TSTP Solution File: SEU138+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU138+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n020.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 08:46:52 EDT 2022

% Result   : Theorem 20.82s 6.11s
% Output   : Proof 24.99s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SEU138+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15  % Command  : ePrincess-casc -timeout=%d %s
% 0.15/0.37  % Computer : n020.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Sun Jun 19 07:31:18 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.57/0.62          ____       _                          
% 0.57/0.62    ___  / __ \_____(_)___  ________  __________
% 0.57/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.57/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.57/0.62  
% 0.57/0.62  A Theorem Prover for First-Order Logic
% 0.57/0.63  (ePrincess v.1.0)
% 0.57/0.63  
% 0.57/0.63  (c) Philipp Rümmer, 2009-2015
% 0.57/0.63  (c) Peter Backeman, 2014-2015
% 0.57/0.63  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.63  Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.63  Bug reports to peter@backeman.se
% 0.57/0.63  
% 0.57/0.63  For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.63  
% 0.57/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.68  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.46/0.96  Prover 0: Preprocessing ...
% 1.84/1.15  Prover 0: Warning: ignoring some quantifiers
% 1.84/1.17  Prover 0: Constructing countermodel ...
% 2.75/1.39  Prover 0: gave up
% 2.75/1.40  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.75/1.42  Prover 1: Preprocessing ...
% 3.21/1.50  Prover 1: Warning: ignoring some quantifiers
% 3.21/1.51  Prover 1: Constructing countermodel ...
% 3.47/1.61  Prover 1: gave up
% 3.47/1.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.81/1.62  Prover 2: Preprocessing ...
% 4.16/1.72  Prover 2: Warning: ignoring some quantifiers
% 4.16/1.72  Prover 2: Constructing countermodel ...
% 4.80/1.84  Prover 2: gave up
% 4.80/1.84  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.80/1.86  Prover 3: Preprocessing ...
% 4.80/1.89  Prover 3: Warning: ignoring some quantifiers
% 4.80/1.89  Prover 3: Constructing countermodel ...
% 5.15/1.97  Prover 3: gave up
% 5.15/1.97  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.47/1.98  Prover 4: Preprocessing ...
% 5.91/2.09  Prover 4: Warning: ignoring some quantifiers
% 6.01/2.09  Prover 4: Constructing countermodel ...
% 10.36/3.18  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.36/3.20  Prover 5: Preprocessing ...
% 10.75/3.28  Prover 5: Warning: ignoring some quantifiers
% 10.75/3.28  Prover 5: Constructing countermodel ...
% 11.41/3.38  Prover 5: gave up
% 11.41/3.38  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 11.41/3.39  Prover 6: Preprocessing ...
% 11.65/3.44  Prover 6: Warning: ignoring some quantifiers
% 11.73/3.44  Prover 6: Constructing countermodel ...
% 11.73/3.50  Prover 6: gave up
% 11.73/3.50  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 11.73/3.51  Prover 7: Preprocessing ...
% 12.07/3.54  Prover 7: Proving ...
