%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET951+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n005.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 : Tue Jul 19 00:23:24 EDT 2022

% Result   : Theorem 2.81s 1.36s
% Output   : Proof 4.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET951+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  9 23:50:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.55/0.60          ____       _                          
% 0.55/0.60    ___  / __ \_____(_)___  ________  __________
% 0.55/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.55/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.55/0.60  
% 0.55/0.60  A Theorem Prover for First-Order Logic
% 0.55/0.60  (ePrincess v.1.0)
% 0.55/0.60  
% 0.55/0.60  (c) Philipp Rümmer, 2009-2015
% 0.55/0.60  (c) Peter Backeman, 2014-2015
% 0.55/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.60  Bug reports to peter@backeman.se
% 0.55/0.60  
% 0.55/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.60  
% 0.55/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.47/0.91  Prover 0: Preprocessing ...
% 1.95/1.13  Prover 0: Warning: ignoring some quantifiers
% 2.15/1.15  Prover 0: Constructing countermodel ...
% 2.81/1.36  Prover 0: proved (709ms)
% 2.81/1.36  
% 2.81/1.36  No countermodel exists, formula is valid
% 2.81/1.36  % SZS status Theorem for theBenchmark
% 2.81/1.36  
% 2.81/1.36  Generating proof ... Warning: ignoring some quantifiers
% 4.08/1.66  found it (size 23)
% 4.08/1.66  
% 4.08/1.66  % SZS output start Proof for theBenchmark
% 4.08/1.66  Assumed formulas after preprocessing and simplification: 
% 4.08/1.66  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : (cartesian_product2(v3, v4) = v6 & cartesian_product2(v1, v2) = v5 & set_intersection2(v5, v6) = v7 & set_intersection2(v2, v4) = v9 & set_intersection2(v1, v3) = v8 & empty(v11) & in(v0, v7) &  ~ empty(v10) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (cartesian_product2(v12, v13) = v14) |  ~ (ordered_pair(v16, v17) = v15) |  ~ in(v17, v13) |  ~ in(v16, v12) | in(v15, v14)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v13 |  ~ (ordered_pair(v14, v15) = v16) |  ~ (ordered_pair(v12, v13) = v16)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v14 = v12 |  ~ (ordered_pair(v14, v15) = v16) |  ~ (ordered_pair(v12, v13) = v16)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (singleton(v12) = v15) |  ~ (unordered_pair(v14, v15) = v16) |  ~ (unordered_pair(v12, v13) = v14) | ordered_pair(v12, v13) = v16) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v13 = v12 |  ~ (cartesian_product2(v15, v14) = v13) |  ~ (cartesian_product2(v15, v14) = v12)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v13 = v12 |  ~ (ordered_pair(v15, v14) = v13) |  ~ (ordered_pair(v15, v14) = v12)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v13 = v12 |  ~ (set_intersection2(v15, v14) = v13) |  ~ (set_intersection2(v15, v14) = v12)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v13 = v12 |  ~ (unordered_pair(v15, v14) = v13) |  ~ (unordered_pair(v15, v14) = v12)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (cartesian_product2(v12, v13) = v14) |  ~ in(v15, v14) |  ? [v16] :  ? [v17] : (ordered_pair(v16, v17) = v15 & in(v17, v13) & in(v16, v12))) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) |  ~ in(v15, v14) | in(v15, v13)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) |  ~ in(v15, v14) | in(v15, v12)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) |  ~ in(v15, v13) |  ~ in(v15, v12) | in(v15, v14)) &  ? [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = v12 |  ~ (cartesian_product2(v13, v14) = v15) |  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] : (( ~ in(v16, v12) |  ! [v20] :  ! [v21] : ( ~ (ordered_pair(v20, v21) = v16) |  ~ in(v21, v14) |  ~ in(v20, v13))) & (in(v16, v12) | (v19 = v16 & ordered_pair(v17, v18) = v16 & in(v18, v14) & in(v17, v13))))) &  ? [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = v12 |  ~ (set_intersection2(v13, v14) = v15) |  ? [v16] : (( ~ in(v16, v14) |  ~ in(v16, v13) |  ~ in(v16, v12)) & (in(v16, v12) | (in(v16, v14) & in(v16, v13))))) &  ! [v12] :  ! [v13] :  ! [v14] : (v13 = v12 |  ~ (singleton(v14) = v13) |  ~ (singleton(v14) = v12)) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) |  ~ empty(v14)) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) |  ? [v15] :  ? [v16] : (singleton(v12) = v16 & unordered_pair(v15, v16) = v14 & unordered_pair(v12, v13) = v15)) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (set_intersection2(v13, v12) = v14) | set_intersection2(v12, v13) = v14) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | set_intersection2(v13, v12) = v14) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (unordered_pair(v13, v12) = v14) | unordered_pair(v12, v13) = v14) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) &  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (set_intersection2(v12, v12) = v13)) &  ! [v12] :  ! [v13] : ( ~ in(v13, v12) |  ~ in(v12, v13)) &  ! [v12] :  ! [v13] : ( ~ in(v13, v9) |  ~ in(v12, v8) |  ? [v14] : ( ~ (v14 = v0) & ordered_pair(v12, v13) = v14)))
