | | | | | (member(pname) = v1 & hAPP(all_92_0, bool, v2, all_333_4) =
% 101.79/14.55 | | | | | v3 & hAPP(pname, v0, v1, pn) = v2 & fun(all_92_0, bool) =
% 101.79/14.55 | | | | | v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v3))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | GROUND_INST: instantiating (12) with x_a, pname, all_155_2, mgt_call,
% 101.79/14.55 | | | | | all_333_4, all_92_0, all_94_0, all_108_1, all_155_3,
% 101.79/14.55 | | | | | all_155_1, all_96_0, all_202_4, all_202_3, all_202_2, g,
% 101.79/14.55 | | | | | all_155_0, simplifying with (25), (27), (29), (40), (43),
% 101.79/14.55 | | | | | (45), (64), (70), (83), (193), (197), (209), (214),
% 101.79/14.55 | | | | | (215), (243), (303), (347) gives:
% 101.79/14.55 | | | | | (359) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (member(pname) = v1
% 101.79/14.55 | | | | | & fun(all_92_0, bool) = v0 & ti(x_a, all_155_2) = v2 &
% 101.79/14.55 | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : !
% 101.79/14.55 | | | | | [v5: $i] : ( ~ (hAPP(all_92_0, bool, v4, all_333_4) = v5) |
% 101.79/14.55 | | | | | ~ (hAPP(pname, v0, v1, v3) = v4) | ~ $i(v3) | ~
% 101.79/14.55 | | | | | hBOOL(v5) | ? [v6: $i] : ( ~ (v6 = v2) & hAPP(pname,
% 101.79/14.55 | | | | | x_a, mgt_call, v3) = v6 & $i(v6))))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | GROUND_INST: instantiating (13) with x_a, pname, mgt_call, pn, u,
% 101.79/14.55 | | | | | all_92_0, all_94_0, all_108_1, all_155_3, all_155_2,
% 101.79/14.55 | | | | | all_155_1, all_96_0, all_202_4, all_202_3, all_202_2,
% 101.79/14.55 | | | | | all_202_1, all_327_2, simplifying with (25), (27), (28),
% 101.79/14.55 | | | | | (29), (30), (40), (43), (45), (68), (70), (83), (193),
% 101.79/14.55 | | | | | (194), (209), (214), (243), (306), (352) gives:
% 101.79/14.55 | | | | | (360) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 101.79/14.55 | | | | | (member(pname) = v1 & hAPP(all_92_0, bool, v2, u) = v3 &
% 101.79/14.55 | | | | | hAPP(pname, v0, v1, pn) = v2 & fun(all_92_0, bool) = v0 &
% 101.79/14.55 | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v3))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | GROUND_INST: instantiating (12) with x_a, pname, all_155_2, mgt_call,
% 101.79/14.55 | | | | | u, all_92_0, all_94_0, all_108_1, all_155_3, all_155_1,
% 101.79/14.55 | | | | | all_96_0, all_202_4, all_202_3, all_202_2, all_202_1,
% 101.79/14.55 | | | | | all_327_2, simplifying with (25), (27), (28), (29), (40),
% 101.79/14.55 | | | | | (43), (45), (70), (83), (193), (194), (209), (214),
% 101.79/14.55 | | | | | (215), (243), (306), (352) gives:
% 101.79/14.55 | | | | | (361) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (member(pname) = v1
% 101.79/14.55 | | | | | & fun(all_92_0, bool) = v0 & ti(x_a, all_155_2) = v2 &
% 101.79/14.55 | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : !
