%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n012.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 00:23:34 EDT 2022

% Result   : Theorem 2.28s 1.21s
% Output   : Proof 3.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n012.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 Jul  9 21:07:43 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.57          ____       _                          
% 0.18/0.57    ___  / __ \_____(_)___  ________  __________
% 0.18/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.18/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.18/0.58  
% 0.18/0.58  A Theorem Prover for First-Order Logic
% 0.18/0.58  (ePrincess v.1.0)
% 0.18/0.58  
% 0.18/0.58  (c) Philipp Rümmer, 2009-2015
% 0.18/0.58  (c) Peter Backeman, 2014-2015
% 0.18/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58  Bug reports to peter@backeman.se
% 0.18/0.58  
% 0.18/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58  
% 0.18/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.64/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.89  Prover 0: Preprocessing ...
% 1.71/1.09  Prover 0: Constructing countermodel ...
% 2.28/1.21  Prover 0: proved (584ms)
% 2.28/1.21  
% 2.28/1.21  No countermodel exists, formula is valid
% 2.28/1.21  % SZS status Theorem for theBenchmark
% 2.28/1.21  
% 2.28/1.21  Generating proof ... found it (size 27)
% 3.09/1.45  
% 3.09/1.45  % SZS output start Proof for theBenchmark
% 3.09/1.45  Assumed formulas after preprocessing and simplification: 
% 3.09/1.45  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (singleton(v1) = v7 & singleton(v0) = v5 & cartesian_product2(v7, v2) = v8 & cartesian_product2(v5, v2) = v6 & cartesian_product2(v3, v2) = v4 & cartesian_product2(v2, v7) = v12 & cartesian_product2(v2, v5) = v11 & cartesian_product2(v2, v3) = v10 & set_union2(v11, v12) = v13 & set_union2(v6, v8) = v9 & unordered_pair(v0, v1) = v3 & empty(v15) &  ~ empty(v14) &  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (cartesian_product2(v18, v17) = v20) |  ~ (cartesian_product2(v18, v16) = v19) |  ~ (set_union2(v19, v20) = v21) |  ? [v22] : (cartesian_product2(v18, v22) = v21 & set_union2(v16, v17) = v22)) &  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (cartesian_product2(v17, v18) = v20) |  ~ (cartesian_product2(v16, v18) = v19) |  ~ (set_union2(v19, v20) = v21) |  ? [v22] : (cartesian_product2(v22, v18) = v21 & set_union2(v16, v17) = v22)) &  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (singleton(v17) = v19) |  ~ (singleton(v16) = v18) |  ~ (set_union2(v18, v19) = v20) | unordered_pair(v16, v17) = v20) &  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (cartesian_product2(v19, v18) = v20) |  ~ (set_union2(v16, v17) = v19) |  ? [v21] :  ? [v22] : (cartesian_product2(v17, v18) = v22 & cartesian_product2(v16, v18) = v21 & set_union2(v21, v22) = v20)) &  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (cartesian_product2(v18, v19) = v20) |  ~ (set_union2(v16, v17) = v19) |  ? [v21] :  ? [v22] : (cartesian_product2(v18, v17) = v22 & cartesian_product2(v18, v16) = v21 & set_union2(v21, v22) = v20)) &  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : (v17 = v16 |  ~ (cartesian_product2(v19, v18) = v17) |  ~ (cartesian_product2(v19, v18) = v16)) &  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : (v17 = v16 |  ~ (set_union2(v19, v18) = v17) |  ~ (set_union2(v19, v18) = v16)) &  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : (v17 = v16 |  ~ (unordered_pair(v19, v18) = v17) |  ~ (unordered_pair(v19, v18) = v16)) &  ! [v16] :  ! [v17] :  ! [v18] : (v17 = v16 |  ~ (singleton(v18) = v17) |  ~ (singleton(v18) = v16)) &  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (set_union2(v17, v16) = v18) |  ~ empty(v18) | empty(v16)) &  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (set_union2(v17, v16) = v18) | set_union2(v16, v17) = v18) &  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (set_union2(v16, v17) = v18) |  ~ empty(v18) | empty(v16)) &  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (set_union2(v16, v17) = v18) | set_union2(v17, v16) = v18) &  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (unordered_pair(v17, v16) = v18) | unordered_pair(v16, v17) = v18) &  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | unordered_pair(v17, v16) = v18) &  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) |  ? [v19] :  ? [v20] : (singleton(v17) = v20 & singleton(v16) = v19 & set_union2(v19, v20) = v18)) &  ! [v16] :  ! [v17] : (v17 = v16 |  ~ (set_union2(v16, v16) = v17)) & ( ~ (v13 = v10) |  ~ (v9 = v4)))
% 3.09/1.49  | 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 yields:
% 3.09/1.49  | (1) singleton(all_0_14_14) = all_0_8_8 & singleton(all_0_15_15) = all_0_10_10 & cartesian_product2(all_0_8_8, all_0_13_13) = all_0_7_7 & cartesian_product2(all_0_10_10, all_0_13_13) = all_0_9_9 & cartesian_product2(all_0_12_12, all_0_13_13) = all_0_11_11 & cartesian_product2(all_0_13_13, all_0_8_8) = all_0_3_3 & cartesian_product2(all_0_13_13, all_0_10_10) = all_0_4_4 & cartesian_product2(all_0_13_13, all_0_12_12) = all_0_5_5 & set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 & set_union2(all_0_9_9, all_0_7_7) = all_0_6_6 & unordered_pair(all_0_15_15, all_0_14_14) = all_0_12_12 & empty(all_0_0_0) &  ~ empty(all_0_1_1) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v2, v1) = v4) |  ~ (cartesian_product2(v2, v0) = v3) |  ~ (set_union2(v3, v4) = v5) |  ? [v6] : (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) |  ~ (cartesian_product2(v0, v2) = v3) |  ~ (set_union2(v3, v4) = v5) |  ? [v6] : (cartesian_product2(v6, v2) = v5 & set_union2(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v1) = v3) |  ~ (singleton(v0) = v2) |  ~ (set_union2(v2, v3) = v4) | unordered_pair(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product2(v3, v2) = v4) |  ~ (set_union2(v0, v1) = v3) |  ? [v5] :  ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & set_union2(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product2(v2, v3) = v4) |  ~ (set_union2(v0, v1) = v3) |  ? [v5] :  ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & set_union2(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(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] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v1) = v4 & singleton(v0) = v3 & set_union2(v3, v4) = v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1)) & ( ~ (all_0_2_2 = all_0_5_5) |  ~ (all_0_6_6 = all_0_11_11))
% 3.09/1.50  |
% 3.09/1.50  | Applying alpha-rule on (1) yields:
% 3.09/1.50  | (2) cartesian_product2(all_0_10_10, all_0_13_13) = all_0_9_9
% 3.09/1.50  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v2, v1) = v4) |  ~ (cartesian_product2(v2, v0) = v3) |  ~ (set_union2(v3, v4) = v5) |  ? [v6] : (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6))
% 3.09/1.50  | (4) cartesian_product2(all_0_13_13, all_0_8_8) = all_0_3_3
% 3.09/1.50  | (5) set_union2(all_0_9_9, all_0_7_7) = all_0_6_6
% 3.09/1.50  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0))
% 3.09/1.50  | (7) cartesian_product2(all_0_12_12, all_0_13_13) = all_0_11_11
% 3.09/1.50  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v1) = v4 & singleton(v0) = v3 & set_union2(v3, v4) = v2))
% 3.09/1.50  | (9)  ~ (all_0_2_2 = all_0_5_5) |  ~ (all_0_6_6 = all_0_11_11)
% 3.09/1.50  | (10) cartesian_product2(all_0_13_13, all_0_12_12) = all_0_5_5
