%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KRS179+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n027.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 : Sun Jul 17 02:56:48 EDT 2022

% Result   : Theorem 9.79s 2.99s
% Output   : Proof 11.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KRS179+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jun  7 06:17:40 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.53/0.58          ____       _                          
% 0.53/0.58    ___  / __ \_____(_)___  ________  __________
% 0.53/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.53/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.53/0.58  
% 0.53/0.58  A Theorem Prover for First-Order Logic
% 0.53/0.58  (ePrincess v.1.0)
% 0.53/0.58  
% 0.53/0.58  (c) Philipp Rümmer, 2009-2015
% 0.53/0.58  (c) Peter Backeman, 2014-2015
% 0.53/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.58  Bug reports to peter@backeman.se
% 0.53/0.58  
% 0.53/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.58  
% 0.53/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.93  Prover 0: Preprocessing ...
% 1.91/1.07  Prover 0: Warning: ignoring some quantifiers
% 2.02/1.09  Prover 0: Constructing countermodel ...
% 9.13/2.84  Prover 0: gave up
% 9.13/2.84  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 9.37/2.86  Prover 1: Preprocessing ...
% 9.79/2.95  Prover 1: Constructing countermodel ...
% 9.79/2.99  Prover 1: proved (151ms)
% 9.79/2.99  
% 9.79/2.99  No countermodel exists, formula is valid
% 9.79/2.99  % SZS status Theorem for theBenchmark
% 9.79/2.99  
% 9.79/2.99  Generating proof ... found it (size 13)
% 11.06/3.21  
% 11.06/3.21  % SZS output start Proof for theBenchmark
% 11.06/3.21  Assumed formulas after preprocessing and simplification: 
% 11.06/3.21  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] :  ? [v25] :  ? [v26] :  ? [v27] : ( ~ (v25 = 0) &  ~ (v14 = 0) &  ~ (v12 = 0) &  ~ (v7 = 0) &  ~ (v3 = 0) & model(v26, v23) = 0 & model(v24, v23) = v25 & model(v21, v17) = 0 & model(v21, v16) = 0 & model(v18, v17) = v20 & model(v18, v16) = v19 & model(v15, v9) = 0 & model(v13, v10) = 0 & model(v13, v9) = v14 & model(v11, v10) = v12 & model(v8, v6) = 0 & model(v4, v6) = v7 & model(v4, v5) = 0 & isa(v1, v2) = 0 & isa(v0, v2) = v3 & isa(v0, v1) = 0 &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] :  ! [v32] : (v32 = 0 |  ~ (xora(v28, v29) = 0) |  ~ (status(v30, v31, v28) = v32) | status(v30, v31, v29) = 0) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] :  ! [v32] : (v30 = 0 |  ~ (nota(v28, v29) = v30) |  ~ (status(v31, v32, v28) = 0) | status(v31, v32, v29) = 0) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] :  ! [v32] : (v30 = 0 |  ~ (mighta(v28, v29) = v30) |  ~ (status(v31, v32, v28) = 0) |  ? [v33] : ( ~ (v33 = 0) & status(v31, v32, v29) = v33)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] :  ! [v32] : (v29 = v28 |  ~ (status(v32, v31, v30) = v29) |  ~ (status(v32, v31, v30) = v28)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : (v31 = 0 |  ~ (not(v29) = v30) |  ~ (model(v28, v30) = v31) | model(v28, v29) = 0) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : (v29 = v28 |  ~ (model(v31, v30) = v29) |  ~ (model(v31, v30) = v28)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : (v29 = v28 |  ~ (xora(v31, v30) = v29) |  ~ (xora(v31, v30) = v28)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : (v29 = v28 |  ~ (nevera(v31, v30) = v29) |  ~ (nevera(v31, v30) = v28)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : (v29 = v28 |  ~ (nota(v31, v30) = v29) |  ~ (nota(v31, v30) = v28)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : (v29 = v28 |  ~ (isa(v31, v30) = v29) |  ~ (isa(v31, v30) = v28)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : (v29 = v28 |  ~ (mighta(v31, v30) = v29) |  ~ (mighta(v31, v30) = v28)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : ( ~ (xora(v28, v29) = 0) |  ~ (status(v30, v31, v28) = 0) |  ? [v32] : ( ~ (v32 = 0) & status(v30, v31, v29) = v32)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : ( ~ (nevera(v28, v29) = 0) |  ~ (status(v30, v31, v28) = 0) |  ? [v32] : ( ~ (v32 = 0) & status(v30, v31, v29) = v32)) &  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : ( ~ (isa(v28, v29) = 0) |  ~ (status(v30, v31, v28) = 0) | status(v30, v31, v29) = 0) &  ! [v28] :  ! [v29] :  ! [v30] : (v30 = 0 |  ~ (xora(v28, v29) = v30) |  ? [v31] :  ? [v32] :  ? [v33] :  ? [v34] : (status(v31, v32, v29) = v34 & status(v31, v32, v28) = v33 & ( ~ (v34 = 0) | v33 = 0) & ( ~ (v33 = 0) | v34 = 0))) &  ! [v28] :  ! [v29] :  ! [v30] : (v30 = 0 |  ~ (nevera(v28, v29) = v30) |  ? [v31] :  ? [v32] : (status(v31, v32, v29) = 0 & status(v31, v32, v28) = 0)) &  ! [v28] :  ! [v29] :  ! [v30] : (v30 = 0 |  ~ (isa(v28, v29) = v30) |  ? [v31] :  ? [v32] :  ? [v33] : ( ~ (v33 = 0) & status(v31, v32, v29) = v33 & status(v31, v32, v28) = 0)) &  ! [v28] :  ! [v29] :  ! [v30] : (v29 = v28 |  ~ (not(v30) = v29) |  ~ (not(v30) = v28)) &  ! [v28] :  ! [v29] :  ! [v30] : ( ~ (not(v29) = v30) |  ~ (model(v28, v30) = 0) |  ? [v31] : ( ~ (v31 = 0) & model(v28, v29) = v31)) &  ! [v28] :  ! [v29] : (v29 = 0 |  ~ (model(v28, v27) = v29)) &  ! [v28] :  ! [v29] : ( ~ (nota(v28, v29) = 0) |  ? [v30] :  ? [v31] :  ? [v32] : ( ~ (v32 = 0) & status(v30, v31, v29) = v32 & status(v30, v31, v28) = 0)) &  ! [v28] :  ! [v29] : ( ~ (mighta(v28, v29) = 0) |  ? [v30] :  ? [v31] : (status(v30, v31, v29) = 0 & status(v30, v31, v28) = 0)) &  ! [v28] :  ~ (model(v28, v22) = 0) &  ! [v28] : ( ~ (model(v28, v9) = 0) | model(v28, v10) = 0) & ( ~ (v20 = 0) |  ~ (v19 = 0)))
% 11.22/3.25  | 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, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25, all_0_26_26, all_0_27_27 yields:
% 11.22/3.25  | (1)  ~ (all_0_2_2 = 0) &  ~ (all_0_13_13 = 0) &  ~ (all_0_15_15 = 0) &  ~ (all_0_20_20 = 0) &  ~ (all_0_24_24 = 0) & model(all_0_1_1, all_0_4_4) = 0 & model(all_0_3_3, all_0_4_4) = all_0_2_2 & model(all_0_6_6, all_0_10_10) = 0 & model(all_0_6_6, all_0_11_11) = 0 & model(all_0_9_9, all_0_10_10) = all_0_7_7 & model(all_0_9_9, all_0_11_11) = all_0_8_8 & model(all_0_12_12, all_0_18_18) = 0 & model(all_0_14_14, all_0_17_17) = 0 & model(all_0_14_14, all_0_18_18) = all_0_13_13 & model(all_0_16_16, all_0_17_17) = all_0_15_15 & model(all_0_19_19, all_0_21_21) = 0 & model(all_0_23_23, all_0_21_21) = all_0_20_20 & model(all_0_23_23, all_0_22_22) = 0 & isa(all_0_26_26, all_0_25_25) = 0 & isa(all_0_27_27, all_0_25_25) = all_0_24_24 & isa(all_0_27_27, all_0_26_26) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (xora(v0, v1) = 0) |  ~ (status(v2, v3, v0) = v4) | status(v2, v3, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = 0 |  ~ (nota(v0, v1) = v2) |  ~ (status(v3, v4, v0) = 0) | status(v3, v4, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = 0 |  ~ (mighta(v0, v1) = v2) |  ~ (status(v3, v4, v0) = 0) |  ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (status(v4, v3, v2) = v1) |  ~ (status(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (not(v1) = v2) |  ~ (model(v0, v2) = v3) | model(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (model(v3, v2) = v1) |  ~ (model(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (xora(v3, v2) = v1) |  ~ (xora(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (nevera(v3, v2) = v1) |  ~ (nevera(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (nota(v3, v2) = v1) |  ~ (nota(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (isa(v3, v2) = v1) |  ~ (isa(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (mighta(v3, v2) = v1) |  ~ (mighta(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (xora(v0, v1) = 0) |  ~ (status(v2, v3, v0) = 0) |  ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (nevera(v0, v1) = 0) |  ~ (status(v2, v3, v0) = 0) |  ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (isa(v0, v1) = 0) |  ~ (status(v2, v3, v0) = 0) | status(v2, v3, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (xora(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (status(v3, v4, v1) = v6 & status(v3, v4, v0) = v5 & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (nevera(v0, v1) = v2) |  ? [v3] :  ? [v4] : (status(v3, v4, v1) = 0 & status(v3, v4, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (isa(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not(v2) = v1) |  ~ (not(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (not(v1) = v2) |  ~ (model(v0, v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & model(v0, v1) = v3)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (model(v0, all_0_0_0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (nota(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4 & status(v2, v3, v0) = 0)) &  ! [v0] :  ! [v1] : ( ~ (mighta(v0, v1) = 0) |  ? [v2] :  ? [v3] : (status(v2, v3, v1) = 0 & status(v2, v3, v0) = 0)) &  ! [v0] :  ~ (model(v0, all_0_5_5) = 0) &  ! [v0] : ( ~ (model(v0, all_0_18_18) = 0) | model(v0, all_0_17_17) = 0) & ( ~ (all_0_7_7 = 0) |  ~ (all_0_8_8 = 0))
% 11.22/3.27  |
% 11.22/3.27  | Applying alpha-rule on (1) yields:
% 11.22/3.27  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (status(v4, v3, v2) = v1) |  ~ (status(v4, v3, v2) = v0))
% 11.22/3.27  | (3)  ! [v0] :  ! [v1] : ( ~ (mighta(v0, v1) = 0) |  ? [v2] :  ? [v3] : (status(v2, v3, v1) = 0 & status(v2, v3, v0) = 0))
% 11.22/3.27  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (not(v1) = v2) |  ~ (model(v0, v2) = v3) | model(v0, v1) = 0)
% 11.22/3.27  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not(v2) = v1) |  ~ (not(v2) = v0))
% 11.22/3.27  | (6) isa(all_0_27_27, all_0_25_25) = all_0_24_24
% 11.22/3.27  | (7)  ~ (all_0_7_7 = 0) |  ~ (all_0_8_8 = 0)
% 11.22/3.27  | (8) model(all_0_9_9, all_0_10_10) = all_0_7_7
% 11.22/3.27  | (9) model(all_0_9_9, all_0_11_11) = all_0_8_8
% 11.22/3.27  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (nevera(v0, v1) = 0) |  ~ (status(v2, v3, v0) = 0) |  ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4))
% 11.22/3.27  | (11)  ! [v0] :  ~ (model(v0, all_0_5_5) = 0)
% 11.22/3.27  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (mighta(v3, v2) = v1) |  ~ (mighta(v3, v2) = v0))
% 11.22/3.27  | (13) model(all_0_14_14, all_0_17_17) = 0
% 11.22/3.27  | (14)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (model(v0, all_0_0_0) = v1))
% 11.22/3.27  | (15) model(all_0_19_19, all_0_21_21) = 0
% 11.22/3.27  | (16)  ~ (all_0_24_24 = 0)