% 101.79/14.55 | | | | | [v5: $i] : ( ~ (hAPP(all_92_0, bool, v4, u) = v5) | ~
% 101.79/14.55 | | | | | (hAPP(pname, v0, v1, v3) = v4) | ~ $i(v3) | ~ hBOOL(v5)
% 101.79/14.55 | | | | | | ? [v6: $i] : ( ~ (v6 = v2) & hAPP(pname, x_a,
% 101.79/14.55 | | | | | mgt_call, v3) = v6 & $i(v6))))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | GROUND_INST: instantiating (12) with x_a, pname, all_323_3, mgt_call,
% 101.79/14.55 | | | | | u, all_92_0, all_94_0, all_108_1, all_155_3, all_323_2,
% 101.79/14.55 | | | | | all_96_0, all_202_4, all_202_3, all_202_2, all_202_1,
% 101.79/14.55 | | | | | all_323_0, simplifying with (25), (27), (28), (29), (40),
% 101.79/14.55 | | | | | (43), (45), (70), (83), (193), (194), (209), (214),
% 101.79/14.55 | | | | | (287), (288), (290), (350) gives:
% 101.79/14.55 | | | | | (362) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (member(pname) = v1
% 101.79/14.55 | | | | | & fun(all_92_0, bool) = v0 & ti(x_a, all_323_3) = v2 &
% 101.79/14.55 | | | | | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : !
% 101.79/14.55 | | | | | [v5: $i] : ( ~ (hAPP(all_92_0, bool, v4, u) = v5) | ~
% 101.79/14.55 | | | | | (hAPP(pname, v0, v1, v3) = v4) | ~ $i(v3) | ~ hBOOL(v5)
% 101.79/14.55 | | | | | | ? [v6: $i] : ( ~ (v6 = v2) & hAPP(pname, x_a,
% 101.79/14.55 | | | | | mgt_call, v3) = v6 & $i(v6))))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | DELTA: instantiating (358) with fresh symbols all_395_0, all_395_1,
% 101.79/14.55 | | | | | all_395_2, all_395_3 gives:
% 101.79/14.55 | | | | | (363) member(pname) = all_395_2 & hAPP(all_92_0, bool, all_395_1,
% 101.79/14.55 | | | | | all_333_4) = all_395_0 & hAPP(pname, all_395_3, all_395_2,
% 101.79/14.55 | | | | | pn) = all_395_1 & fun(all_92_0, bool) = all_395_3 &
% 101.79/14.55 | | | | | $i(all_395_0) & $i(all_395_1) & $i(all_395_2) & $i(all_395_3)
% 101.79/14.55 | | | | | & ~ hBOOL(all_395_0)
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | ALPHA: (363) implies:
% 101.79/14.55 | | | | | (364) member(pname) = all_395_2
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | DELTA: instantiating (356) with fresh symbols all_397_0, all_397_1,
% 101.79/14.55 | | | | | all_397_2, all_397_3 gives:
% 101.79/14.55 | | | | | (365) member(pname) = all_397_2 & hAPP(all_92_0, bool, all_397_1,
% 101.79/14.55 | | | | | all_328_2) = all_397_0 & hAPP(pname, all_397_3, all_397_2,
% 101.79/14.55 | | | | | pn) = all_397_1 & fun(all_92_0, bool) = all_397_3 &
% 101.79/14.55 | | | | | $i(all_397_0) & $i(all_397_1) & $i(all_397_2) & $i(all_397_3)
% 101.79/14.55 | | | | | & ~ hBOOL(all_397_0)
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | ALPHA: (365) implies:
% 101.79/14.55 | | | | | (366) fun(all_92_0, bool) = all_397_3
% 101.79/14.55 | | | | | (367) member(pname) = all_397_2
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | DELTA: instantiating (360) with fresh symbols all_401_0, all_401_1,
% 101.79/14.55 | | | | | all_401_2, all_401_3 gives:
% 101.79/14.55 | | | | | (368) member(pname) = all_401_2 & hAPP(all_92_0, bool, all_401_1,
% 101.79/14.55 | | | | | u) = all_401_0 & hAPP(pname, all_401_3, all_401_2, pn) =
% 101.79/14.55 | | | | | all_401_1 & fun(all_92_0, bool) = all_401_3 & $i(all_401_0) &
% 101.79/14.55 | | | | | $i(all_401_1) & $i(all_401_2) & $i(all_401_3) & ~
% 101.79/14.55 | | | | | hBOOL(all_401_0)
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | ALPHA: (368) implies:
% 101.79/14.55 | | | | | (369) ~ hBOOL(all_401_0)
% 101.79/14.55 | | | | | (370) fun(all_92_0, bool) = all_401_3
% 101.79/14.55 | | | | | (371) hAPP(pname, all_401_3, all_401_2, pn) = all_401_1
% 101.79/14.55 | | | | | (372) hAPP(all_92_0, bool, all_401_1, u) = all_401_0