% 20.82/6.11  Prover 7: proved (2605ms)
% 20.82/6.11  Prover 4: stopped
% 20.82/6.11  
% 20.82/6.11  % SZS status Theorem for theBenchmark
% 20.82/6.11  
% 20.82/6.11  Generating proof ... found it (size 53)
% 24.99/7.38  
% 24.99/7.38  % SZS output start Proof for theBenchmark
% 24.99/7.38  Assumed formulas after preprocessing and simplification: 
% 24.99/7.38  | (0)  ? [v0] : (empty(v0) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (set_difference(v4, v3) = v2) |  ~ (set_difference(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (set_intersection2(v4, v3) = v2) |  ~ (set_intersection2(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v2) = v3) |  ! [v4] : (v4 = v3 |  ? [v5] : (( ~ in(v5, v4) |  ~ in(v5, v1) | in(v5, v2)) & (in(v5, v4) | (in(v5, v1) &  ~ in(v5, v2)))))) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v1) &  ~ in(v4, v2))) &  ! [v4] : ( ~ in(v4, v1) | in(v4, v3) | in(v4, v2)))) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | set_intersection2(v2, v1) = v3) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) |  ! [v4] : (v4 = v3 |  ? [v5] : (( ~ in(v5, v4) |  ~ in(v5, v2) |  ~ in(v5, v1)) & (in(v5, v4) | (in(v5, v2) & in(v5, v1)))))) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v2) & in(v4, v1))) &  ! [v4] : ( ~ in(v4, v2) |  ~ in(v4, v1) | in(v4, v3)))) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_difference(v1, v0) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_intersection2(v1, v1) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ empty(v2) |  ~ empty(v1)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ subset(v2, v1) |  ~ subset(v1, v2)) &  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_difference(v0, v1) = v2)) &  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v1, v0) = v2)) &  ! [v1] :  ! [v2] : ( ~ empty(v2) |  ~ in(v1, v2)) &  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ! [v3] : ( ~ in(v3, v1) | in(v3, v2))) &  ! [v1] :  ! [v2] : ( ~ in(v2, v1) |  ~ in(v1, v2)) &  ! [v1] :  ! [v2] : (subset(v1, v2) |  ? [v3] : (in(v3, v1) &  ~ in(v3, v2))) &  ! [v1] : (v1 = v0 |  ~ empty(v1)) &  ! [v1] : subset(v1, v1) &  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = v4) & set_difference(v1, v3) = v4 & set_difference(v1, v2) = v3 & set_intersection2(v1, v2) = v5) &  ? [v1] :  ~ empty(v1) &  ? [v1] : empty(v1))
% 24.99/7.41  | Instantiating (0) with all_0_0_0 yields:
% 24.99/7.41  | (1) empty(all_0_0_0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) &  ~ in(v4, v1)))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) &  ~ in(v3, v1))) &  ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) &  ! [v3] : ( ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2)))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, all_0_0_0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] : (v1 = all_0_0_0 |  ~ (set_difference(all_0_0_0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = all_0_0_0 |  ~ (set_intersection2(v0, all_0_0_0) = v1)) &  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : (subset(v0, v1) |  ? [v2] : (in(v2, v0) &  ~ in(v2, v1))) &  ! [v0] : (v0 = all_0_0_0 |  ~ empty(v0)) &  ! [v0] : subset(v0, v0) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = v3) & set_difference(v0, v2) = v3 & set_difference(v0, v1) = v2 & set_intersection2(v0, v1) = v4) &  ? [v0] :  ~ empty(v0) &  ? [v0] : empty(v0)
% 24.99/7.42  |
% 24.99/7.42  | Applying alpha-rule on (1) yields:
% 24.99/7.42  | (2)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 24.99/7.42  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0))
% 24.99/7.42  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 24.99/7.42  | (5) empty(all_0_0_0)
% 24.99/7.42  | (6)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 24.99/7.42  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) &  ~ in(v4, v1))))))
% 24.99/7.42  | (8)  ! [v0] :  ! [v1] : (v1 = all_0_0_0 |  ~ (set_intersection2(v0, all_0_0_0) = v1))
% 24.99/7.42  | (9)  ? [v0] :  ~ empty(v0)
% 24.99/7.42  | (10)  ! [v0] : subset(v0, v0)
% 24.99/7.42  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) &  ! [v3] : ( ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2))))