% 11.22/3.27  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = 0 |  ~ (mighta(v0, v1) = v2) |  ~ (status(v3, v4, v0) = 0) |  ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5))
% 11.22/3.27  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (nevera(v0, v1) = v2) |  ? [v3] :  ? [v4] : (status(v3, v4, v1) = 0 & status(v3, v4, v0) = 0))
% 11.22/3.27  | (19)  ! [v0] : ( ~ (model(v0, all_0_18_18) = 0) | model(v0, all_0_17_17) = 0)
% 11.22/3.27  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (model(v3, v2) = v1) |  ~ (model(v3, v2) = v0))
% 11.22/3.27  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (xora(v3, v2) = v1) |  ~ (xora(v3, v2) = v0))
% 11.22/3.27  | (22) model(all_0_6_6, all_0_11_11) = 0
% 11.22/3.27  | (23) isa(all_0_27_27, all_0_26_26) = 0
% 11.22/3.27  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (xora(v0, v1) = 0) |  ~ (status(v2, v3, v0) = 0) |  ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4))
% 11.22/3.27  | (25) model(all_0_12_12, all_0_18_18) = 0
% 11.22/3.27  | (26) model(all_0_3_3, all_0_4_4) = all_0_2_2
% 11.22/3.27  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (xora(v0, v1) = 0) |  ~ (status(v2, v3, v0) = v4) | status(v2, v3, v1) = 0)
% 11.22/3.27  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (nevera(v3, v2) = v1) |  ~ (nevera(v3, v2) = v0))
% 11.22/3.27  | (29) model(all_0_16_16, all_0_17_17) = all_0_15_15
% 11.22/3.27  | (30)  ~ (all_0_2_2 = 0)
% 11.22/3.27  | (31)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (xora(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (status(v3, v4, v1) = v6 & status(v3, v4, v0) = v5 & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0)))
% 11.22/3.27  | (32) model(all_0_1_1, all_0_4_4) = 0
% 11.22/3.27  | (33) model(all_0_14_14, all_0_18_18) = all_0_13_13
% 11.22/3.27  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (isa(v0, v1) = 0) |  ~ (status(v2, v3, v0) = 0) | status(v2, v3, v1) = 0)
% 11.22/3.27  | (35)  ~ (all_0_15_15 = 0)
% 11.22/3.27  | (36)  ~ (all_0_13_13 = 0)
% 11.22/3.27  | (37)  ~ (all_0_20_20 = 0)
% 11.22/3.28  | (38)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (isa(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0))
% 11.22/3.28  | (39) model(all_0_6_6, all_0_10_10) = 0
% 11.22/3.28  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (isa(v3, v2) = v1) |  ~ (isa(v3, v2) = v0))
% 11.22/3.28  | (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (not(v1) = v2) |  ~ (model(v0, v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & model(v0, v1) = v3))
% 11.22/3.28  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (nota(v3, v2) = v1) |  ~ (nota(v3, v2) = v0))
% 11.22/3.28  | (43) model(all_0_23_23, all_0_21_21) = all_0_20_20
% 11.22/3.28  | (44) model(all_0_23_23, all_0_22_22) = 0
% 11.22/3.28  | (45) isa(all_0_26_26, all_0_25_25) = 0
% 11.22/3.28  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = 0 |  ~ (nota(v0, v1) = v2) |  ~ (status(v3, v4, v0) = 0) | status(v3, v4, v1) = 0)
% 11.22/3.28  | (47)  ! [v0] :  ! [v1] : ( ~ (nota(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4 & status(v2, v3, v0) = 0))
% 11.22/3.28  |
% 11.22/3.28  | Instantiating formula (38) with all_0_24_24, all_0_25_25, all_0_27_27 and discharging atoms isa(all_0_27_27, all_0_25_25) = all_0_24_24, yields:
% 11.22/3.28  | (48) all_0_24_24 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & status(v0, v1, all_0_25_25) = v2 & status(v0, v1, all_0_27_27) = 0)
% 11.22/3.28  |
% 11.22/3.28  +-Applying beta-rule and splitting (48), into two cases.