% 101.79/14.55 | | | | | (373) member(pname) = all_401_2
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | DELTA: instantiating (362) with fresh symbols all_409_0, all_409_1,
% 101.79/14.55 | | | | | all_409_2 gives:
% 101.79/14.55 | | | | | (374) member(pname) = all_409_1 & fun(all_92_0, bool) = all_409_2 &
% 101.79/14.55 | | | | | ti(x_a, all_323_3) = all_409_0 & $i(all_409_0) &
% 101.79/14.55 | | | | | $i(all_409_1) & $i(all_409_2) & ! [v0: $i] : ! [v1: $i] :
% 101.79/14.55 | | | | | ! [v2: $i] : ( ~ (hAPP(all_92_0, bool, v1, u) = v2) | ~
% 101.79/14.55 | | | | | (hAPP(pname, all_409_2, all_409_1, v0) = v1) | ~ $i(v0) |
% 101.79/14.55 | | | | | ~ hBOOL(v2) | ? [v3: any] : ( ~ (v3 = all_409_0) &
% 101.79/14.55 | | | | | hAPP(pname, x_a, mgt_call, v0) = v3 & $i(v3)))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | ALPHA: (374) implies:
% 101.79/14.55 | | | | | (375) member(pname) = all_409_1
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | DELTA: instantiating (357) with fresh symbols all_412_0, all_412_1,
% 101.79/14.55 | | | | | all_412_2 gives:
% 101.79/14.55 | | | | | (376) member(pname) = all_412_1 & fun(all_92_0, bool) = all_412_2 &
% 101.79/14.55 | | | | | ti(x_a, all_155_2) = all_412_0 & $i(all_412_0) &
% 101.79/14.55 | | | | | $i(all_412_1) & $i(all_412_2) & ! [v0: $i] : ! [v1: $i] :
% 101.79/14.55 | | | | | ! [v2: $i] : ( ~ (hAPP(all_92_0, bool, v1, all_328_2) = v2) |
% 101.79/14.55 | | | | | ~ (hAPP(pname, all_412_2, all_412_1, v0) = v1) | ~ $i(v0)
% 101.79/14.55 | | | | | | ~ hBOOL(v2) | ? [v3: any] : ( ~ (v3 = all_412_0) &
% 101.79/14.55 | | | | | hAPP(pname, x_a, mgt_call, v0) = v3 & $i(v3)))
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | ALPHA: (376) implies:
% 101.79/14.55 | | | | | (377) fun(all_92_0, bool) = all_412_2
% 101.79/14.55 | | | | | (378) member(pname) = all_412_1
% 101.79/14.55 | | | | |
% 101.79/14.55 | | | | | DELTA: instantiating (359) with fresh symbols all_415_0, all_415_1,
% 101.79/14.55 | | | | | all_415_2 gives:
% 101.79/14.56 | | | | | (379) member(pname) = all_415_1 & fun(all_92_0, bool) = all_415_2 &
% 101.79/14.56 | | | | | ti(x_a, all_155_2) = all_415_0 & $i(all_415_0) &
% 101.79/14.56 | | | | | $i(all_415_1) & $i(all_415_2) & ! [v0: $i] : ! [v1: $i] :
% 101.79/14.56 | | | | | ! [v2: $i] : ( ~ (hAPP(all_92_0, bool, v1, all_333_4) = v2) |
% 101.79/14.56 | | | | | ~ (hAPP(pname, all_415_2, all_415_1, v0) = v1) | ~ $i(v0)
% 101.79/14.56 | | | | | | ~ hBOOL(v2) | ? [v3: any] : ( ~ (v3 = all_415_0) &
% 101.79/14.56 | | | | | hAPP(pname, x_a, mgt_call, v0) = v3 & $i(v3)))
% 101.79/14.56 | | | | |
% 101.79/14.56 | | | | | ALPHA: (379) implies:
% 101.79/14.56 | | | | | (380) fun(all_92_0, bool) = all_415_2
% 101.79/14.56 | | | | | (381) member(pname) = all_415_1
% 101.79/14.56 | | | | |
% 101.79/14.56 | | | | | DELTA: instantiating (361) with fresh symbols all_418_0, all_418_1,
% 101.79/14.56 | | | | | all_418_2 gives:
% 101.79/14.56 | | | | | (382) member(pname) = all_418_1 & fun(all_92_0, bool) = all_418_2 &
% 101.79/14.56 | | | | | ti(x_a, all_155_2) = all_418_0 & $i(all_418_0) &
% 101.79/14.56 | | | | | $i(all_418_1) & $i(all_418_2) & ! [v0: $i] : ! [v1: $i] :
% 101.79/14.56 | | | | | ! [v2: $i] : ( ~ (hAPP(all_92_0, bool, v1, u) = v2) | ~
% 101.79/14.56 | | | | | (hAPP(pname, all_418_2, all_418_1, v0) = v1) | ~ $i(v0) |
% 101.79/14.56 | | | | | ~ hBOOL(v2) | ? [v3: any] : ( ~ (v3 = all_418_0) &
% 101.79/14.56 | | | | | hAPP(pname, x_a, mgt_call, v0) = v3 & $i(v3)))
% 101.79/14.56 | | | | |
% 101.79/14.56 | | | | | ALPHA: (382) implies:
% 101.79/14.56 | | | | | (383) member(pname) = all_418_1
% 101.79/14.56 | | | | |
% 101.79/14.56 | | | | | REDUCE: (346), (353), (355) imply:
% 101.79/14.56 | | | | | (384) ~ (all_247_8 = all_202_1)
% 101.79/14.56 | | | | |
% 101.79/14.56 | | | | | SIMP: (384) implies:
% 101.79/14.56 | | | | | (385) ~ (all_247_8 = all_202_1)
% 101.79/14.56 | | | | |
% 101.79/14.56 | | | | | BETA: splitting (354) gives:
% 101.79/14.56 | | | | |
% 101.79/14.56 | | | | | Case 1:
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | (386) all_308_0 = all_308_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (353), (386) imply:
% 101.79/14.56 | | | | | | (387) all_308_1 = all_202_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (387) implies:
% 101.79/14.56 | | | | | | (388) all_308_1 = all_202_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (355), (388) imply:
% 101.79/14.56 | | | | | | (389) all_247_8 = all_202_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | REDUCE: (385), (389) imply:
% 101.79/14.56 | | | | | | (390) $false
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | CLOSE: (390) is inconsistent.
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | Case 2:
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (36) with all_150_3, all_412_2, bool,
% 101.79/14.56 | | | | | | all_92_0, simplifying with (213), (377) gives:
% 101.79/14.56 | | | | | | (391) all_412_2 = all_150_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (36) with all_412_2, all_415_2, bool,
% 101.79/14.56 | | | | | | all_92_0, simplifying with (377), (380) gives:
% 101.79/14.56 | | | | | | (392) all_415_2 = all_412_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (36) with all_401_3, all_415_2, bool,
% 101.79/14.56 | | | | | | all_92_0, simplifying with (370), (380) gives:
% 101.79/14.56 | | | | | | (393) all_415_2 = all_401_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (36) with all_397_3, all_415_2, bool,
% 101.79/14.56 | | | | | | all_92_0, simplifying with (366), (380) gives:
% 101.79/14.56 | | | | | | (394) all_415_2 = all_397_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (34) with all_397_2, all_412_1, pname,
% 101.79/14.56 | | | | | | simplifying with (367), (378) gives:
% 101.79/14.56 | | | | | | (395) all_412_1 = all_397_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (34) with all_150_2, all_415_1, pname,
% 101.79/14.56 | | | | | | simplifying with (62), (381) gives:
% 101.79/14.56 | | | | | | (396) all_415_1 = all_150_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (34) with all_412_1, all_415_1, pname,
% 101.79/14.56 | | | | | | simplifying with (378), (381) gives:
% 101.79/14.56 | | | | | | (397) all_415_1 = all_412_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (34) with all_409_1, all_415_1, pname,
% 101.79/14.56 | | | | | | simplifying with (375), (381) gives:
% 101.79/14.56 | | | | | | (398) all_415_1 = all_409_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (34) with all_401_2, all_415_1, pname,
% 101.79/14.56 | | | | | | simplifying with (373), (381) gives:
% 101.79/14.56 | | | | | | (399) all_415_1 = all_401_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (34) with all_401_2, all_418_1, pname,
% 101.79/14.56 | | | | | | simplifying with (373), (383) gives:
% 101.79/14.56 | | | | | | (400) all_418_1 = all_401_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (34) with all_395_2, all_418_1, pname,
% 101.79/14.56 | | | | | | simplifying with (364), (383) gives:
% 101.79/14.56 | | | | | | (401) all_418_1 = all_395_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (400), (401) imply:
% 101.79/14.56 | | | | | | (402) all_401_2 = all_395_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (402) implies:
% 101.79/14.56 | | | | | | (403) all_401_2 = all_395_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (397), (398) imply:
% 101.79/14.56 | | | | | | (404) all_412_1 = all_409_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (404) implies:
% 101.79/14.56 | | | | | | (405) all_412_1 = all_409_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (396), (398) imply:
% 101.79/14.56 | | | | | | (406) all_409_1 = all_150_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (398), (399) imply:
% 101.79/14.56 | | | | | | (407) all_409_1 = all_401_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (392), (393) imply:
% 101.79/14.56 | | | | | | (408) all_412_2 = all_401_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (408) implies:
% 101.79/14.56 | | | | | | (409) all_412_2 = all_401_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (393), (394) imply:
% 101.79/14.56 | | | | | | (410) all_401_3 = all_397_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (395), (405) imply:
% 101.79/14.56 | | | | | | (411) all_409_1 = all_397_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (411) implies:
% 101.79/14.56 | | | | | | (412) all_409_1 = all_397_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (391), (409) imply:
% 101.79/14.56 | | | | | | (413) all_401_3 = all_150_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (413) implies:
% 101.79/14.56 | | | | | | (414) all_401_3 = all_150_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (407), (412) imply:
% 101.79/14.56 | | | | | | (415) all_401_2 = all_397_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (415) implies:
% 101.79/14.56 | | | | | | (416) all_401_2 = all_397_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (406), (412) imply:
% 101.79/14.56 | | | | | | (417) all_397_2 = all_150_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (403), (416) imply:
% 101.79/14.56 | | | | | | (418) all_397_2 = all_395_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (418) implies:
% 101.79/14.56 | | | | | | (419) all_397_2 = all_395_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (410), (414) imply:
% 101.79/14.56 | | | | | | (420) all_397_3 = all_150_3
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (417), (419) imply:
% 101.79/14.56 | | | | | | (421) all_395_2 = all_150_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | SIMP: (421) implies:
% 101.79/14.56 | | | | | | (422) all_395_2 = all_150_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | COMBINE_EQS: (403), (422) imply:
% 101.79/14.56 | | | | | | (423) all_401_2 = all_150_2
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | REDUCE: (371), (414), (423) imply:
% 101.79/14.56 | | | | | | (424) hAPP(pname, all_150_3, all_150_2, pn) = all_401_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (38) with all_150_1, all_401_1, pn,
% 101.79/14.56 | | | | | | all_150_2, all_150_3, pname, simplifying with (60),
% 101.79/14.56 | | | | | | (424) gives:
% 101.79/14.56 | | | | | | (425) all_401_1 = all_150_1
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | REDUCE: (372), (425) imply:
% 101.79/14.56 | | | | | | (426) hAPP(all_92_0, bool, all_150_1, u) = all_401_0
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | GROUND_INST: instantiating (38) with all_150_0, all_401_0, u,
% 101.79/14.56 | | | | | | all_150_1, bool, all_92_0, simplifying with (198),
% 101.79/14.56 | | | | | | (426) gives:
% 101.79/14.56 | | | | | | (427) all_401_0 = all_150_0
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | REDUCE: (369), (427) imply:
% 101.79/14.56 | | | | | | (428) ~ hBOOL(all_150_0)
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | PRED_UNIFY: (57), (428) imply:
% 101.79/14.56 | | | | | | (429) $false
% 101.79/14.56 | | | | | |
% 101.79/14.56 | | | | | | CLOSE: (429) is inconsistent.