% 24.99/7.42  | (12)  ? [v0] : empty(v0)
% 24.99/7.42  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 24.99/7.42  | (14)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = v3) & set_difference(v0, v2) = v3 & set_difference(v0, v1) = v2 & set_intersection2(v0, v1) = v4)
% 24.99/7.42  | (15)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, all_0_0_0) = v1))
% 24.99/7.42  | (16)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 24.99/7.42  | (17)  ! [v0] :  ! [v1] : (v1 = all_0_0_0 |  ~ (set_difference(all_0_0_0, v0) = v1))
% 24.99/7.42  | (18)  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ! [v2] : ( ~ in(v2, v0) | in(v2, v1)))
% 24.99/7.42  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0))))))
% 24.99/7.42  | (20)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 24.99/7.42  | (21)  ! [v0] :  ! [v1] : (subset(v0, v1) |  ? [v2] : (in(v2, v0) &  ~ in(v2, v1)))
% 24.99/7.42  | (22)  ! [v0] : (v0 = all_0_0_0 |  ~ empty(v0))
% 24.99/7.42  | (23)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 24.99/7.42  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) &  ~ in(v3, v1))) &  ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1))))
% 24.99/7.42  |
% 24.99/7.42  | Instantiating (14) with all_5_0_2, all_5_1_3, all_5_2_4, all_5_3_5, all_5_4_6 yields:
% 24.99/7.42  | (25)  ~ (all_5_0_2 = all_5_1_3) & set_difference(all_5_4_6, all_5_2_4) = all_5_1_3 & set_difference(all_5_4_6, all_5_3_5) = all_5_2_4 & set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2
% 24.99/7.42  |
% 24.99/7.42  | Applying alpha-rule on (25) yields:
% 24.99/7.42  | (26)  ~ (all_5_0_2 = all_5_1_3)
% 24.99/7.42  | (27) set_difference(all_5_4_6, all_5_2_4) = all_5_1_3
% 24.99/7.42  | (28) set_difference(all_5_4_6, all_5_3_5) = all_5_2_4
% 24.99/7.42  | (29) set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2
% 24.99/7.42  |
% 24.99/7.42  | Instantiating formula (7) with all_5_1_3, all_5_2_4, all_5_4_6 and discharging atoms set_difference(all_5_4_6, all_5_2_4) = all_5_1_3, yields:
% 24.99/7.43  | (30)  ! [v0] : (v0 = all_5_1_3 |  ? [v1] : (( ~ in(v1, v0) |  ~ in(v1, all_5_4_6) | in(v1, all_5_2_4)) & (in(v1, v0) | (in(v1, all_5_4_6) &  ~ in(v1, all_5_2_4)))))
% 24.99/7.43  |
% 24.99/7.43  | Instantiating formula (24) with all_5_2_4, all_5_3_5, all_5_4_6 and discharging atoms set_difference(all_5_4_6, all_5_3_5) = all_5_2_4, yields:
% 24.99/7.43  | (31)  ! [v0] : ( ~ in(v0, all_5_2_4) | (in(v0, all_5_4_6) &  ~ in(v0, all_5_3_5))) &  ! [v0] : ( ~ in(v0, all_5_4_6) | in(v0, all_5_2_4) | in(v0, all_5_3_5))
% 24.99/7.43  |
% 24.99/7.43  | Applying alpha-rule on (31) yields:
% 24.99/7.43  | (32)  ! [v0] : ( ~ in(v0, all_5_2_4) | (in(v0, all_5_4_6) &  ~ in(v0, all_5_3_5)))
% 24.99/7.43  | (33)  ! [v0] : ( ~ in(v0, all_5_4_6) | in(v0, all_5_2_4) | in(v0, all_5_3_5))
% 24.99/7.43  |
% 24.99/7.43  | Instantiating formula (13) with all_5_0_2, all_5_3_5, all_5_4_6 and discharging atoms set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2, yields:
% 24.99/7.43  | (34) set_intersection2(all_5_3_5, all_5_4_6) = all_5_0_2
% 24.99/7.43  |
% 24.99/7.43  | Instantiating formula (11) with all_5_0_2, all_5_4_6, all_5_3_5 and discharging atoms set_intersection2(all_5_3_5, all_5_4_6) = all_5_0_2, yields:
% 24.99/7.43  | (35)  ! [v0] : ( ~ in(v0, all_5_0_2) | (in(v0, all_5_3_5) & in(v0, all_5_4_6))) &  ! [v0] : ( ~ in(v0, all_5_3_5) |  ~ in(v0, all_5_4_6) | in(v0, all_5_0_2))
% 24.99/7.43  |
% 24.99/7.43  | Applying alpha-rule on (35) yields:
% 24.99/7.43  | (36)  ! [v0] : ( ~ in(v0, all_5_0_2) | (in(v0, all_5_3_5) & in(v0, all_5_4_6)))
% 24.99/7.43  | (37)  ! [v0] : ( ~ in(v0, all_5_3_5) |  ~ in(v0, all_5_4_6) | in(v0, all_5_0_2))
% 24.99/7.43  |
% 24.99/7.43  | Introducing new symbol ex_58_0_14 defined by:
% 24.99/7.43  | (38) ex_58_0_14 = all_5_0_2
% 24.99/7.43  |
% 24.99/7.43  | Instantiating formula (30) with ex_58_0_14 yields:
% 24.99/7.43  | (39) ex_58_0_14 = all_5_1_3 |  ? [v0] : (( ~ in(v0, ex_58_0_14) |  ~ in(v0, all_5_4_6) | in(v0, all_5_2_4)) & (in(v0, ex_58_0_14) | (in(v0, all_5_4_6) &  ~ in(v0, all_5_2_4))))
% 24.99/7.43  |
% 24.99/7.43  +-Applying beta-rule and splitting (39), into two cases.
