TSTP Solution File: SWW469+5 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 : 600s
% DateTime : Thu Jul 21 00:04:00 EDT 2022
% Result : Theorem 20.62s 6.27s
% Output : Proof 23.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 4 21:11:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.57 ____ _
% 0.19/0.57 ___ / __ \_____(_)___ ________ __________
% 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.35/1.09 Prover 0: Preprocessing ...
% 5.69/1.80 Prover 0: Warning: ignoring some quantifiers
% 5.69/1.84 Prover 0: Constructing countermodel ...
% 19.25/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.67/6.03 Prover 1: Preprocessing ...
% 20.55/6.22 Prover 1: Warning: ignoring some quantifiers
% 20.62/6.23 Prover 1: Constructing countermodel ...
% 20.62/6.26 Prover 1: proved (345ms)
% 20.62/6.27 Prover 0: stopped
% 20.62/6.27
% 20.62/6.27 No countermodel exists, formula is valid
% 20.62/6.27 % SZS status Theorem for theBenchmark
% 20.62/6.27
% 20.62/6.27 Generating proof ... Warning: ignoring some quantifiers
% 22.28/6.65 found it (size 6)
% 22.28/6.65
% 22.28/6.65 % SZS output start Proof for theBenchmark
% 22.28/6.65 Assumed formulas after preprocessing and simplification:
% 22.28/6.65 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & ~ (v1 = 0) & enum(bool) = 0 & hBOOL(hoare_1883395792gleton) = 0 & hBOOL(induct_true) = 0 & hBOOL(induct_false) = v1 & fun(state, bool) = v0 & ti(state, v5) = v7 & ti(state, v4) = v6 & ti(state, v2) = v3 & ti(bool, hoare_1883395792gleton) = hoare_1883395792gleton & ti(bool, induct_true) = induct_true & ti(bool, induct_false) = induct_false & cl_HOL_Oequal(state) = 0 & cl_HOL_Oequal(com) = 0 & cl_HOL_Oequal(bool) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (member(v8) = v24) | ~ (hAPP(v18, v19, v20, v12) = v21) | ~ (hAPP(v16, v17, v21, v13) = v22) | ~ (hAPP(v15, bool, v27, v14) = v28) | ~ (hAPP(v15, bool, v25, v14) = v26) | ~ (hAPP(v15, bool, v22, v14) = v23) | ~ (hAPP(v8, v17, v24, v11) = v25) | ~ (hAPP(v8, v17, v24, v10) = v27) | ~ (type_definition(v9, v8) = v20) | ~ (fun(v16, v17) = v19) | ~ (fun(v15, bool) = v17) | ~ (fun(v9, v8) = v18) | ~ (fun(v8, v9) = v16) | ~ (fun(v8, bool) = v15) | ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ? [v34] : ? [v35] : (hBOOL(v28) = v31 & hBOOL(v26) = v30 & hBOOL(v23) = v29 & hAPP(v8, v9, v13, v11) = v32 & hAPP(v8, v9, v13, v10) = v33 & ti(v8, v11) = v34 & ti(v8, v10) = v35 & ( ~ (v31 = 0) | ~ (v30 = 0) | ~ (v29 = 0) | (( ~ (v35 = v34) | v33 = v32) & ( ~ (v33 = v32) | v35 = v34))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : ( ~ (hAPP(v18, v19, v20, v21) = v22) | ~ (hAPP(v16, v17, v22, v23) = v24) | ~ (hAPP(v14, v14, v25, v26) = v27) | ~ (hAPP(v14, bool, v24, v27) = v28) | ~ (type_definition(v15, v13) = v20) | ~ (collect(v13) = v25) | ~ (hoare_1580379338ep_set(v8) = v26) | ~ (hoare_2037801986triple(v8) = v21) | ~ (sum_sum(state, v8) = v11) | ~ (sum_sum(com, v9) = v10) | ~ (node(v10, v11) = v12) | ~ (hoare_509422987triple(v8) = v15) | ~ (hoare_244953527triple(v8) = v23) | ~ (fun(v16, v17) = v19) | ~ (fun(v15, v13) = v18) | ~ (fun(v14, bool) = v17) | ~ (fun(v13, v15) = v16) | ~ (fun(v13, bool) = v14) | ~ (fun(v12, bool) = v13) | ~ (fun(v8, v0) = v9) | hBOOL(v28) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (member(v8) = v23) | ~ (hAPP(v17, v18, v19, v11) = v20) | ~ (hAPP(v15, v16, v20, v12) = v21) | ~ (hAPP(v14, bool, v25, v13) = v26) | ~ (hAPP(v14, bool, v21, v13) = v22) | ~ (hAPP(v9, v8, v11, v10) = v24) | ~ (hAPP(v8, v16, v23, v24) = v25) | ~ (type_definition(v9, v8) = v19) | ~ (fun(v15, v16) = v18) | ~ (fun(v14, bool) = v16) | ~ (fun(v9, v8) = v17) | ~ (fun(v8, v9) = v15) | ~ (fun(v8, bool) = v14) | ? [v27] : ? [v28] : (hBOOL(v26) = v28 & hBOOL(v22) = v27 & ( ~ (v27 = 0) | v28 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (member(v15) = v18) | ~ (hAPP(v16, v16, v20, v21) = v22) | ~ (hAPP(v16, bool, v24, v22) = v25) | ~ (hAPP(v16, bool, v19, v22) = v23) | ~ (hAPP(v15, v17, v18, v10) = v19) | ~ (hAPP(v15, v17, v18, v9) = v24) | ~ (collect(v15) = v20) | ~ (hoare_1580379338ep_set(v8) = v21) | ~ (sum_sum(state, v8) = v13) | ~ (sum_sum(com, v11) = v12) | ~ (node(v12, v13) = v14) | ~ (fun(v16, bool) = v17) | ~ (fun(v15, bool) = v16) | ~ (fun(v14, bool) = v15) | ~ (fun(v8, v0) = v11) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (hBOOL(v25) = v27 & hBOOL(v23) = v26 & hAPP(v15, v28, v29, v10) = v30 & hAPP(v15, v28, v29, v9) = v31 & hoare_509422987triple(v8) = v28 & hoare_244953527triple(v8) = v29 & ( ~ (v27 = 0) | ~ (v26 = 0) | (( ~ (v31 = v30) | v10 = v9) & ( ~ (v10 = v9) | v31 = v30))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (member(v14) = v17) | ~ (hAPP(v18, v14, v19, v9) = v20) | ~ (hAPP(v15, v15, v22, v23) = v24) | ~ (hAPP(v15, bool, v21, v24) = v25) | ~ (hAPP(v14, v16, v17, v20) = v21) | ~ (collect(v14) = v22) | ~ (hoare_1580379338ep_set(v8) = v23) | ~ (hoare_2037801986triple(v8) = v19) | ~ (sum_sum(state, v8) = v12) | ~ (sum_sum(com, v10) = v11) | ~ (node(v11, v12) = v13) | ~ (hoare_509422987triple(v8) = v18) | ~ (fun(v15, bool) = v16) | ~ (fun(v14, bool) = v15) | ~ (fun(v13, bool) = v14) | ~ (fun(v8, v0) = v10) | hBOOL(v25) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (member(v8) = v23) | ~ (hAPP(v17, v18, v19, v11) = v20) | ~ (hAPP(v15, v16, v20, v12) = v21) | ~ (hAPP(v14, bool, v24, v13) = v25) | ~ (hAPP(v14, bool, v21, v13) = v22) | ~ (hAPP(v8, v16, v23, v10) = v24) | ~ (type_definition(v9, v8) = v19) | ~ (fun(v15, v16) = v18) | ~ (fun(v14, bool) = v16) | ~ (fun(v9, v8) = v17) | ~ (fun(v8, v9) = v15) | ~ (fun(v8, bool) = v14) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (hBOOL(v25) = v27 & hBOOL(v22) = v26 & hAPP(v9, v8, v11, v28) = v29 & hAPP(v8, v9, v12, v10) = v28 & ti(v8, v10) = v30 & ( ~ (v27 = 0) | ~ (v26 = 0) | v30 = v29))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (member(v8) = v23) | ~ (hAPP(v17, v18, v19, v11) = v20) | ~ (hAPP(v15, v16, v20, v12) = v21) | ~ (hAPP(v14, bool, v24, v13) = v25) | ~ (hAPP(v14, bool, v21, v13) = v22) | ~ (hAPP(v8, v16, v23, v10) = v24) | ~ (type_definition(v9, v8) = v19) | ~ (fun(v15, v16) = v18) | ~ (fun(v14, bool) = v16) | ~ (fun(v9, v8) = v17) | ~ (fun(v8, v9) = v15) | ~ (fun(v8, bool) = v14) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (hBOOL(v25) = v27 & hBOOL(v22) = v26 & ti(v8, v10) = v28 & ( ~ (v27 = 0) | ~ (v26 = 0) | (v30 = v28 & hAPP(v9, v8, v11, v29) = v28)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (hAPP(v18, v19, v20, v12) = v21) | ~ (hAPP(v16, v17, v21, v13) = v22) | ~ (hAPP(v15, bool, v22, v14) = v23) | ~ (type_definition(v9, v8) = v20) | ~ (fun(v16, v17) = v19) | ~ (fun(v15, bool) = v17) | ~ (fun(v9, v8) = v18) | ~ (fun(v8, v9) = v16) | ~ (fun(v8, bool) = v15) | ~ (ti(v9, v11) = v25) | ~ (ti(v9, v10) = v24) | ? [v26] : ? [v27] : ? [v28] : (hBOOL(v23) = v26 & hAPP(v9, v8, v12, v11) = v28 & hAPP(v9, v8, v12, v10) = v27 & ( ~ (v26 = 0) | (( ~ (v28 = v27) | v25 = v24) & ( ~ (v25 = v24) | v28 = v27))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (hAPP(v18, v19, v20, v12) = v21) | ~ (hAPP(v16, v17, v21, v13) = v22) | ~ (hAPP(v15, bool, v22, v14) = v23) | ~ (hAPP(v9, bool, v11, v10) = v24) | ~ (type_definition(v9, v8) = v20) | ~ (fun(v16, v17) = v19) | ~ (fun(v15, bool) = v17) | ~ (fun(v9, v8) = v18) | ~ (fun(v8, v9) = v16) | ~ (fun(v8, bool) = v15) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ? [v34] : (member(v8) = v26 & hBOOL(v24) = v27 & hBOOL(v23) = v25 & ( ~ (v25 = 0) | v27 = 0 | (v31 = 0 & ~ (v34 = 0) & hBOOL(v33) = v34 & hBOOL(v30) = 0 & hAPP(v15, bool, v29, v14) = v30 & hAPP(v9, bool, v11, v32) = v33 & hAPP(v8, v17, v26, v28) = v29 & hAPP(v8, v9, v13, v28) = v32)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (hAPP(v18, v19, v20, v12) = v21) | ~ (hAPP(v16, v17, v21, v13) = v22) | ~ (hAPP(v15, bool, v22, v14) = v23) | ~ (hAPP(v8, bool, v10, v11) = v24) | ~ (type_definition(v9, v8) = v20) | ~ (fun(v16, v17) = v19) | ~ (fun(v15, bool) = v17) | ~ (fun(v9, v8) = v18) | ~ (fun(v8, v9) = v16) | ~ (fun(v8, bool) = v15) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (( ~ (v28 = 0) & hBOOL(v27) = v28 & hAPP(v9, v8, v12, v25) = v26 & hAPP(v8, bool, v10, v26) = v27) | (member(v8) = v26 & hBOOL(v28) = v29 & hBOOL(v24) = v30 & hBOOL(v23) = v25 & hAPP(v15, bool, v27, v14) = v28 & hAPP(v8, v17, v26, v11) = v27 & ( ~ (v29 = 0) | ~ (v25 = 0) | v30 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (hAPP(v17, v18, v19, v11) = v20) | ~ (hAPP(v15, v16, v20, v12) = v21) | ~ (hAPP(v14, bool, v21, v13) = v22) | ~ (hAPP(v9, v8, v11, v10) = v23) | ~ (hAPP(v8, v9, v12, v23) = v24) | ~ (type_definition(v9, v8) = v19) | ~ (fun(v15, v16) = v18) | ~ (fun(v14, bool) = v16) | ~ (fun(v9, v8) = v17) | ~ (fun(v8, v9) = v15) | ~ (fun(v8, bool) = v14) | ? [v25] : ? [v26] : (hBOOL(v22) = v25 & ti(v9, v10) = v26 & ( ~ (v25 = 0) | v26 = v24))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (hAPP(v17, v18, v19, v11) = v20) | ~ (hAPP(v15, v16, v20, v12) = v21) | ~ (hAPP(v14, bool, v21, v13) = v22) | ~ (type_definition(v9, v8) = v19) | ~ (fun(v15, v16) = v18) | ~ (fun(v14, bool) = v16) | ~ (fun(v9, v8) = v17) | ~ (fun(v8, v9) = v15) | ~ (fun(v8, bool) = v14) | ~ (ti(v9, v10) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (member(v8) = v25 & hBOOL(v22) = v24 & ( ~ (v24 = 0) | (v30 = 0 & v27 = v23 & hBOOL(v29) = 0 & hAPP(v14, bool, v28, v13) = v29 & hAPP(v8, v16, v25, v26) = v28 & hAPP(v8, v9, v12, v26) = v23)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (member(v14) = v17) | ~ (hAPP(v15, v15, v19, v20) = v21) | ~ (hAPP(v15, bool, v18, v21) = v22) | ~ (hAPP(v14, v16, v17, v9) = v18) | ~ (collect(v14) = v19) | ~ (hoare_1580379338ep_set(v8) = v20) | ~ (sum_sum(state, v8) = v12) | ~ (sum_sum(com, v10) = v11) | ~ (node(v11, v12) = v13) | ~ (fun(v15, bool) = v16) | ~ (fun(v14, bool) = v15) | ~ (fun(v13, bool) = v14) | ~ (fun(v8, v0) = v10) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (hBOOL(v22) = v23 & hAPP(v24, v14, v25, v27) = v28 & hAPP(v14, v24, v26, v9) = v27 & hoare_2037801986triple(v8) = v25 & hoare_509422987triple(v8) = v24 & hoare_244953527triple(v8) = v26 & ( ~ (v23 = 0) | v28 = v9))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (member(v14) = v17) | ~ (hAPP(v15, v15, v19, v20) = v21) | ~ (hAPP(v15, bool, v18, v21) = v22) | ~ (hAPP(v14, v16, v17, v9) = v18) | ~ (collect(v14) = v19) | ~ (hoare_1580379338ep_set(v8) = v20) | ~ (sum_sum(state, v8) = v12) | ~ (sum_sum(com, v10) = v11) | ~ (node(v11, v12) = v13) | ~ (fun(v15, bool) = v16) | ~ (fun(v14, bool) = v15) | ~ (fun(v13, bool) = v14) | ~ (fun(v8, v0) = v10) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (hBOOL(v22) = v23 & hoare_2037801986triple(v8) = v25 & hoare_509422987triple(v8) = v24 & ( ~ (v23 = 0) | (v27 = v9 & hAPP(v24, v14, v25, v26) = v9)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v9 | ~ (hAPP(v15, v14, v17, v9) = v18) | ~ (hAPP(v14, v15, v16, v18) = v19) | ~ (hoare_2037801986triple(v8) = v17) | ~ (sum_sum(state, v8) = v12) | ~ (sum_sum(com, v10) = v11) | ~ (node(v11, v12) = v13) | ~ (hoare_509422987triple(v8) = v15) | ~ (hoare_244953527triple(v8) = v16) | ~ (fun(v13, bool) = v14) | ~ (fun(v8, v0) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (hAPP(v10, v15, v16, v9) = v18) | ~ (hAPP(v10, v15, v16, v9) = v17) | ~ (hoare_2037801986triple(v8) = v16) | ~ (sum_sum(state, v8) = v13) | ~ (sum_sum(com, v11) = v12) | ~ (node(v12, v13) = v14) | ~ (hoare_509422987triple(v8) = v10) | ~ (fun(v14, bool) = v15) | ~ (fun(v8, v0) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v10 = v9 | ~ (hAPP(v11, v16, v17, v10) = v18) | ~ (hAPP(v11, v16, v17, v9) = v18) | ~ (hoare_2037801986triple(v8) = v17) | ~ (sum_sum(state, v8) = v14) | ~ (sum_sum(com, v12) = v13) | ~ (node(v13, v14) = v15) | ~ (hoare_509422987triple(v8) = v11) | ~ (fun(v15, bool) = v16) | ~ (fun(v8, v0) = v12)) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (hAPP(v15, v15, v16, v17) = v18) | ~ (collect(v14) = v16) | ~ (hoare_1580379338ep_set(v9) = v17) | ~ (sum_sum(state, v9) = v12) | ~ (sum_sum(com, v10) = v11) | ~ (node(v11, v12) = v13) | ~ (fun(v14, bool) = v15) | ~ (fun(v13, bool) = v14) | ~ (fun(v9, v0) = v10) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (member(v14) = v22 & hBOOL(v25) = 0 & hAPP(v15, bool, v24, v18) = v25 & hAPP(v14, v21, v22, v23) = v24 & hAPP(v14, v19, v20, v23) = v8 & hoare_509422987triple(v9) = v19 & hoare_244953527triple(v9) = v20 & fun(v15, bool) = v21)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (type_definition(v8, v9) = v16) | ~ (fun(v12, bool) = v13) | ~ (fun(v11, v13) = v14) | ~ (fun(v10, v14) = v15) | ~ (fun(v9, v8) = v11) | ~ (fun(v9, bool) = v12) | ~ (fun(v8, v9) = v10) | ~ (ti(v15, v16) = v17)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (hoare_2037801986triple(v8) = v16) | ~ (sum_sum(state, v8) = v12) | ~ (sum_sum(com, v10) = v11) | ~ (node(v11, v12) = v13) | ~ (hoare_509422987triple(v8) = v9) | ~ (fun(v13, bool) = v14) | ~ (fun(v9, v14) = v15) | ~ (fun(v8, v0) = v10) | ~ (ti(v15, v16) = v17)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (sum_sum(state, v8) = v11) | ~ (sum_sum(com, v9) = v10) | ~ (node(v10, v11) = v12) | ~ (hoare_509422987triple(v8) = v14) | ~ (hoare_244953527triple(v8) = v16) | ~ (fun(v13, v14) = v15) | ~ (fun(v12, bool) = v13) | ~ (fun(v8, v0) = v9) | ~ (ti(v15, v16) = v17)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | ~ (hoare_1580379338ep_set(v8) = v15) | ~ (sum_sum(state, v8) = v11) | ~ (sum_sum(com, v9) = v10) | ~ (node(v10, v11) = v12) | ~ (fun(v13, bool) = v14) | ~ (fun(v12, bool) = v13) | ~ (fun(v8, v0) = v9) | ~ (ti(v14, v15) = v16)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (hAPP(v15, bool, v9, v10) = v16) | ~ (sum_sum(state, v8) = v13) | ~ (sum_sum(com, v11) = v12) | ~ (node(v12, v13) = v14) | ~ (fun(v14, bool) = v15) | ~ (fun(v8, v0) = v11) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : (member(v15) = v19 & hBOOL(v24) = v25 & hBOOL(v16) = v28 & hAPP(v17, v17, v21, v22) = v23 & hAPP(v17, bool, v20, v23) = v24 & hAPP(v15, v18, v19, v10) = v20 & collect(v15) = v21 & hoare_1580379338ep_set(v8) = v22 & hoare_2037801986triple(v8) = v27 & hoare_509422987triple(v8) = v26 & fun(v17, bool) = v18 & fun(v15, bool) = v17 & ( ~ (v25 = 0) | v28 = 0 | ( ~ (v32 = 0) & hBOOL(v31) = v32 & hAPP(v26, v15, v27, v29) = v30 & hAPP(v15, bool, v9, v30) = v31)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v10 = v9 | ~ (hAPP(v11, v12, v13, v9) = v14) | ~ (hAPP(v11, bool, v14, v10) = v15) | ~ (hoare_509422987triple(v8) = v11) | ~ (fun(v11, bool) = v12) | ~ (equal_equal(v11) = v13) | ? [v16] : ( ~ (v16 = 0) & hBOOL(v15) = v16)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (member(v8) = v13) | ~ (hAPP(v11, bool, v14, v10) = v15) | ~ (hAPP(v8, v12, v13, v9) = v14) | ~ (fun(v11, bool) = v12) | ~ (fun(v8, bool) = v11) | ? [v16] : ? [v17] : ? [v18] : (hBOOL(v17) = v18 & hBOOL(v15) = v16 & hAPP(v8, bool, v10, v9) = v17 & ( ~ (v16 = 0) | v18 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (member(v8) = v13) | ~ (hAPP(v11, bool, v14, v10) = v15) | ~ (hAPP(v8, v12, v13, v9) = v14) | ~ (fun(v11, bool) = v12) | ~ (fun(v8, bool) = v11) | ? [v16] : ? [v17] : ? [v18] : (hBOOL(v16) = v17 & hBOOL(v15) = v18 & hAPP(v8, bool, v10, v9) = v16 & ( ~ (v17 = 0) | v18 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (fun(v8, v9) = v12) | ~ (ti(v12, v11) = v14) | ~ (ti(v12, v10) = v13) | ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = v16) & hAPP(v8, v9, v11, v15) = v17 & hAPP(v8, v9, v10, v15) = v16)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (hAPP(v10, v11, v12, v9) = v13) | ~ (hAPP(v10, bool, v13, v9) = v14) | ~ (hoare_509422987triple(v8) = v10) | ~ (fun(v10, bool) = v11) | ~ (equal_equal(v10) = v12) | hBOOL(v14) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (hAPP(v8, v11, v12, v9) = v13) | ~ (hAPP(v8, bool, v13, v10) = v14) | ~ (fequal(v8) = v12) | ~ (fun(v8, bool) = v11) | ? [v15] : ? [v16] : ? [v17] : (hBOOL(v14) = v17 & ti(v8, v10) = v16 & ti(v8, v9) = v15 & ( ~ (v16 = v15) | v17 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (hAPP(v8, v11, v12, v9) = v13) | ~ (hAPP(v8, bool, v13, v10) = v14) | ~ (fequal(v8) = v12) | ~ (fun(v8, bool) = v11) | ? [v15] : ? [v16] : ? [v17] : (hBOOL(v14) = v15 & ti(v8, v10) = v17 & ti(v8, v9) = v16 & ( ~ (v15 = 0) | v17 = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (hAPP(v8, v11, v12, v9) = v13) | ~ (hAPP(v8, bool, v13, v10) = v14) | ~ (induct_equal(v8) = v12) | ~ (fun(v8, bool) = v11) | ? [v15] : ? [v16] : ? [v17] : (hBOOL(v14) = v17 & ti(v8, v10) = v16 & ti(v8, v9) = v15 & ( ~ (v16 = v15) | v17 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (hAPP(v8, v11, v12, v9) = v13) | ~ (hAPP(v8, bool, v13, v10) = v14) | ~ (induct_equal(v8) = v12) | ~ (fun(v8, bool) = v11) | ? [v15] : ? [v16] : ? [v17] : (hBOOL(v14) = v15 & ti(v8, v10) = v17 & ti(v8, v9) = v16 & ( ~ (v15 = 0) | v17 = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (hAPP(v8, v9, v13, v11) = v14) | ~ (fun(v8, v9) = v12) | ~ (ti(v12, v10) = v13) | hAPP(v8, v9, v10, v11) = v14) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (member(v8) = v12) | ~ (fun(v9, bool) = v10) | ~ (fun(v8, v10) = v11) | ~ (fun(v8, bool) = v9) | ~ (ti(v11, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (hAPP(v9, v8, v10, v11) = v12) | ~ (ti(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (hAPP(v13, v12, v11, v10) = v9) | ~ (hAPP(v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (hAPP(v8, v9, v10, v12) = v13) | ~ (ti(v8, v11) = v12) | hAPP(v8, v9, v10, v11) = v13) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (fequal(v8) = v11) | ~ (fun(v8, v9) = v10) | ~ (fun(v8, bool) = v9) | ~ (ti(v10, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (collect(v8) = v11) | ~ (fun(v9, v9) = v10) | ~ (fun(v8, bool) = v9) | ~ (ti(v10, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (induct_equal(v8) = v11) | ~ (fun(v8, v9) = v10) | ~ (fun(v8, bool) = v9) | ~ (ti(v10, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (fun(v8, v9) = v10) | ~ (fun(v8, bool) = v9) | ~ (equal_equal(v8) = v11) | ~ (ti(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & cl_HOL_Oequal(v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (hAPP(v11, bool, v10, v9) = v12) | ~ (hoare_509422987triple(v8) = v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : (member(v17) = v20 & hBOOL(v12) = v25 & hAPP(v18, v18, v21, v22) = v23 & collect(v17) = v21 & hoare_1580379338ep_set(v8) = v22 & sum_sum(state, v8) = v15 & sum_sum(com, v13) = v14 & node(v14, v15) = v16 & hoare_244953527triple(v8) = v24 & fun(v18, bool) = v19 & fun(v17, bool) = v18 & fun(v16, bool) = v17 & fun(v8, v0) = v13 & (v25 = 0 | (v29 = 0 & ~ (v32 = 0) & hBOOL(v31) = v32 & hBOOL(v28) = 0 & hAPP(v18, bool, v27, v23) = v28 & hAPP(v17, v19, v20, v26) = v27 & hAPP(v17, v11, v24, v26) = v30 & hAPP(v11, bool, v10, v30) = v31)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (hAPP(v10, v10, v11, v9) = v12) | ~ (collect(v8) = v11) | ~ (fun(v8, bool) = v10) | ti(v10, v9) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (ti(v8, v10) = v11) | ~ (ti(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (type_definition(v11, v10) = v9) | ~ (type_definition(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (sum_sum(v11, v10) = v9) | ~ (sum_sum(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (node(v11, v10) = v9) | ~ (node(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (fun(v11, v10) = v9) | ~ (fun(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ti(v11, v10) = v9) | ~ (ti(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (undefined(v8) = v9) | ~ (ti(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (enum(v10) = v9) | ~ (enum(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (member(v10) = v9) | ~ (member(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hBOOL(v10) = v9) | ~ (hBOOL(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (fequal(v10) = v9) | ~ (fequal(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (collect(v10) = v9) | ~ (collect(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hoare_1580379338ep_set(v10) = v9) | ~ (hoare_1580379338ep_set(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hoare_2037801986triple(v10) = v9) | ~ (hoare_2037801986triple(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hoare_509422987triple(v10) = v9) | ~ (hoare_509422987triple(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hoare_244953527triple(v10) = v9) | ~ (hoare_244953527triple(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (undefined(v10) = v9) | ~ (undefined(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (induct_equal(v10) = v9) | ~ (induct_equal(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (equal_equal(v10) = v9) | ~ (equal_equal(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (cl_HOL_Oequal(v10) = v9) | ~ (cl_HOL_Oequal(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum_sum(v8, v9) = v10) | cl_HOL_Oequal(v10) = 0) & ! [v8] : ! [v9] : (v9 = v3 | ~ (ti(state, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (enum(v9) = 0) | ~ (enum(v8) = 0) | ? [v10] : (enum(v10) = 0 & sum_sum(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (enum(v9) = 0) | ~ (enum(v8) = 0) | ? [v10] : (enum(v10) = 0 & fun(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (enum(v8) = 0) | ~ (cl_HOL_Oequal(v9) = 0) | ? [v10] : (fun(v8, v9) = v10 & cl_HOL_Oequal(v10) = 0)) & ! [v8] : ! [v9] : ( ~ (fequal(v8) = v9) | ? [v10] : ? [v11] : (equal_equal(v8) = v11 & cl_HOL_Oequal(v8) = v10 & ( ~ (v10 = 0) | v11 = v9))) & ! [v8] : ! [v9] : ( ~ (hoare_509422987triple(v8) = v9) | cl_HOL_Oequal(v9) = 0) & ! [v8] : ! [v9] : ( ~ (fun(v8, bool) = v9) | ? [v10] : ? [v11] : (equal_equal(v8) = v11 & cl_HOL_Oequal(v8) = v10 & ( ~ (v10 = 0) | ! [v12] : ! [v13] : ! [v14] : ( ~ (hAPP(v8, v9, v11, v12) = v13) | ~ (hAPP(v8, bool, v13, v12) = v14) | hBOOL(v14) = 0)))) & ! [v8] : ! [v9] : ( ~ (fun(v8, bool) = v9) | ? [v10] : ? [v11] : (equal_equal(v8) = v11 & cl_HOL_Oequal(v8) = v10 & ( ~ (v10 = 0) | ( ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (hAPP(v8, v9, v11, v12) = v14) | ~ (hAPP(v8, bool, v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : (hBOOL(v15) = v18 & ti(v8, v13) = v17 & ti(v8, v12) = v16 & ( ~ (v17 = v16) | v18 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (hAPP(v8, v9, v11, v12) = v14) | ~ (hAPP(v8, bool, v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : (hBOOL(v15) = v16 & ti(v8, v13) = v18 & ti(v8, v12) = v17 & ( ~ (v16 = 0) | v18 = v17))))))) & ! [v8] : ! [v9] : ( ~ (ti(bool, v8) = v9) | ? [v10] : ? [v11] : (hBOOL(v9) = v11 & hBOOL(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (ti(bool, v8) = v9) | ? [v10] : ? [v11] : (hBOOL(v9) = v10 & hBOOL(v8) = v11 & ( ~ (v10 = 0) | v11 = 0))))
% 22.68/6.75 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 22.68/6.75 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_6_6 = 0) & enum(bool) = 0 & hBOOL(hoare_1883395792gleton) = 0 & hBOOL(induct_true) = 0 & hBOOL(induct_false) = all_0_6_6 & fun(state, bool) = all_0_7_7 & ti(state, all_0_2_2) = all_0_0_0 & ti(state, all_0_3_3) = all_0_1_1 & ti(state, all_0_5_5) = all_0_4_4 & ti(bool, hoare_1883395792gleton) = hoare_1883395792gleton & ti(bool, induct_true) = induct_true & ti(bool, induct_false) = induct_false & cl_HOL_Oequal(state) = 0 & cl_HOL_Oequal(com) = 0 & cl_HOL_Oequal(bool) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (member(v0) = v16) | ~ (hAPP(v10, v11, v12, v4) = v13) | ~ (hAPP(v8, v9, v13, v5) = v14) | ~ (hAPP(v7, bool, v19, v6) = v20) | ~ (hAPP(v7, bool, v17, v6) = v18) | ~ (hAPP(v7, bool, v14, v6) = v15) | ~ (hAPP(v0, v9, v16, v3) = v17) | ~ (hAPP(v0, v9, v16, v2) = v19) | ~ (type_definition(v1, v0) = v12) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, bool) = v9) | ~ (fun(v1, v0) = v10) | ~ (fun(v0, v1) = v8) | ~ (fun(v0, bool) = v7) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (hBOOL(v20) = v23 & hBOOL(v18) = v22 & hBOOL(v15) = v21 & hAPP(v0, v1, v5, v3) = v24 & hAPP(v0, v1, v5, v2) = v25 & ti(v0, v3) = v26 & ti(v0, v2) = v27 & ( ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | (( ~ (v27 = v26) | v25 = v24) & ( ~ (v25 = v24) | v27 = v26))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (hAPP(v10, v11, v12, v13) = v14) | ~ (hAPP(v8, v9, v14, v15) = v16) | ~ (hAPP(v6, v6, v17, v18) = v19) | ~ (hAPP(v6, bool, v16, v19) = v20) | ~ (type_definition(v7, v5) = v12) | ~ (collect(v5) = v17) | ~ (hoare_1580379338ep_set(v0) = v18) | ~ (hoare_2037801986triple(v0) = v13) | ~ (sum_sum(state, v0) = v3) | ~ (sum_sum(com, v1) = v2) | ~ (node(v2, v3) = v4) | ~ (hoare_509422987triple(v0) = v7) | ~ (hoare_244953527triple(v0) = v15) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, v5) = v10) | ~ (fun(v6, bool) = v9) | ~ (fun(v5, v7) = v8) | ~ (fun(v5, bool) = v6) | ~ (fun(v4, bool) = v5) | ~ (fun(v0, all_0_7_7) = v1) | hBOOL(v20) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (member(v0) = v15) | ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v17, v5) = v18) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (hAPP(v1, v0, v3, v2) = v16) | ~ (hAPP(v0, v8, v15, v16) = v17) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ? [v19] : ? [v20] : (hBOOL(v18) = v20 & hBOOL(v14) = v19 & ( ~ (v19 = 0) | v20 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (member(v7) = v10) | ~ (hAPP(v8, v8, v12, v13) = v14) | ~ (hAPP(v8, bool, v16, v14) = v17) | ~ (hAPP(v8, bool, v11, v14) = v15) | ~ (hAPP(v7, v9, v10, v2) = v11) | ~ (hAPP(v7, v9, v10, v1) = v16) | ~ (collect(v7) = v12) | ~ (hoare_1580379338ep_set(v0) = v13) | ~ (sum_sum(state, v0) = v5) | ~ (sum_sum(com, v3) = v4) | ~ (node(v4, v5) = v6) | ~ (fun(v8, bool) = v9) | ~ (fun(v7, bool) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v0, all_0_7_7) = v3) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (hBOOL(v17) = v19 & hBOOL(v15) = v18 & hAPP(v7, v20, v21, v2) = v22 & hAPP(v7, v20, v21, v1) = v23 & hoare_509422987triple(v0) = v20 & hoare_244953527triple(v0) = v21 & ( ~ (v19 = 0) | ~ (v18 = 0) | (( ~ (v23 = v22) | v2 = v1) & ( ~ (v2 = v1) | v23 = v22))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (member(v6) = v9) | ~ (hAPP(v10, v6, v11, v1) = v12) | ~ (hAPP(v7, v7, v14, v15) = v16) | ~ (hAPP(v7, bool, v13, v16) = v17) | ~ (hAPP(v6, v8, v9, v12) = v13) | ~ (collect(v6) = v14) | ~ (hoare_1580379338ep_set(v0) = v15) | ~ (hoare_2037801986triple(v0) = v11) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (hoare_509422987triple(v0) = v10) | ~ (fun(v7, bool) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, bool) = v6) | ~ (fun(v0, all_0_7_7) = v2) | hBOOL(v17) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (member(v0) = v15) | ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v16, v5) = v17) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (hAPP(v0, v8, v15, v2) = v16) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (hBOOL(v17) = v19 & hBOOL(v14) = v18 & hAPP(v1, v0, v3, v20) = v21 & hAPP(v0, v1, v4, v2) = v20 & ti(v0, v2) = v22 & ( ~ (v19 = 0) | ~ (v18 = 0) | v22 = v21))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (member(v0) = v15) | ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v16, v5) = v17) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (hAPP(v0, v8, v15, v2) = v16) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (hBOOL(v17) = v19 & hBOOL(v14) = v18 & ti(v0, v2) = v20 & ( ~ (v19 = 0) | ~ (v18 = 0) | (v22 = v20 & hAPP(v1, v0, v3, v21) = v20)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (hAPP(v10, v11, v12, v4) = v13) | ~ (hAPP(v8, v9, v13, v5) = v14) | ~ (hAPP(v7, bool, v14, v6) = v15) | ~ (type_definition(v1, v0) = v12) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, bool) = v9) | ~ (fun(v1, v0) = v10) | ~ (fun(v0, v1) = v8) | ~ (fun(v0, bool) = v7) | ~ (ti(v1, v3) = v17) | ~ (ti(v1, v2) = v16) | ? [v18] : ? [v19] : ? [v20] : (hBOOL(v15) = v18 & hAPP(v1, v0, v4, v3) = v20 & hAPP(v1, v0, v4, v2) = v19 & ( ~ (v18 = 0) | (( ~ (v20 = v19) | v17 = v16) & ( ~ (v17 = v16) | v20 = v19))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (hAPP(v10, v11, v12, v4) = v13) | ~ (hAPP(v8, v9, v13, v5) = v14) | ~ (hAPP(v7, bool, v14, v6) = v15) | ~ (hAPP(v1, bool, v3, v2) = v16) | ~ (type_definition(v1, v0) = v12) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, bool) = v9) | ~ (fun(v1, v0) = v10) | ~ (fun(v0, v1) = v8) | ~ (fun(v0, bool) = v7) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (member(v0) = v18 & hBOOL(v16) = v19 & hBOOL(v15) = v17 & ( ~ (v17 = 0) | v19 = 0 | (v23 = 0 & ~ (v26 = 0) & hBOOL(v25) = v26 & hBOOL(v22) = 0 & hAPP(v7, bool, v21, v6) = v22 & hAPP(v1, bool, v3, v24) = v25 & hAPP(v0, v9, v18, v20) = v21 & hAPP(v0, v1, v5, v20) = v24)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (hAPP(v10, v11, v12, v4) = v13) | ~ (hAPP(v8, v9, v13, v5) = v14) | ~ (hAPP(v7, bool, v14, v6) = v15) | ~ (hAPP(v0, bool, v2, v3) = v16) | ~ (type_definition(v1, v0) = v12) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, bool) = v9) | ~ (fun(v1, v0) = v10) | ~ (fun(v0, v1) = v8) | ~ (fun(v0, bool) = v7) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v20 = 0) & hBOOL(v19) = v20 & hAPP(v1, v0, v4, v17) = v18 & hAPP(v0, bool, v2, v18) = v19) | (member(v0) = v18 & hBOOL(v20) = v21 & hBOOL(v16) = v22 & hBOOL(v15) = v17 & hAPP(v7, bool, v19, v6) = v20 & hAPP(v0, v9, v18, v3) = v19 & ( ~ (v21 = 0) | ~ (v17 = 0) | v22 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (hAPP(v1, v0, v3, v2) = v15) | ~ (hAPP(v0, v1, v4, v15) = v16) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ? [v17] : ? [v18] : (hBOOL(v14) = v17 & ti(v1, v2) = v18 & ( ~ (v17 = 0) | v18 = v16))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ~ (ti(v1, v2) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (member(v0) = v17 & hBOOL(v14) = v16 & ( ~ (v16 = 0) | (v22 = 0 & v19 = v15 & hBOOL(v21) = 0 & hAPP(v6, bool, v20, v5) = v21 & hAPP(v0, v8, v17, v18) = v20 & hAPP(v0, v1, v4, v18) = v15)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (member(v6) = v9) | ~ (hAPP(v7, v7, v11, v12) = v13) | ~ (hAPP(v7, bool, v10, v13) = v14) | ~ (hAPP(v6, v8, v9, v1) = v10) | ~ (collect(v6) = v11) | ~ (hoare_1580379338ep_set(v0) = v12) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (fun(v7, bool) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, bool) = v6) | ~ (fun(v0, all_0_7_7) = v2) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (hBOOL(v14) = v15 & hAPP(v16, v6, v17, v19) = v20 & hAPP(v6, v16, v18, v1) = v19 & hoare_2037801986triple(v0) = v17 & hoare_509422987triple(v0) = v16 & hoare_244953527triple(v0) = v18 & ( ~ (v15 = 0) | v20 = v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (member(v6) = v9) | ~ (hAPP(v7, v7, v11, v12) = v13) | ~ (hAPP(v7, bool, v10, v13) = v14) | ~ (hAPP(v6, v8, v9, v1) = v10) | ~ (collect(v6) = v11) | ~ (hoare_1580379338ep_set(v0) = v12) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (fun(v7, bool) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, bool) = v6) | ~ (fun(v0, all_0_7_7) = v2) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (hBOOL(v14) = v15 & hoare_2037801986triple(v0) = v17 & hoare_509422987triple(v0) = v16 & ( ~ (v15 = 0) | (v19 = v1 & hAPP(v16, v6, v17, v18) = v1)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v1 | ~ (hAPP(v7, v6, v9, v1) = v10) | ~ (hAPP(v6, v7, v8, v10) = v11) | ~ (hoare_2037801986triple(v0) = v9) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (hoare_509422987triple(v0) = v7) | ~ (hoare_244953527triple(v0) = v8) | ~ (fun(v5, bool) = v6) | ~ (fun(v0, all_0_7_7) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (hAPP(v2, v7, v8, v1) = v10) | ~ (hAPP(v2, v7, v8, v1) = v9) | ~ (hoare_2037801986triple(v0) = v8) | ~ (sum_sum(state, v0) = v5) | ~ (sum_sum(com, v3) = v4) | ~ (node(v4, v5) = v6) | ~ (hoare_509422987triple(v0) = v2) | ~ (fun(v6, bool) = v7) | ~ (fun(v0, all_0_7_7) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v2 = v1 | ~ (hAPP(v3, v8, v9, v2) = v10) | ~ (hAPP(v3, v8, v9, v1) = v10) | ~ (hoare_2037801986triple(v0) = v9) | ~ (sum_sum(state, v0) = v6) | ~ (sum_sum(com, v4) = v5) | ~ (node(v5, v6) = v7) | ~ (hoare_509422987triple(v0) = v3) | ~ (fun(v7, bool) = v8) | ~ (fun(v0, all_0_7_7) = v4)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (hAPP(v7, v7, v8, v9) = v10) | ~ (collect(v6) = v8) | ~ (hoare_1580379338ep_set(v1) = v9) | ~ (sum_sum(state, v1) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, bool) = v6) | ~ (fun(v1, all_0_7_7) = v2) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (member(v6) = v14 & hBOOL(v17) = 0 & hAPP(v7, bool, v16, v10) = v17 & hAPP(v6, v13, v14, v15) = v16 & hAPP(v6, v11, v12, v15) = v0 & hoare_509422987triple(v1) = v11 & hoare_244953527triple(v1) = v12 & fun(v7, bool) = v13)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (type_definition(v0, v1) = v8) | ~ (fun(v4, bool) = v5) | ~ (fun(v3, v5) = v6) | ~ (fun(v2, v6) = v7) | ~ (fun(v1, v0) = v3) | ~ (fun(v1, bool) = v4) | ~ (fun(v0, v1) = v2) | ~ (ti(v7, v8) = v9)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (hoare_2037801986triple(v0) = v8) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (hoare_509422987triple(v0) = v1) | ~ (fun(v5, bool) = v6) | ~ (fun(v1, v6) = v7) | ~ (fun(v0, all_0_7_7) = v2) | ~ (ti(v7, v8) = v9)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (sum_sum(state, v0) = v3) | ~ (sum_sum(com, v1) = v2) | ~ (node(v2, v3) = v4) | ~ (hoare_509422987triple(v0) = v6) | ~ (hoare_244953527triple(v0) = v8) | ~ (fun(v5, v6) = v7) | ~ (fun(v4, bool) = v5) | ~ (fun(v0, all_0_7_7) = v1) | ~ (ti(v7, v8) = v9)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (hoare_1580379338ep_set(v0) = v7) | ~ (sum_sum(state, v0) = v3) | ~ (sum_sum(com, v1) = v2) | ~ (node(v2, v3) = v4) | ~ (fun(v5, bool) = v6) | ~ (fun(v4, bool) = v5) | ~ (fun(v0, all_0_7_7) = v1) | ~ (ti(v6, v7) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (hAPP(v7, bool, v1, v2) = v8) | ~ (sum_sum(state, v0) = v5) | ~ (sum_sum(com, v3) = v4) | ~ (node(v4, v5) = v6) | ~ (fun(v6, bool) = v7) | ~ (fun(v0, all_0_7_7) = v3) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (member(v7) = v11 & hBOOL(v16) = v17 & hBOOL(v8) = v20 & hAPP(v9, v9, v13, v14) = v15 & hAPP(v9, bool, v12, v15) = v16 & hAPP(v7, v10, v11, v2) = v12 & collect(v7) = v13 & hoare_1580379338ep_set(v0) = v14 & hoare_2037801986triple(v0) = v19 & hoare_509422987triple(v0) = v18 & fun(v9, bool) = v10 & fun(v7, bool) = v9 & ( ~ (v17 = 0) | v20 = 0 | ( ~ (v24 = 0) & hBOOL(v23) = v24 & hAPP(v18, v7, v19, v21) = v22 & hAPP(v7, bool, v1, v22) = v23)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v2 = v1 | ~ (hAPP(v3, v4, v5, v1) = v6) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (hoare_509422987triple(v0) = v3) | ~ (fun(v3, bool) = v4) | ~ (equal_equal(v3) = v5) | ? [v8] : ( ~ (v8 = 0) & hBOOL(v7) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (member(v0) = v5) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (hAPP(v0, v4, v5, v1) = v6) | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ? [v8] : ? [v9] : ? [v10] : (hBOOL(v9) = v10 & hBOOL(v7) = v8 & hAPP(v0, bool, v2, v1) = v9 & ( ~ (v8 = 0) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (member(v0) = v5) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (hAPP(v0, v4, v5, v1) = v6) | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ? [v8] : ? [v9] : ? [v10] : (hBOOL(v8) = v9 & hBOOL(v7) = v10 & hAPP(v0, bool, v2, v1) = v8 & ( ~ (v9 = 0) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (fun(v0, v1) = v4) | ~ (ti(v4, v3) = v6) | ~ (ti(v4, v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = v8) & hAPP(v0, v1, v3, v7) = v9 & hAPP(v0, v1, v2, v7) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v2, v3, v4, v1) = v5) | ~ (hAPP(v2, bool, v5, v1) = v6) | ~ (hoare_509422987triple(v0) = v2) | ~ (fun(v2, bool) = v3) | ~ (equal_equal(v2) = v4) | hBOOL(v6) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v3, v4, v1) = v5) | ~ (hAPP(v0, bool, v5, v2) = v6) | ~ (fequal(v0) = v4) | ~ (fun(v0, bool) = v3) | ? [v7] : ? [v8] : ? [v9] : (hBOOL(v6) = v9 & ti(v0, v2) = v8 & ti(v0, v1) = v7 & ( ~ (v8 = v7) | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v3, v4, v1) = v5) | ~ (hAPP(v0, bool, v5, v2) = v6) | ~ (fequal(v0) = v4) | ~ (fun(v0, bool) = v3) | ? [v7] : ? [v8] : ? [v9] : (hBOOL(v6) = v7 & ti(v0, v2) = v9 & ti(v0, v1) = v8 & ( ~ (v7 = 0) | v9 = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v3, v4, v1) = v5) | ~ (hAPP(v0, bool, v5, v2) = v6) | ~ (induct_equal(v0) = v4) | ~ (fun(v0, bool) = v3) | ? [v7] : ? [v8] : ? [v9] : (hBOOL(v6) = v9 & ti(v0, v2) = v8 & ti(v0, v1) = v7 & ( ~ (v8 = v7) | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v3, v4, v1) = v5) | ~ (hAPP(v0, bool, v5, v2) = v6) | ~ (induct_equal(v0) = v4) | ~ (fun(v0, bool) = v3) | ? [v7] : ? [v8] : ? [v9] : (hBOOL(v6) = v7 & ti(v0, v2) = v9 & ti(v0, v1) = v8 & ( ~ (v7 = 0) | v9 = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v1, v5, v3) = v6) | ~ (fun(v0, v1) = v4) | ~ (ti(v4, v2) = v5) | hAPP(v0, v1, v2, v3) = v6) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (member(v0) = v4) | ~ (fun(v1, bool) = v2) | ~ (fun(v0, v2) = v3) | ~ (fun(v0, bool) = v1) | ~ (ti(v3, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (hAPP(v1, v0, v2, v3) = v4) | ~ (ti(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (hAPP(v5, v4, v3, v2) = v1) | ~ (hAPP(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (hAPP(v0, v1, v2, v4) = v5) | ~ (ti(v0, v3) = v4) | hAPP(v0, v1, v2, v3) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (fequal(v0) = v3) | ~ (fun(v0, v1) = v2) | ~ (fun(v0, bool) = v1) | ~ (ti(v2, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (collect(v0) = v3) | ~ (fun(v1, v1) = v2) | ~ (fun(v0, bool) = v1) | ~ (ti(v2, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (induct_equal(v0) = v3) | ~ (fun(v0, v1) = v2) | ~ (fun(v0, bool) = v1) | ~ (ti(v2, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (fun(v0, v1) = v2) | ~ (fun(v0, bool) = v1) | ~ (equal_equal(v0) = v3) | ~ (ti(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & cl_HOL_Oequal(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (hAPP(v3, bool, v2, v1) = v4) | ~ (hoare_509422987triple(v0) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (member(v9) = v12 & hBOOL(v4) = v17 & hAPP(v10, v10, v13, v14) = v15 & collect(v9) = v13 & hoare_1580379338ep_set(v0) = v14 & sum_sum(state, v0) = v7 & sum_sum(com, v5) = v6 & node(v6, v7) = v8 & hoare_244953527triple(v0) = v16 & fun(v10, bool) = v11 & fun(v9, bool) = v10 & fun(v8, bool) = v9 & fun(v0, all_0_7_7) = v5 & (v17 = 0 | (v21 = 0 & ~ (v24 = 0) & hBOOL(v23) = v24 & hBOOL(v20) = 0 & hAPP(v10, bool, v19, v15) = v20 & hAPP(v9, v11, v12, v18) = v19 & hAPP(v9, v3, v16, v18) = v22 & hAPP(v3, bool, v2, v22) = v23)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (hAPP(v2, v2, v3, v1) = v4) | ~ (collect(v0) = v3) | ~ (fun(v0, bool) = v2) | ti(v2, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (ti(v0, v2) = v3) | ~ (ti(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (type_definition(v3, v2) = v1) | ~ (type_definition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum_sum(v3, v2) = v1) | ~ (sum_sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (node(v3, v2) = v1) | ~ (node(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (fun(v3, v2) = v1) | ~ (fun(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ti(v3, v2) = v1) | ~ (ti(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (undefined(v0) = v1) | ~ (ti(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (enum(v2) = v1) | ~ (enum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (member(v2) = v1) | ~ (member(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (fequal(v2) = v1) | ~ (fequal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (collect(v2) = v1) | ~ (collect(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hoare_1580379338ep_set(v2) = v1) | ~ (hoare_1580379338ep_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hoare_2037801986triple(v2) = v1) | ~ (hoare_2037801986triple(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hoare_509422987triple(v2) = v1) | ~ (hoare_509422987triple(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hoare_244953527triple(v2) = v1) | ~ (hoare_244953527triple(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (undefined(v2) = v1) | ~ (undefined(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (induct_equal(v2) = v1) | ~ (induct_equal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equal_equal(v2) = v1) | ~ (equal_equal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cl_HOL_Oequal(v2) = v1) | ~ (cl_HOL_Oequal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_sum(v0, v1) = v2) | cl_HOL_Oequal(v2) = 0) & ! [v0] : ! [v1] : (v1 = all_0_4_4 | ~ (ti(state, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (enum(v1) = 0) | ~ (enum(v0) = 0) | ? [v2] : (enum(v2) = 0 & sum_sum(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (enum(v1) = 0) | ~ (enum(v0) = 0) | ? [v2] : (enum(v2) = 0 & fun(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (enum(v0) = 0) | ~ (cl_HOL_Oequal(v1) = 0) | ? [v2] : (fun(v0, v1) = v2 & cl_HOL_Oequal(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (fequal(v0) = v1) | ? [v2] : ? [v3] : (equal_equal(v0) = v3 & cl_HOL_Oequal(v0) = v2 & ( ~ (v2 = 0) | v3 = v1))) & ! [v0] : ! [v1] : ( ~ (hoare_509422987triple(v0) = v1) | cl_HOL_Oequal(v1) = 0) & ! [v0] : ! [v1] : ( ~ (fun(v0, bool) = v1) | ? [v2] : ? [v3] : (equal_equal(v0) = v3 & cl_HOL_Oequal(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v1, v3, v4) = v5) | ~ (hAPP(v0, bool, v5, v4) = v6) | hBOOL(v6) = 0)))) & ! [v0] : ! [v1] : ( ~ (fun(v0, bool) = v1) | ? [v2] : ? [v3] : (equal_equal(v0) = v3 & cl_HOL_Oequal(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (hAPP(v0, v1, v3, v4) = v6) | ~ (hAPP(v0, bool, v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : (hBOOL(v7) = v10 & ti(v0, v5) = v9 & ti(v0, v4) = v8 & ( ~ (v9 = v8) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (hAPP(v0, v1, v3, v4) = v6) | ~ (hAPP(v0, bool, v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : (hBOOL(v7) = v8 & ti(v0, v5) = v10 & ti(v0, v4) = v9 & ( ~ (v8 = 0) | v10 = v9))))))) & ! [v0] : ! [v1] : ( ~ (ti(bool, v0) = v1) | ? [v2] : ? [v3] : (hBOOL(v1) = v3 & hBOOL(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (ti(bool, v0) = v1) | ? [v2] : ? [v3] : (hBOOL(v1) = v2 & hBOOL(v0) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 22.68/6.78 |
% 22.68/6.78 | Applying alpha-rule on (1) yields:
% 22.68/6.78 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (undefined(v2) = v1) | ~ (undefined(v2) = v0))
% 22.68/6.78 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (fequal(v0) = v3) | ~ (fun(v0, v1) = v2) | ~ (fun(v0, bool) = v1) | ~ (ti(v2, v3) = v4))
% 22.68/6.78 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (sum_sum(state, v0) = v3) | ~ (sum_sum(com, v1) = v2) | ~ (node(v2, v3) = v4) | ~ (hoare_509422987triple(v0) = v6) | ~ (hoare_244953527triple(v0) = v8) | ~ (fun(v5, v6) = v7) | ~ (fun(v4, bool) = v5) | ~ (fun(v0, all_0_7_7) = v1) | ~ (ti(v7, v8) = v9))
% 22.68/6.78 | (5) ! [v0] : ! [v1] : ( ~ (fun(v0, bool) = v1) | ? [v2] : ? [v3] : (equal_equal(v0) = v3 & cl_HOL_Oequal(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (hAPP(v0, v1, v3, v4) = v6) | ~ (hAPP(v0, bool, v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : (hBOOL(v7) = v10 & ti(v0, v5) = v9 & ti(v0, v4) = v8 & ( ~ (v9 = v8) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (hAPP(v0, v1, v3, v4) = v6) | ~ (hAPP(v0, bool, v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : (hBOOL(v7) = v8 & ti(v0, v5) = v10 & ti(v0, v4) = v9 & ( ~ (v8 = 0) | v10 = v9)))))))
% 22.68/6.78 | (6) ! [v0] : ! [v1] : ( ~ (ti(bool, v0) = v1) | ? [v2] : ? [v3] : (hBOOL(v1) = v3 & hBOOL(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.68/6.78 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (member(v6) = v9) | ~ (hAPP(v7, v7, v11, v12) = v13) | ~ (hAPP(v7, bool, v10, v13) = v14) | ~ (hAPP(v6, v8, v9, v1) = v10) | ~ (collect(v6) = v11) | ~ (hoare_1580379338ep_set(v0) = v12) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (fun(v7, bool) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, bool) = v6) | ~ (fun(v0, all_0_7_7) = v2) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (hBOOL(v14) = v15 & hoare_2037801986triple(v0) = v17 & hoare_509422987triple(v0) = v16 & ( ~ (v15 = 0) | (v19 = v1 & hAPP(v16, v6, v17, v18) = v1))))
% 22.68/6.78 | (8) hBOOL(induct_false) = all_0_6_6
% 22.68/6.78 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (hAPP(v1, v0, v3, v2) = v15) | ~ (hAPP(v0, v1, v4, v15) = v16) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ? [v17] : ? [v18] : (hBOOL(v14) = v17 & ti(v1, v2) = v18 & ( ~ (v17 = 0) | v18 = v16)))
% 22.68/6.78 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (member(v0) = v15) | ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v17, v5) = v18) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (hAPP(v1, v0, v3, v2) = v16) | ~ (hAPP(v0, v8, v15, v16) = v17) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ? [v19] : ? [v20] : (hBOOL(v18) = v20 & hBOOL(v14) = v19 & ( ~ (v19 = 0) | v20 = 0)))
% 23.09/6.78 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (member(v0) = v16) | ~ (hAPP(v10, v11, v12, v4) = v13) | ~ (hAPP(v8, v9, v13, v5) = v14) | ~ (hAPP(v7, bool, v19, v6) = v20) | ~ (hAPP(v7, bool, v17, v6) = v18) | ~ (hAPP(v7, bool, v14, v6) = v15) | ~ (hAPP(v0, v9, v16, v3) = v17) | ~ (hAPP(v0, v9, v16, v2) = v19) | ~ (type_definition(v1, v0) = v12) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, bool) = v9) | ~ (fun(v1, v0) = v10) | ~ (fun(v0, v1) = v8) | ~ (fun(v0, bool) = v7) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (hBOOL(v20) = v23 & hBOOL(v18) = v22 & hBOOL(v15) = v21 & hAPP(v0, v1, v5, v3) = v24 & hAPP(v0, v1, v5, v2) = v25 & ti(v0, v3) = v26 & ti(v0, v2) = v27 & ( ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | (( ~ (v27 = v26) | v25 = v24) & ( ~ (v25 = v24) | v27 = v26)))))
% 23.09/6.78 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (collect(v0) = v3) | ~ (fun(v1, v1) = v2) | ~ (fun(v0, bool) = v1) | ~ (ti(v2, v3) = v4))
% 23.09/6.78 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equal_equal(v2) = v1) | ~ (equal_equal(v2) = v0))
% 23.09/6.78 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v3, v4, v1) = v5) | ~ (hAPP(v0, bool, v5, v2) = v6) | ~ (induct_equal(v0) = v4) | ~ (fun(v0, bool) = v3) | ? [v7] : ? [v8] : ? [v9] : (hBOOL(v6) = v9 & ti(v0, v2) = v8 & ti(v0, v1) = v7 & ( ~ (v8 = v7) | v9 = 0)))
% 23.09/6.78 | (15) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (hAPP(v7, v7, v8, v9) = v10) | ~ (collect(v6) = v8) | ~ (hoare_1580379338ep_set(v1) = v9) | ~ (sum_sum(state, v1) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, bool) = v6) | ~ (fun(v1, all_0_7_7) = v2) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (member(v6) = v14 & hBOOL(v17) = 0 & hAPP(v7, bool, v16, v10) = v17 & hAPP(v6, v13, v14, v15) = v16 & hAPP(v6, v11, v12, v15) = v0 & hoare_509422987triple(v1) = v11 & hoare_244953527triple(v1) = v12 & fun(v7, bool) = v13))
% 23.09/6.79 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v2 = v1 | ~ (hAPP(v3, v8, v9, v2) = v10) | ~ (hAPP(v3, v8, v9, v1) = v10) | ~ (hoare_2037801986triple(v0) = v9) | ~ (sum_sum(state, v0) = v6) | ~ (sum_sum(com, v4) = v5) | ~ (node(v5, v6) = v7) | ~ (hoare_509422987triple(v0) = v3) | ~ (fun(v7, bool) = v8) | ~ (fun(v0, all_0_7_7) = v4))
% 23.09/6.79 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v1, v5, v3) = v6) | ~ (fun(v0, v1) = v4) | ~ (ti(v4, v2) = v5) | hAPP(v0, v1, v2, v3) = v6)
% 23.09/6.79 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0))
% 23.09/6.79 | (19) ti(state, all_0_2_2) = all_0_0_0
% 23.09/6.79 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (hAPP(v3, bool, v2, v1) = v4) | ~ (hoare_509422987triple(v0) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (member(v9) = v12 & hBOOL(v4) = v17 & hAPP(v10, v10, v13, v14) = v15 & collect(v9) = v13 & hoare_1580379338ep_set(v0) = v14 & sum_sum(state, v0) = v7 & sum_sum(com, v5) = v6 & node(v6, v7) = v8 & hoare_244953527triple(v0) = v16 & fun(v10, bool) = v11 & fun(v9, bool) = v10 & fun(v8, bool) = v9 & fun(v0, all_0_7_7) = v5 & (v17 = 0 | (v21 = 0 & ~ (v24 = 0) & hBOOL(v23) = v24 & hBOOL(v20) = 0 & hAPP(v10, bool, v19, v15) = v20 & hAPP(v9, v11, v12, v18) = v19 & hAPP(v9, v3, v16, v18) = v22 & hAPP(v3, bool, v2, v22) = v23))))
% 23.09/6.79 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (member(v2) = v1) | ~ (member(v2) = v0))
% 23.09/6.79 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hoare_2037801986triple(v2) = v1) | ~ (hoare_2037801986triple(v2) = v0))