% 3.09/1.50  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 3.09/1.50  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v1) = v3) |  ~ (singleton(v0) = v2) |  ~ (set_union2(v2, v3) = v4) | unordered_pair(v0, v1) = v4)
% 3.09/1.50  | (13) unordered_pair(all_0_15_15, all_0_14_14) = all_0_12_12
% 3.09/1.50  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product2(v2, v3) = v4) |  ~ (set_union2(v0, v1) = v3) |  ? [v5] :  ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & set_union2(v5, v6) = v4))
% 3.09/1.50  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.09/1.50  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.09/1.51  | (17) singleton(all_0_14_14) = all_0_8_8
% 3.09/1.51  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 3.09/1.51  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0))
% 3.09/1.51  | (20) empty(all_0_0_0)
% 3.09/1.51  | (21)  ~ empty(all_0_1_1)
% 3.09/1.51  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0))
% 3.09/1.51  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 3.09/1.51  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 3.09/1.51  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product2(v3, v2) = v4) |  ~ (set_union2(v0, v1) = v3) |  ? [v5] :  ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & set_union2(v5, v6) = v4))
% 3.09/1.51  | (26) cartesian_product2(all_0_8_8, all_0_13_13) = all_0_7_7
% 3.09/1.51  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 3.09/1.51  | (28)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 3.09/1.51  | (29) cartesian_product2(all_0_13_13, all_0_10_10) = all_0_4_4
% 3.09/1.51  | (30) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2
% 3.09/1.51  | (31) singleton(all_0_15_15) = all_0_10_10
% 3.09/1.51  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) |  ~ (cartesian_product2(v0, v2) = v3) |  ~ (set_union2(v3, v4) = v5) |  ? [v6] : (cartesian_product2(v6, v2) = v5 & set_union2(v0, v1) = v6))
% 3.09/1.51  |
% 3.09/1.51  | Instantiating formula (3) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_13_13, all_0_8_8, all_0_10_10 and discharging atoms cartesian_product2(all_0_13_13, all_0_8_8) = all_0_3_3, cartesian_product2(all_0_13_13, all_0_10_10) = all_0_4_4, set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 3.09/1.51  | (33)  ? [v0] : (cartesian_product2(all_0_13_13, v0) = all_0_2_2 & set_union2(all_0_10_10, all_0_8_8) = v0)
% 3.09/1.51  |
% 3.09/1.51  | Instantiating formula (32) with all_0_6_6, all_0_7_7, all_0_9_9, all_0_13_13, all_0_8_8, all_0_10_10 and discharging atoms cartesian_product2(all_0_8_8, all_0_13_13) = all_0_7_7, cartesian_product2(all_0_10_10, all_0_13_13) = all_0_9_9, set_union2(all_0_9_9, all_0_7_7) = all_0_6_6, yields:
% 3.09/1.51  | (34)  ? [v0] : (cartesian_product2(v0, all_0_13_13) = all_0_6_6 & set_union2(all_0_10_10, all_0_8_8) = v0)
% 3.09/1.51  |
% 3.09/1.51  | Instantiating formula (8) with all_0_12_12, all_0_14_14, all_0_15_15 and discharging atoms unordered_pair(all_0_15_15, all_0_14_14) = all_0_12_12, yields:
% 3.09/1.51  | (35)  ? [v0] :  ? [v1] : (singleton(all_0_14_14) = v1 & singleton(all_0_15_15) = v0 & set_union2(v0, v1) = all_0_12_12)
% 3.09/1.51  |
% 3.09/1.51  | Instantiating (34) with all_9_0_16 yields:
% 3.09/1.51  | (36) cartesian_product2(all_9_0_16, all_0_13_13) = all_0_6_6 & set_union2(all_0_10_10, all_0_8_8) = all_9_0_16
% 3.09/1.51  |
% 3.09/1.51  | Applying alpha-rule on (36) yields:
% 3.09/1.51  | (37) cartesian_product2(all_9_0_16, all_0_13_13) = all_0_6_6
% 3.09/1.51  | (38) set_union2(all_0_10_10, all_0_8_8) = all_9_0_16
% 3.09/1.51  |
% 3.09/1.51  | Instantiating (35) with all_11_0_17, all_11_1_18 yields:
% 3.09/1.51  | (39) singleton(all_0_14_14) = all_11_0_17 & singleton(all_0_15_15) = all_11_1_18 & set_union2(all_11_1_18, all_11_0_17) = all_0_12_12