% 101.79/14.56 | | | | | |
% 101.79/14.57 | | | | | End of split
% 101.79/14.57 | | | | |
% 101.79/14.57 | | | | Case 2:
% 101.79/14.57 | | | | |
% 101.79/14.57 | | | | | (430) hAPP(all_94_0, all_108_1, all_178_0, all_202_1) = all_322_1 &
% 101.79/14.57 | | | | | hAPP(all_94_0, bool, all_322_1, all_247_8) = all_322_0 &
% 101.79/14.57 | | | | | $i(all_322_0) & $i(all_322_1) & hBOOL(all_322_0) &
% 101.79/14.57 | | | | | hBOOL(all_247_0)
% 101.79/14.57 | | | | |
% 101.79/14.57 | | | | | ALPHA: (430) implies:
% 101.79/14.57 | | | | | (431) hBOOL(all_247_0)
% 101.79/14.57 | | | | |
% 101.79/14.57 | | | | | PRED_UNIFY: (107), (431) imply:
% 101.79/14.57 | | | | | (432) $false
% 101.79/14.57 | | | | |
% 101.79/14.57 | | | | | CLOSE: (432) is inconsistent.
% 101.79/14.57 | | | | |
% 101.79/14.57 | | | | End of split
% 101.79/14.57 | | | |
% 101.79/14.57 | | | Case 2:
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | (433) hAPP(all_94_0, bool, all_333_10, g) = all_333_9 &
% 101.79/14.57 | | | | finite_finite(x_a) = all_333_10 & $i(all_333_9) &
% 101.79/14.57 | | | | $i(all_333_10) & ~ hBOOL(all_333_9)
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | ALPHA: (433) implies:
% 101.79/14.57 | | | | (434) ~ hBOOL(all_333_9)
% 101.79/14.57 | | | | (435) finite_finite(x_a) = all_333_10
% 101.79/14.57 | | | | (436) hAPP(all_94_0, bool, all_333_10, g) = all_333_9
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | GROUND_INST: instantiating (32) with all_321_1, all_333_10, x_a,
% 101.79/14.57 | | | | simplifying with (312), (435) gives:
% 101.79/14.57 | | | | (437) all_333_10 = all_321_1
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | GROUND_INST: instantiating (32) with all_318_2, all_333_10, x_a,
% 101.79/14.57 | | | | simplifying with (283), (435) gives:
% 101.79/14.57 | | | | (438) all_333_10 = all_318_2
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | COMBINE_EQS: (437), (438) imply:
% 101.79/14.57 | | | | (439) all_321_1 = all_318_2
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | SIMP: (439) implies:
% 101.79/14.57 | | | | (440) all_321_1 = all_318_2
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | REDUCE: (436), (438) imply:
% 101.79/14.57 | | | | (441) hAPP(all_94_0, bool, all_318_2, g) = all_333_9
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | REDUCE: (313), (440) imply:
% 101.79/14.57 | | | | (442) hAPP(all_94_0, bool, all_318_2, g) = all_321_0
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | GROUND_INST: instantiating (38) with all_321_0, all_333_9, g, all_318_2,
% 101.79/14.57 | | | | bool, all_94_0, simplifying with (441), (442) gives:
% 101.79/14.57 | | | | (443) all_333_9 = all_321_0
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | REDUCE: (434), (443) imply:
% 101.79/14.57 | | | | (444) ~ hBOOL(all_321_0)
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | PRED_UNIFY: (311), (444) imply:
% 101.79/14.57 | | | | (445) $false
% 101.79/14.57 | | | |
% 101.79/14.57 | | | | CLOSE: (445) is inconsistent.