% 24.99/7.43  |-Branch one:
% 24.99/7.43  | (40) ex_58_0_14 = all_5_1_3
% 24.99/7.43  |
% 24.99/7.43  	| Combining equations (38,40) yields a new equation:
% 24.99/7.43  	| (41) all_5_0_2 = all_5_1_3
% 24.99/7.43  	|
% 24.99/7.43  	| Simplifying 41 yields:
% 24.99/7.43  	| (42) all_5_0_2 = all_5_1_3
% 24.99/7.43  	|
% 24.99/7.43  	| Equations (42) can reduce 26 to:
% 24.99/7.43  	| (43) $false
% 24.99/7.43  	|
% 24.99/7.43  	|-The branch is then unsatisfiable
% 24.99/7.43  |-Branch two:
% 24.99/7.43  | (44)  ? [v0] : (( ~ in(v0, ex_58_0_14) |  ~ in(v0, all_5_4_6) | in(v0, all_5_2_4)) & (in(v0, ex_58_0_14) | (in(v0, all_5_4_6) &  ~ in(v0, all_5_2_4))))
% 24.99/7.43  |
% 24.99/7.43  	| Instantiating (44) with all_61_0_15 yields:
% 24.99/7.43  	| (45) ( ~ in(all_61_0_15, ex_58_0_14) |  ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4)) & (in(all_61_0_15, ex_58_0_14) | (in(all_61_0_15, all_5_4_6) &  ~ in(all_61_0_15, all_5_2_4)))
% 24.99/7.43  	|
% 24.99/7.43  	| Applying alpha-rule on (45) yields:
% 24.99/7.43  	| (46)  ~ in(all_61_0_15, ex_58_0_14) |  ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4)
% 24.99/7.43  	| (47) in(all_61_0_15, ex_58_0_14) | (in(all_61_0_15, all_5_4_6) &  ~ in(all_61_0_15, all_5_2_4))
% 24.99/7.43  	|
% 24.99/7.43  	+-Applying beta-rule and splitting (46), into two cases.
% 24.99/7.43  	|-Branch one:
% 24.99/7.43  	| (48)  ~ in(all_61_0_15, ex_58_0_14)
% 24.99/7.43  	|
% 24.99/7.43  		+-Applying beta-rule and splitting (47), into two cases.
% 24.99/7.43  		|-Branch one:
% 24.99/7.43  		| (49) in(all_61_0_15, ex_58_0_14)
% 24.99/7.43  		|
% 24.99/7.43  			| Using (49) and (48) yields:
% 24.99/7.43  			| (50) $false
% 24.99/7.43  			|
% 24.99/7.43  			|-The branch is then unsatisfiable
% 24.99/7.43  		|-Branch two:
% 24.99/7.43  		| (51) in(all_61_0_15, all_5_4_6) &  ~ in(all_61_0_15, all_5_2_4)
% 24.99/7.43  		|
% 24.99/7.43  			| Applying alpha-rule on (51) yields:
% 24.99/7.43  			| (52) in(all_61_0_15, all_5_4_6)
% 24.99/7.43  			| (53)  ~ in(all_61_0_15, all_5_2_4)
% 24.99/7.43  			|
% 24.99/7.43  			| Instantiating formula (37) with all_61_0_15 and discharging atoms in(all_61_0_15, all_5_4_6), yields:
% 24.99/7.43  			| (54)  ~ in(all_61_0_15, all_5_3_5) | in(all_61_0_15, all_5_0_2)
% 24.99/7.43  			|
% 24.99/7.43  			| Instantiating formula (33) with all_61_0_15 and discharging atoms in(all_61_0_15, all_5_4_6),  ~ in(all_61_0_15, all_5_2_4), yields:
% 24.99/7.43  			| (55) in(all_61_0_15, all_5_3_5)
% 24.99/7.43  			|
% 24.99/7.43  			+-Applying beta-rule and splitting (54), into two cases.