% 23.09/6.79 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (hAPP(v10, v11, v12, v4) = v13) | ~ (hAPP(v8, v9, v13, v5) = v14) | ~ (hAPP(v7, bool, v14, v6) = v15) | ~ (hAPP(v0, bool, v2, v3) = v16) | ~ (type_definition(v1, v0) = v12) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, bool) = v9) | ~ (fun(v1, v0) = v10) | ~ (fun(v0, v1) = v8) | ~ (fun(v0, bool) = v7) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v20 = 0) & hBOOL(v19) = v20 & hAPP(v1, v0, v4, v17) = v18 & hAPP(v0, bool, v2, v18) = v19) | (member(v0) = v18 & hBOOL(v20) = v21 & hBOOL(v16) = v22 & hBOOL(v15) = v17 & hAPP(v7, bool, v19, v6) = v20 & hAPP(v0, v9, v18, v3) = v19 & ( ~ (v21 = 0) | ~ (v17 = 0) | v22 = 0))))
% 23.09/6.79 | (24) ti(state, all_0_5_5) = all_0_4_4
% 23.09/6.79 | (25) ti(bool, induct_false) = induct_false
% 23.09/6.79 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (hAPP(v2, v7, v8, v1) = v10) | ~ (hAPP(v2, v7, v8, v1) = v9) | ~ (hoare_2037801986triple(v0) = v8) | ~ (sum_sum(state, v0) = v5) | ~ (sum_sum(com, v3) = v4) | ~ (node(v4, v5) = v6) | ~ (hoare_509422987triple(v0) = v2) | ~ (fun(v6, bool) = v7) | ~ (fun(v0, all_0_7_7) = v3))
% 23.09/6.79 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (induct_equal(v2) = v1) | ~ (induct_equal(v2) = v0))
% 23.09/6.79 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (member(v0) = v5) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (hAPP(v0, v4, v5, v1) = v6) | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ? [v8] : ? [v9] : ? [v10] : (hBOOL(v8) = v9 & hBOOL(v7) = v10 & hAPP(v0, bool, v2, v1) = v8 & ( ~ (v9 = 0) | v10 = 0)))
% 23.09/6.79 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (node(v3, v2) = v1) | ~ (node(v3, v2) = v0))
% 23.09/6.79 | (30) cl_HOL_Oequal(bool) = 0
% 23.09/6.79 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (ti(v0, v2) = v3) | ~ (ti(v0, v1) = v2))
% 23.09/6.79 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (collect(v2) = v1) | ~ (collect(v2) = v0))
% 23.09/6.79 | (33) ! [v0] : ! [v1] : ( ~ (enum(v0) = 0) | ~ (cl_HOL_Oequal(v1) = 0) | ? [v2] : (fun(v0, v1) = v2 & cl_HOL_Oequal(v2) = 0))
% 23.09/6.79 | (34) hBOOL(induct_true) = 0
% 23.09/6.79 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (enum(v2) = v1) | ~ (enum(v2) = v0))
% 23.09/6.79 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v2 = v1 | ~ (hAPP(v3, v4, v5, v1) = v6) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (hoare_509422987triple(v0) = v3) | ~ (fun(v3, bool) = v4) | ~ (equal_equal(v3) = v5) | ? [v8] : ( ~ (v8 = 0) & hBOOL(v7) = v8))
% 23.09/6.79 | (37) ! [v0] : ! [v1] : ( ~ (fun(v0, bool) = v1) | ? [v2] : ? [v3] : (equal_equal(v0) = v3 & cl_HOL_Oequal(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v1, v3, v4) = v5) | ~ (hAPP(v0, bool, v5, v4) = v6) | hBOOL(v6) = 0))))
% 23.09/6.79 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (hoare_1580379338ep_set(v0) = v7) | ~ (sum_sum(state, v0) = v3) | ~ (sum_sum(com, v1) = v2) | ~ (node(v2, v3) = v4) | ~ (fun(v5, bool) = v6) | ~ (fun(v4, bool) = v5) | ~ (fun(v0, all_0_7_7) = v1) | ~ (ti(v6, v7) = v8))
% 23.09/6.79 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (member(v6) = v9) | ~ (hAPP(v10, v6, v11, v1) = v12) | ~ (hAPP(v7, v7, v14, v15) = v16) | ~ (hAPP(v7, bool, v13, v16) = v17) | ~ (hAPP(v6, v8, v9, v12) = v13) | ~ (collect(v6) = v14) | ~ (hoare_1580379338ep_set(v0) = v15) | ~ (hoare_2037801986triple(v0) = v11) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (hoare_509422987triple(v0) = v10) | ~ (fun(v7, bool) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, bool) = v6) | ~ (fun(v0, all_0_7_7) = v2) | hBOOL(v17) = 0)
% 23.09/6.79 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (hAPP(v5, v4, v3, v2) = v1) | ~ (hAPP(v5, v4, v3, v2) = v0))
% 23.09/6.79 | (41) enum(bool) = 0
% 23.09/6.79 | (42) ~ (all_0_0_0 = all_0_1_1)
% 23.09/6.79 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (hAPP(v10, v11, v12, v4) = v13) | ~ (hAPP(v8, v9, v13, v5) = v14) | ~ (hAPP(v7, bool, v14, v6) = v15) | ~ (type_definition(v1, v0) = v12) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, bool) = v9) | ~ (fun(v1, v0) = v10) | ~ (fun(v0, v1) = v8) | ~ (fun(v0, bool) = v7) | ~ (ti(v1, v3) = v17) | ~ (ti(v1, v2) = v16) | ? [v18] : ? [v19] : ? [v20] : (hBOOL(v15) = v18 & hAPP(v1, v0, v4, v3) = v20 & hAPP(v1, v0, v4, v2) = v19 & ( ~ (v18 = 0) | (( ~ (v20 = v19) | v17 = v16) & ( ~ (v17 = v16) | v20 = v19)))))
% 23.09/6.80 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v1 | ~ (hAPP(v7, v6, v9, v1) = v10) | ~ (hAPP(v6, v7, v8, v10) = v11) | ~ (hoare_2037801986triple(v0) = v9) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (hoare_509422987triple(v0) = v7) | ~ (hoare_244953527triple(v0) = v8) | ~ (fun(v5, bool) = v6) | ~ (fun(v0, all_0_7_7) = v2))
% 23.09/6.80 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (hAPP(v2, v2, v3, v1) = v4) | ~ (collect(v0) = v3) | ~ (fun(v0, bool) = v2) | ti(v2, v1) = v4)
% 23.09/6.80 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (fun(v3, v2) = v1) | ~ (fun(v3, v2) = v0))
% 23.09/6.80 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ~ (ti(v1, v2) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (member(v0) = v17 & hBOOL(v14) = v16 & ( ~ (v16 = 0) | (v22 = 0 & v19 = v15 & hBOOL(v21) = 0 & hAPP(v6, bool, v20, v5) = v21 & hAPP(v0, v8, v17, v18) = v20 & hAPP(v0, v1, v4, v18) = v15))))
% 23.09/6.80 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hoare_244953527triple(v2) = v1) | ~ (hoare_244953527triple(v2) = v0))
% 23.09/6.80 | (49) ! [v0] : ! [v1] : ( ~ (ti(bool, v0) = v1) | ? [v2] : ? [v3] : (hBOOL(v1) = v2 & hBOOL(v0) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 23.09/6.80 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ti(v3, v2) = v1) | ~ (ti(v3, v2) = v0))
% 23.09/6.80 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (fun(v0, v1) = v4) | ~ (ti(v4, v3) = v6) | ~ (ti(v4, v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = v8) & hAPP(v0, v1, v3, v7) = v9 & hAPP(v0, v1, v2, v7) = v8))
% 23.09/6.80 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (induct_equal(v0) = v3) | ~ (fun(v0, v1) = v2) | ~ (fun(v0, bool) = v1) | ~ (ti(v2, v3) = v4))
% 23.09/6.80 | (53) fun(state, bool) = all_0_7_7
% 23.09/6.80 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (member(v0) = v5) | ~ (hAPP(v3, bool, v6, v2) = v7) | ~ (hAPP(v0, v4, v5, v1) = v6) | ~ (fun(v3, bool) = v4) | ~ (fun(v0, bool) = v3) | ? [v8] : ? [v9] : ? [v10] : (hBOOL(v9) = v10 & hBOOL(v7) = v8 & hAPP(v0, bool, v2, v1) = v9 & ( ~ (v8 = 0) | v10 = 0)))
% 23.09/6.80 | (55) ~ (all_0_6_6 = 0)
% 23.09/6.80 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (fequal(v2) = v1) | ~ (fequal(v2) = v0))
% 23.09/6.80 | (57) cl_HOL_Oequal(com) = 0
% 23.09/6.80 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hoare_1580379338ep_set(v2) = v1) | ~ (hoare_1580379338ep_set(v2) = v0))
% 23.09/6.80 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (member(v0) = v15) | ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v16, v5) = v17) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (hAPP(v0, v8, v15, v2) = v16) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (hBOOL(v17) = v19 & hBOOL(v14) = v18 & ti(v0, v2) = v20 & ( ~ (v19 = 0) | ~ (v18 = 0) | (v22 = v20 & hAPP(v1, v0, v3, v21) = v20))))
% 23.09/6.80 | (60) ti(bool, induct_true) = induct_true
% 23.09/6.80 | (61) cl_HOL_Oequal(state) = 0
% 23.09/6.80 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (type_definition(v3, v2) = v1) | ~ (type_definition(v3, v2) = v0))
% 23.09/6.80 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (type_definition(v0, v1) = v8) | ~ (fun(v4, bool) = v5) | ~ (fun(v3, v5) = v6) | ~ (fun(v2, v6) = v7) | ~ (fun(v1, v0) = v3) | ~ (fun(v1, bool) = v4) | ~ (fun(v0, v1) = v2) | ~ (ti(v7, v8) = v9))
% 23.09/6.80 | (64) ! [v0] : ! [v1] : ( ~ (enum(v1) = 0) | ~ (enum(v0) = 0) | ? [v2] : (enum(v2) = 0 & fun(v0, v1) = v2))
% 23.09/6.80 | (65) ! [v0] : ! [v1] : ( ~ (enum(v1) = 0) | ~ (enum(v0) = 0) | ? [v2] : (enum(v2) = 0 & sum_sum(v0, v1) = v2))