% 11.22/3.28  |-Branch one:
% 11.22/3.28  | (49) all_0_24_24 = 0
% 11.22/3.28  |
% 11.22/3.28  	| Equations (49) can reduce 16 to:
% 11.22/3.28  	| (50) $false
% 11.22/3.28  	|
% 11.22/3.28  	|-The branch is then unsatisfiable
% 11.22/3.28  |-Branch two:
% 11.22/3.28  | (16)  ~ (all_0_24_24 = 0)
% 11.22/3.28  | (52)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & status(v0, v1, all_0_25_25) = v2 & status(v0, v1, all_0_27_27) = 0)
% 11.22/3.28  |
% 11.22/3.28  	| Instantiating (52) with all_37_0_28, all_37_1_29, all_37_2_30 yields:
% 11.22/3.28  	| (53)  ~ (all_37_0_28 = 0) & status(all_37_2_30, all_37_1_29, all_0_25_25) = all_37_0_28 & status(all_37_2_30, all_37_1_29, all_0_27_27) = 0
% 11.22/3.28  	|
% 11.22/3.28  	| Applying alpha-rule on (53) yields:
% 11.22/3.28  	| (54)  ~ (all_37_0_28 = 0)
% 11.22/3.28  	| (55) status(all_37_2_30, all_37_1_29, all_0_25_25) = all_37_0_28
% 11.22/3.28  	| (56) status(all_37_2_30, all_37_1_29, all_0_27_27) = 0
% 11.22/3.28  	|
% 11.22/3.28  	| Instantiating formula (34) with all_37_1_29, all_37_2_30, all_0_26_26, all_0_27_27 and discharging atoms isa(all_0_27_27, all_0_26_26) = 0, status(all_37_2_30, all_37_1_29, all_0_27_27) = 0, yields:
% 11.22/3.28  	| (57) status(all_37_2_30, all_37_1_29, all_0_26_26) = 0
% 11.22/3.28  	|
% 11.22/3.28  	| Instantiating formula (34) with all_37_1_29, all_37_2_30, all_0_25_25, all_0_26_26 and discharging atoms isa(all_0_26_26, all_0_25_25) = 0, status(all_37_2_30, all_37_1_29, all_0_26_26) = 0, yields:
% 11.22/3.28  	| (58) status(all_37_2_30, all_37_1_29, all_0_25_25) = 0
% 11.22/3.28  	|
% 11.22/3.28  	| Instantiating formula (2) with all_37_2_30, all_37_1_29, all_0_25_25, 0, all_37_0_28 and discharging atoms status(all_37_2_30, all_37_1_29, all_0_25_25) = all_37_0_28, status(all_37_2_30, all_37_1_29, all_0_25_25) = 0, yields:
% 11.22/3.28  	| (59) all_37_0_28 = 0
% 11.22/3.28  	|
% 11.22/3.28  	| Equations (59) can reduce 54 to:
% 11.22/3.28  	| (50) $false
% 11.22/3.28  	|
% 11.22/3.28  	|-The branch is then unsatisfiable
% 11.22/3.28  % SZS output end Proof for theBenchmark
% 11.22/3.28  
% 11.22/3.28  2692ms
%------------------------------------------------------------------------------