% 3.09/1.51  |
% 3.09/1.51  | Applying alpha-rule on (39) yields:
% 3.09/1.51  | (40) singleton(all_0_14_14) = all_11_0_17
% 3.33/1.51  | (41) singleton(all_0_15_15) = all_11_1_18
% 3.33/1.51  | (42) set_union2(all_11_1_18, all_11_0_17) = all_0_12_12
% 3.33/1.51  |
% 3.33/1.51  | Instantiating (33) with all_13_0_19 yields:
% 3.33/1.51  | (43) cartesian_product2(all_0_13_13, all_13_0_19) = all_0_2_2 & set_union2(all_0_10_10, all_0_8_8) = all_13_0_19
% 3.33/1.51  |
% 3.33/1.51  | Applying alpha-rule on (43) yields:
% 3.33/1.51  | (44) cartesian_product2(all_0_13_13, all_13_0_19) = all_0_2_2
% 3.33/1.51  | (45) set_union2(all_0_10_10, all_0_8_8) = all_13_0_19
% 3.33/1.51  |
% 3.33/1.52  | Instantiating formula (27) with all_0_14_14, all_11_0_17, all_0_8_8 and discharging atoms singleton(all_0_14_14) = all_11_0_17, singleton(all_0_14_14) = all_0_8_8, yields:
% 3.33/1.52  | (46) all_11_0_17 = all_0_8_8
% 3.33/1.52  |
% 3.33/1.52  | Instantiating formula (27) with all_0_15_15, all_11_1_18, all_0_10_10 and discharging atoms singleton(all_0_15_15) = all_11_1_18, singleton(all_0_15_15) = all_0_10_10, yields:
% 3.33/1.52  | (47) all_11_1_18 = all_0_10_10
% 3.33/1.52  |
% 3.33/1.52  | Instantiating formula (11) with all_0_10_10, all_0_8_8, all_9_0_16, all_13_0_19 and discharging atoms set_union2(all_0_10_10, all_0_8_8) = all_13_0_19, set_union2(all_0_10_10, all_0_8_8) = all_9_0_16, yields:
% 3.33/1.52  | (48) all_13_0_19 = all_9_0_16
% 3.33/1.52  |
% 3.33/1.52  | From (48) and (44) follows:
% 3.33/1.52  | (49) cartesian_product2(all_0_13_13, all_9_0_16) = all_0_2_2
% 3.33/1.52  |
% 3.33/1.52  | From (47)(46) and (42) follows:
% 3.33/1.52  | (50) set_union2(all_0_10_10, all_0_8_8) = all_0_12_12
% 3.33/1.52  |
% 3.33/1.52  | From (48) and (45) follows:
% 3.33/1.52  | (38) set_union2(all_0_10_10, all_0_8_8) = all_9_0_16
% 3.33/1.52  |
% 3.33/1.52  | Instantiating formula (11) with all_0_10_10, all_0_8_8, all_0_12_12, all_9_0_16 and discharging atoms set_union2(all_0_10_10, all_0_8_8) = all_9_0_16, set_union2(all_0_10_10, all_0_8_8) = all_0_12_12, yields:
% 3.33/1.52  | (52) all_9_0_16 = all_0_12_12
% 3.33/1.52  |
% 3.33/1.52  | From (52) and (37) follows:
% 3.33/1.52  | (53) cartesian_product2(all_0_12_12, all_0_13_13) = all_0_6_6
% 3.33/1.52  |
% 3.33/1.52  | From (52) and (49) follows:
% 3.33/1.52  | (54) cartesian_product2(all_0_13_13, all_0_12_12) = all_0_2_2
% 3.33/1.52  |
% 3.33/1.52  | Instantiating formula (6) with all_0_12_12, all_0_13_13, all_0_6_6, all_0_11_11 and discharging atoms cartesian_product2(all_0_12_12, all_0_13_13) = all_0_6_6, cartesian_product2(all_0_12_12, all_0_13_13) = all_0_11_11, yields:
% 3.33/1.52  | (55) all_0_6_6 = all_0_11_11
% 3.33/1.52  |
% 3.33/1.52  | Instantiating formula (6) with all_0_13_13, all_0_12_12, all_0_2_2, all_0_5_5 and discharging atoms cartesian_product2(all_0_13_13, all_0_12_12) = all_0_2_2, cartesian_product2(all_0_13_13, all_0_12_12) = all_0_5_5, yields:
% 3.33/1.52  | (56) all_0_2_2 = all_0_5_5
% 3.33/1.52  |
% 3.33/1.52  +-Applying beta-rule and splitting (9), into two cases.
% 3.33/1.52  |-Branch one:
% 3.33/1.52  | (57)  ~ (all_0_2_2 = all_0_5_5)
% 3.33/1.52  |
% 3.33/1.52  	| Equations (56) can reduce 57 to:
% 3.33/1.52  	| (58) $false
% 3.33/1.52  	|
% 3.33/1.52  	|-The branch is then unsatisfiable
% 3.33/1.52  |-Branch two:
% 3.33/1.52  | (56) all_0_2_2 = all_0_5_5
% 3.33/1.52  | (60)  ~ (all_0_6_6 = all_0_11_11)
% 3.33/1.52  |
% 3.33/1.52  	| Equations (55) can reduce 60 to:
% 3.33/1.52  	| (58) $false
% 3.33/1.52  	|
% 3.33/1.52  	|-The branch is then unsatisfiable
% 3.33/1.52  % SZS output end Proof for theBenchmark
% 3.33/1.52  
% 3.33/1.52  935ms
%------------------------------------------------------------------------------