% 23.09/6.80 | (66) ! [v0] : ! [v1] : ( ~ (fequal(v0) = v1) | ? [v2] : ? [v3] : (equal_equal(v0) = v3 & cl_HOL_Oequal(v0) = v2 & ( ~ (v2 = 0) | v3 = v1)))
% 23.09/6.80 | (67) ! [v0] : ! [v1] : (v1 = all_0_4_4 | ~ (ti(state, v0) = v1))
% 23.09/6.80 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (undefined(v0) = v1) | ~ (ti(v0, v1) = v2))
% 23.09/6.80 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cl_HOL_Oequal(v2) = v1) | ~ (cl_HOL_Oequal(v2) = v0))
% 23.09/6.80 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (member(v6) = v9) | ~ (hAPP(v7, v7, v11, v12) = v13) | ~ (hAPP(v7, bool, v10, v13) = v14) | ~ (hAPP(v6, v8, v9, v1) = v10) | ~ (collect(v6) = v11) | ~ (hoare_1580379338ep_set(v0) = v12) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (fun(v7, bool) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v5, bool) = v6) | ~ (fun(v0, all_0_7_7) = v2) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (hBOOL(v14) = v15 & hAPP(v16, v6, v17, v19) = v20 & hAPP(v6, v16, v18, v1) = v19 & hoare_2037801986triple(v0) = v17 & hoare_509422987triple(v0) = v16 & hoare_244953527triple(v0) = v18 & ( ~ (v15 = 0) | v20 = v1)))
% 23.09/6.80 | (71) hBOOL(hoare_1883395792gleton) = 0
% 23.09/6.80 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (member(v7) = v10) | ~ (hAPP(v8, v8, v12, v13) = v14) | ~ (hAPP(v8, bool, v16, v14) = v17) | ~ (hAPP(v8, bool, v11, v14) = v15) | ~ (hAPP(v7, v9, v10, v2) = v11) | ~ (hAPP(v7, v9, v10, v1) = v16) | ~ (collect(v7) = v12) | ~ (hoare_1580379338ep_set(v0) = v13) | ~ (sum_sum(state, v0) = v5) | ~ (sum_sum(com, v3) = v4) | ~ (node(v4, v5) = v6) | ~ (fun(v8, bool) = v9) | ~ (fun(v7, bool) = v8) | ~ (fun(v6, bool) = v7) | ~ (fun(v0, all_0_7_7) = v3) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (hBOOL(v17) = v19 & hBOOL(v15) = v18 & hAPP(v7, v20, v21, v2) = v22 & hAPP(v7, v20, v21, v1) = v23 & hoare_509422987triple(v0) = v20 & hoare_244953527triple(v0) = v21 & ( ~ (v19 = 0) | ~ (v18 = 0) | (( ~ (v23 = v22) | v2 = v1) & ( ~ (v2 = v1) | v23 = v22)))))
% 23.09/6.81 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum_sum(v3, v2) = v1) | ~ (sum_sum(v3, v2) = v0))
% 23.09/6.81 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hoare_509422987triple(v2) = v1) | ~ (hoare_509422987triple(v2) = v0))
% 23.09/6.81 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (member(v0) = v4) | ~ (fun(v1, bool) = v2) | ~ (fun(v0, v2) = v3) | ~ (fun(v0, bool) = v1) | ~ (ti(v3, v4) = v5))
% 23.09/6.81 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_sum(v0, v1) = v2) | cl_HOL_Oequal(v2) = 0)
% 23.09/6.81 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v3, v4, v1) = v5) | ~ (hAPP(v0, bool, v5, v2) = v6) | ~ (induct_equal(v0) = v4) | ~ (fun(v0, bool) = v3) | ? [v7] : ? [v8] : ? [v9] : (hBOOL(v6) = v7 & ti(v0, v2) = v9 & ti(v0, v1) = v8 & ( ~ (v7 = 0) | v9 = v8)))
% 23.09/6.81 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (hAPP(v0, v1, v2, v4) = v5) | ~ (ti(v0, v3) = v4) | hAPP(v0, v1, v2, v3) = v5)
% 23.09/6.81 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (hAPP(v7, bool, v1, v2) = v8) | ~ (sum_sum(state, v0) = v5) | ~ (sum_sum(com, v3) = v4) | ~ (node(v4, v5) = v6) | ~ (fun(v6, bool) = v7) | ~ (fun(v0, all_0_7_7) = v3) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (member(v7) = v11 & hBOOL(v16) = v17 & hBOOL(v8) = v20 & hAPP(v9, v9, v13, v14) = v15 & hAPP(v9, bool, v12, v15) = v16 & hAPP(v7, v10, v11, v2) = v12 & collect(v7) = v13 & hoare_1580379338ep_set(v0) = v14 & hoare_2037801986triple(v0) = v19 & hoare_509422987triple(v0) = v18 & fun(v9, bool) = v10 & fun(v7, bool) = v9 & ( ~ (v17 = 0) | v20 = 0 | ( ~ (v24 = 0) & hBOOL(v23) = v24 & hAPP(v18, v7, v19, v21) = v22 & hAPP(v7, bool, v1, v22) = v23))))
% 23.09/6.81 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v3, v4, v1) = v5) | ~ (hAPP(v0, bool, v5, v2) = v6) | ~ (fequal(v0) = v4) | ~ (fun(v0, bool) = v3) | ? [v7] : ? [v8] : ? [v9] : (hBOOL(v6) = v9 & ti(v0, v2) = v8 & ti(v0, v1) = v7 & ( ~ (v8 = v7) | v9 = 0)))
% 23.09/6.81 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (hoare_2037801986triple(v0) = v8) | ~ (sum_sum(state, v0) = v4) | ~ (sum_sum(com, v2) = v3) | ~ (node(v3, v4) = v5) | ~ (hoare_509422987triple(v0) = v1) | ~ (fun(v5, bool) = v6) | ~ (fun(v1, v6) = v7) | ~ (fun(v0, all_0_7_7) = v2) | ~ (ti(v7, v8) = v9))
% 23.09/6.81 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (hAPP(v10, v11, v12, v4) = v13) | ~ (hAPP(v8, v9, v13, v5) = v14) | ~ (hAPP(v7, bool, v14, v6) = v15) | ~ (hAPP(v1, bool, v3, v2) = v16) | ~ (type_definition(v1, v0) = v12) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, bool) = v9) | ~ (fun(v1, v0) = v10) | ~ (fun(v0, v1) = v8) | ~ (fun(v0, bool) = v7) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (member(v0) = v18 & hBOOL(v16) = v19 & hBOOL(v15) = v17 & ( ~ (v17 = 0) | v19 = 0 | (v23 = 0 & ~ (v26 = 0) & hBOOL(v25) = v26 & hBOOL(v22) = 0 & hAPP(v7, bool, v21, v6) = v22 & hAPP(v1, bool, v3, v24) = v25 & hAPP(v0, v9, v18, v20) = v21 & hAPP(v0, v1, v5, v20) = v24))))
% 23.09/6.81 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v2, v3, v4, v1) = v5) | ~ (hAPP(v2, bool, v5, v1) = v6) | ~ (hoare_509422987triple(v0) = v2) | ~ (fun(v2, bool) = v3) | ~ (equal_equal(v2) = v4) | hBOOL(v6) = 0)
% 23.09/6.81 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (hAPP(v0, v3, v4, v1) = v5) | ~ (hAPP(v0, bool, v5, v2) = v6) | ~ (fequal(v0) = v4) | ~ (fun(v0, bool) = v3) | ? [v7] : ? [v8] : ? [v9] : (hBOOL(v6) = v7 & ti(v0, v2) = v9 & ti(v0, v1) = v8 & ( ~ (v7 = 0) | v9 = v8)))
% 23.09/6.81 | (85) ! [v0] : ! [v1] : ( ~ (hoare_509422987triple(v0) = v1) | cl_HOL_Oequal(v1) = 0)
% 23.09/6.81 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (hAPP(v1, v0, v2, v3) = v4) | ~ (ti(v0, v4) = v5))
% 23.09/6.81 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (hAPP(v10, v11, v12, v13) = v14) | ~ (hAPP(v8, v9, v14, v15) = v16) | ~ (hAPP(v6, v6, v17, v18) = v19) | ~ (hAPP(v6, bool, v16, v19) = v20) | ~ (type_definition(v7, v5) = v12) | ~ (collect(v5) = v17) | ~ (hoare_1580379338ep_set(v0) = v18) | ~ (hoare_2037801986triple(v0) = v13) | ~ (sum_sum(state, v0) = v3) | ~ (sum_sum(com, v1) = v2) | ~ (node(v2, v3) = v4) | ~ (hoare_509422987triple(v0) = v7) | ~ (hoare_244953527triple(v0) = v15) | ~ (fun(v8, v9) = v11) | ~ (fun(v7, v5) = v10) | ~ (fun(v6, bool) = v9) | ~ (fun(v5, v7) = v8) | ~ (fun(v5, bool) = v6) | ~ (fun(v4, bool) = v5) | ~ (fun(v0, all_0_7_7) = v1) | hBOOL(v20) = 0)
% 23.09/6.81 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (member(v0) = v15) | ~ (hAPP(v9, v10, v11, v3) = v12) | ~ (hAPP(v7, v8, v12, v4) = v13) | ~ (hAPP(v6, bool, v16, v5) = v17) | ~ (hAPP(v6, bool, v13, v5) = v14) | ~ (hAPP(v0, v8, v15, v2) = v16) | ~ (type_definition(v1, v0) = v11) | ~ (fun(v7, v8) = v10) | ~ (fun(v6, bool) = v8) | ~ (fun(v1, v0) = v9) | ~ (fun(v0, v1) = v7) | ~ (fun(v0, bool) = v6) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (hBOOL(v17) = v19 & hBOOL(v14) = v18 & hAPP(v1, v0, v3, v20) = v21 & hAPP(v0, v1, v4, v2) = v20 & ti(v0, v2) = v22 & ( ~ (v19 = 0) | ~ (v18 = 0) | v22 = v21)))
% 23.09/6.81 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (fun(v0, v1) = v2) | ~ (fun(v0, bool) = v1) | ~ (equal_equal(v0) = v3) | ~ (ti(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & cl_HOL_Oequal(v0) = v5))
% 23.09/6.81 | (90) ti(bool, hoare_1883395792gleton) = hoare_1883395792gleton
% 23.09/6.82 | (91) ti(state, all_0_3_3) = all_0_1_1
% 23.09/6.82 |
% 23.09/6.82 | Instantiating formula (67) with all_0_0_0, all_0_2_2 and discharging atoms ti(state, all_0_2_2) = all_0_0_0, yields:
% 23.09/6.82 | (92) all_0_0_0 = all_0_4_4
% 23.09/6.82 |
% 23.09/6.82 | Instantiating formula (67) with all_0_1_1, all_0_3_3 and discharging atoms ti(state, all_0_3_3) = all_0_1_1, yields:
% 23.09/6.82 | (93) all_0_1_1 = all_0_4_4
% 23.09/6.82 |
% 23.09/6.82 | Equations (92,93) can reduce 42 to:
% 23.09/6.82 | (94) $false
% 23.09/6.82 |
% 23.09/6.82 |-The branch is then unsatisfiable
% 23.09/6.82 % SZS output end Proof for theBenchmark
% 23.09/6.82
% 23.09/6.82 6231ms
%------------------------------------------------------------------------------