% 4.34/1.70  | 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 yields:
% 4.34/1.70  | (1) cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5 & cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6 & set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4 & set_intersection2(all_0_9_9, all_0_7_7) = all_0_2_2 & set_intersection2(all_0_10_10, all_0_8_8) = all_0_3_3 & empty(all_0_0_0) & in(all_0_11_11, all_0_4_4) &  ~ empty(all_0_1_1) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ (ordered_pair(v4, v5) = v3) |  ~ in(v5, v1) |  ~ in(v4, v0) | in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v1 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v0 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ in(v3, v2) |  ? [v4] :  ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (cartesian_product2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (( ~ in(v4, v0) |  ! [v8] :  ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) |  ~ in(v9, v2) |  ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v2) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ in(v1, all_0_2_2) |  ~ in(v0, all_0_3_3) |  ? [v2] : ( ~ (v2 = all_0_11_11) & ordered_pair(v0, v1) = v2))
% 4.34/1.71  |
% 4.34/1.71  | Applying alpha-rule on (1) yields:
% 4.34/1.71  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 4.34/1.71  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 4.34/1.71  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v1 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4))
% 4.34/1.71  | (5) cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6
% 4.34/1.71  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1))
% 4.34/1.71  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 4.34/1.71  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 4.34/1.71  | (9)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 4.34/1.71  | (10)  ! [v0] :  ! [v1] : ( ~ in(v1, all_0_2_2) |  ~ in(v0, all_0_3_3) |  ? [v2] : ( ~ (v2 = all_0_11_11) & ordered_pair(v0, v1) = v2))
% 4.34/1.71  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ in(v3, v2) |  ? [v4] :  ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0)))
% 4.34/1.71  | (12) set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4
% 4.34/1.71  | (13) set_intersection2(all_0_10_10, all_0_8_8) = all_0_3_3
% 4.34/1.71  | (14) empty(all_0_0_0)
% 4.34/1.71  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v0 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4))
% 4.34/1.72  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.34/1.72  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 4.34/1.72  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2))
% 4.34/1.72  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 4.34/1.72  | (20) cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5
% 4.34/1.72  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 4.34/1.72  | (22) set_intersection2(all_0_9_9, all_0_7_7) = all_0_2_2
% 4.34/1.72  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ (ordered_pair(v4, v5) = v3) |  ~ in(v5, v1) |  ~ in(v4, v0) | in(v3, v2))
% 4.34/1.72  | (24)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 4.34/1.72  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 4.34/1.72  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v0))
% 4.34/1.72  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 4.34/1.72  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0))
% 4.34/1.72  | (29)  ~ empty(all_0_1_1)
% 4.34/1.72  | (30)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (cartesian_product2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (( ~ in(v4, v0) |  ! [v8] :  ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) |  ~ in(v9, v2) |  ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1)))))
% 4.34/1.72  | (31)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v2) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1)))))
% 4.34/1.72  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 4.34/1.72  | (33) in(all_0_11_11, all_0_4_4)
% 4.34/1.72  |
% 4.34/1.72  | Instantiating formula (6) with all_0_11_11, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_0_11_11, all_0_4_4), yields:
% 4.34/1.72  | (34) in(all_0_11_11, all_0_5_5)
% 4.34/1.72  |
% 4.34/1.72  | Instantiating formula (26) with all_0_11_11, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_0_11_11, all_0_4_4), yields:
% 4.34/1.72  | (35) in(all_0_11_11, all_0_6_6)
% 4.34/1.72  |
% 4.34/1.72  | Instantiating formula (11) with all_0_11_11, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5, in(all_0_11_11, all_0_5_5), yields:
% 4.34/1.72  | (36)  ? [v0] :  ? [v1] : (ordered_pair(v0, v1) = all_0_11_11 & in(v1, all_0_7_7) & in(v0, all_0_8_8))
% 4.34/1.72  |
% 4.34/1.72  | Instantiating formula (11) with all_0_11_11, all_0_6_6, all_0_9_9, all_0_10_10 and discharging atoms cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6, in(all_0_11_11, all_0_6_6), yields:
% 4.34/1.72  | (37)  ? [v0] :  ? [v1] : (ordered_pair(v0, v1) = all_0_11_11 & in(v1, all_0_9_9) & in(v0, all_0_10_10))
% 4.34/1.73  |
% 4.34/1.73  | Instantiating (37) with all_18_0_14, all_18_1_15 yields:
% 4.34/1.73  | (38) ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11 & in(all_18_0_14, all_0_9_9) & in(all_18_1_15, all_0_10_10)
% 4.34/1.73  |
% 4.34/1.73  | Applying alpha-rule on (38) yields:
% 4.34/1.73  | (39) ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11
% 4.34/1.73  | (40) in(all_18_0_14, all_0_9_9)
% 4.34/1.73  | (41) in(all_18_1_15, all_0_10_10)
% 4.34/1.73  |
% 4.34/1.73  | Instantiating (36) with all_20_0_16, all_20_1_17 yields:
% 4.34/1.73  | (42) ordered_pair(all_20_1_17, all_20_0_16) = all_0_11_11 & in(all_20_0_16, all_0_7_7) & in(all_20_1_17, all_0_8_8)
% 4.34/1.73  |
% 4.34/1.73  | Applying alpha-rule on (42) yields:
% 4.34/1.73  | (43) ordered_pair(all_20_1_17, all_20_0_16) = all_0_11_11
% 4.34/1.73  | (44) in(all_20_0_16, all_0_7_7)
% 4.34/1.73  | (45) in(all_20_1_17, all_0_8_8)
% 4.34/1.73  |
% 4.34/1.73  | Instantiating formula (4) with all_0_11_11, all_18_0_14, all_18_1_15, all_20_0_16, all_20_1_17 and discharging atoms ordered_pair(all_20_1_17, all_20_0_16) = all_0_11_11, ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11, yields:
% 4.34/1.73  | (46) all_20_0_16 = all_18_0_14
% 4.34/1.73  |
% 4.34/1.73  | Instantiating formula (15) with all_0_11_11, all_18_0_14, all_18_1_15, all_20_0_16, all_20_1_17 and discharging atoms ordered_pair(all_20_1_17, all_20_0_16) = all_0_11_11, ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11, yields:
% 4.34/1.73  | (47) all_20_1_17 = all_18_1_15
% 4.34/1.73  |
% 4.34/1.73  | From (47)(46) and (43) follows:
% 4.34/1.73  | (39) ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11
% 4.34/1.73  |
% 4.34/1.73  | From (46) and (44) follows:
% 4.34/1.73  | (49) in(all_18_0_14, all_0_7_7)
% 4.34/1.73  |
% 4.34/1.73  | From (47) and (45) follows:
% 4.34/1.73  | (50) in(all_18_1_15, all_0_8_8)
% 4.34/1.73  |
% 4.34/1.73  | Instantiating formula (18) with all_18_0_14, all_0_2_2, all_0_7_7, all_0_9_9 and discharging atoms set_intersection2(all_0_9_9, all_0_7_7) = all_0_2_2, in(all_18_0_14, all_0_7_7), in(all_18_0_14, all_0_9_9), yields:
% 4.34/1.73  | (51) in(all_18_0_14, all_0_2_2)
% 4.34/1.73  |
% 4.34/1.73  | Instantiating formula (18) with all_18_1_15, all_0_3_3, all_0_8_8, all_0_10_10 and discharging atoms set_intersection2(all_0_10_10, all_0_8_8) = all_0_3_3, in(all_18_1_15, all_0_8_8), in(all_18_1_15, all_0_10_10), yields:
% 4.34/1.73  | (52) in(all_18_1_15, all_0_3_3)
% 4.34/1.73  |
% 4.34/1.73  | Instantiating formula (10) with all_18_0_14, all_18_1_15 and discharging atoms in(all_18_0_14, all_0_2_2), in(all_18_1_15, all_0_3_3), yields:
% 4.34/1.73  | (53)  ? [v0] : ( ~ (v0 = all_0_11_11) & ordered_pair(all_18_1_15, all_18_0_14) = v0)
% 4.34/1.73  |
% 4.34/1.73  | Instantiating (53) with all_40_0_20 yields:
% 4.34/1.73  | (54)  ~ (all_40_0_20 = all_0_11_11) & ordered_pair(all_18_1_15, all_18_0_14) = all_40_0_20
% 4.34/1.73  |
% 4.34/1.73  | Applying alpha-rule on (54) yields:
% 4.34/1.73  | (55)  ~ (all_40_0_20 = all_0_11_11)
% 4.34/1.73  | (56) ordered_pair(all_18_1_15, all_18_0_14) = all_40_0_20
% 4.34/1.73  |
% 4.34/1.73  | Instantiating formula (21) with all_18_1_15, all_18_0_14, all_40_0_20, all_0_11_11 and discharging atoms ordered_pair(all_18_1_15, all_18_0_14) = all_40_0_20, ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11, yields:
% 4.34/1.73  | (57) all_40_0_20 = all_0_11_11
% 4.34/1.73  |
% 4.34/1.73  | Equations (57) can reduce 55 to:
% 4.34/1.73  | (58) $false
% 4.34/1.73  |
% 4.34/1.73  |-The branch is then unsatisfiable
% 4.34/1.73  % SZS output end Proof for theBenchmark
% 4.34/1.73  
% 4.34/1.73  1122ms
%------------------------------------------------------------------------------