% 101.79/14.57 | | | |
% 101.79/14.57 | | | End of split
% 101.79/14.57 | | |
% 101.79/14.57 | | Case 2:
% 101.79/14.57 | | |
% 101.79/14.57 | | | (446) hAPP(all_92_0, bool, all_321_3, u) = all_321_2 &
% 101.79/14.57 | | | finite_finite(pname) = all_321_3 & $i(all_321_2) & $i(all_321_3)
% 101.79/14.57 | | | & ~ hBOOL(all_321_2)
% 101.79/14.57 | | |
% 101.79/14.57 | | | ALPHA: (446) implies:
% 101.79/14.57 | | | (447) ~ hBOOL(all_321_2)
% 101.79/14.57 | | | (448) finite_finite(pname) = all_321_3
% 101.79/14.57 | | | (449) hAPP(all_92_0, bool, all_321_3, u) = all_321_2
% 101.79/14.57 | | |
% 101.79/14.57 | | | GROUND_INST: instantiating (32) with all_112_1, all_321_3, pname,
% 101.79/14.57 | | | simplifying with (54), (448) gives:
% 101.79/14.57 | | | (450) all_321_3 = all_112_1
% 101.79/14.57 | | |
% 101.79/14.57 | | | REDUCE: (449), (450) imply:
% 101.79/14.57 | | | (451) hAPP(all_92_0, bool, all_112_1, u) = all_321_2
% 101.79/14.57 | | |
% 101.79/14.57 | | | GROUND_INST: instantiating (38) with all_112_0, all_321_2, u, all_112_1,
% 101.79/14.57 | | | bool, all_92_0, simplifying with (199), (451) gives:
% 101.79/14.57 | | | (452) all_321_2 = all_112_0
% 101.79/14.57 | | |
% 101.79/14.57 | | | REDUCE: (447), (452) imply:
% 101.79/14.57 | | | (453) ~ hBOOL(all_112_0)
% 101.79/14.57 | | |
% 101.79/14.57 | | | PRED_UNIFY: (51), (453) imply:
% 101.79/14.57 | | | (454) $false
% 101.79/14.57 | | |
% 101.79/14.57 | | | CLOSE: (454) is inconsistent.
% 101.79/14.57 | | |
% 101.79/14.57 | | End of split
% 101.79/14.57 | |
% 101.79/14.57 | Case 2:
% 101.79/14.57 | |
% 101.79/14.57 | | (455) hAPP(all_94_0, all_108_1, all_178_0, g) = all_327_1 &
% 101.79/14.57 | | hAPP(all_94_0, bool, all_327_1, all_202_1) = all_327_0 &
% 101.79/14.57 | | $i(all_327_0) & $i(all_327_1) & ~ hBOOL(all_327_0)
% 101.79/14.57 | |
% 101.79/14.57 | | ALPHA: (455) implies:
% 101.79/14.57 | | (456) ~ hBOOL(all_327_0)
% 101.79/14.57 | | (457) hAPP(all_94_0, bool, all_327_1, all_202_1) = all_327_0
% 101.79/14.57 | | (458) hAPP(all_94_0, all_108_1, all_178_0, g) = all_327_1
% 101.79/14.57 | |
% 101.79/14.57 | | GROUND_INST: instantiating (38) with all_202_7, all_327_1, g, all_178_0,
% 101.79/14.57 | | all_108_1, all_94_0, simplifying with (242), (458) gives:
% 101.79/14.57 | | (459) all_327_1 = all_202_7
% 101.79/14.57 | |
% 101.79/14.57 | | REDUCE: (457), (459) imply:
% 101.79/14.57 | | (460) hAPP(all_94_0, bool, all_202_7, all_202_1) = all_327_0
% 101.79/14.57 | |
% 101.79/14.57 | | GROUND_INST: instantiating (38) with all_202_0, all_327_0, all_202_1,
% 101.79/14.57 | | all_202_7, bool, all_94_0, simplifying with (196), (460) gives:
% 101.79/14.57 | | (461) all_327_0 = all_202_0
% 101.79/14.57 | |
% 101.79/14.57 | | REDUCE: (456), (461) imply:
% 101.79/14.57 | | (462) ~ hBOOL(all_202_0)
% 101.79/14.57 | |
% 101.79/14.57 | | PRED_UNIFY: (76), (462) imply:
% 101.79/14.57 | | (463) $false
% 101.79/14.57 | |
% 101.79/14.57 | | CLOSE: (463) is inconsistent.
% 101.79/14.57 | |
% 101.79/14.57 | End of split
% 101.79/14.57 |
% 101.79/14.57 End of proof
% 101.79/14.58 % SZS output end Proof for theBenchmark
% 101.79/14.58
% 101.79/14.58 13871ms
%------------------------------------------------------------------------------