% 24.99/7.43  			|-Branch one:
% 24.99/7.43  			| (56)  ~ in(all_61_0_15, all_5_3_5)
% 24.99/7.43  			|
% 24.99/7.43  				| Using (55) and (56) yields:
% 24.99/7.43  				| (50) $false
% 24.99/7.43  				|
% 24.99/7.43  				|-The branch is then unsatisfiable
% 24.99/7.43  			|-Branch two:
% 24.99/7.43  			| (58) in(all_61_0_15, all_5_0_2)
% 24.99/7.43  			|
% 24.99/7.43  				| From (38) and (48) follows:
% 24.99/7.43  				| (59)  ~ in(all_61_0_15, all_5_0_2)
% 24.99/7.43  				|
% 24.99/7.43  				| Using (58) and (59) yields:
% 24.99/7.43  				| (50) $false
% 24.99/7.43  				|
% 24.99/7.43  				|-The branch is then unsatisfiable
% 24.99/7.43  	|-Branch two:
% 24.99/7.43  	| (49) in(all_61_0_15, ex_58_0_14)
% 24.99/7.43  	| (62)  ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4)
% 24.99/7.44  	|
% 24.99/7.44  		| Instantiating formula (36) with all_61_0_15 yields:
% 24.99/7.44  		| (63)  ~ in(all_61_0_15, all_5_0_2) | (in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6))
% 24.99/7.44  		|
% 24.99/7.44  		| Instantiating formula (32) with all_61_0_15 yields:
% 24.99/7.44  		| (64)  ~ in(all_61_0_15, all_5_2_4) | (in(all_61_0_15, all_5_4_6) &  ~ in(all_61_0_15, all_5_3_5))
% 24.99/7.44  		|
% 24.99/7.44  		+-Applying beta-rule and splitting (62), into two cases.
% 24.99/7.44  		|-Branch one:
% 24.99/7.44  		| (65)  ~ in(all_61_0_15, all_5_4_6)
% 24.99/7.44  		|
% 24.99/7.44  			+-Applying beta-rule and splitting (63), into two cases.
% 24.99/7.44  			|-Branch one:
% 24.99/7.44  			| (59)  ~ in(all_61_0_15, all_5_0_2)
% 24.99/7.44  			|
% 24.99/7.44  				| From (38) and (49) follows:
% 24.99/7.44  				| (58) in(all_61_0_15, all_5_0_2)
% 24.99/7.44  				|
% 24.99/7.44  				| Using (58) and (59) yields:
% 24.99/7.44  				| (50) $false
% 24.99/7.44  				|
% 24.99/7.44  				|-The branch is then unsatisfiable
% 24.99/7.44  			|-Branch two:
% 24.99/7.44  			| (69) in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6)
% 24.99/7.44  			|
% 24.99/7.44  				| Applying alpha-rule on (69) yields:
% 24.99/7.44  				| (55) in(all_61_0_15, all_5_3_5)
% 24.99/7.44  				| (52) in(all_61_0_15, all_5_4_6)
% 24.99/7.44  				|
% 24.99/7.44  				| Using (52) and (65) yields:
% 24.99/7.44  				| (50) $false
% 24.99/7.44  				|
% 24.99/7.44  				|-The branch is then unsatisfiable
% 24.99/7.44  		|-Branch two:
% 24.99/7.44  		| (73) in(all_61_0_15, all_5_2_4)
% 24.99/7.44  		|
% 24.99/7.44  			+-Applying beta-rule and splitting (64), into two cases.
% 24.99/7.44  			|-Branch one:
% 24.99/7.44  			| (53)  ~ in(all_61_0_15, all_5_2_4)
% 24.99/7.44  			|
% 24.99/7.44  				| Using (73) and (53) yields:
% 24.99/7.44  				| (50) $false
% 24.99/7.44  				|
% 24.99/7.44  				|-The branch is then unsatisfiable
% 24.99/7.44  			|-Branch two:
% 24.99/7.44  			| (76) in(all_61_0_15, all_5_4_6) &  ~ in(all_61_0_15, all_5_3_5)
% 24.99/7.44  			|
% 24.99/7.44  				| Applying alpha-rule on (76) yields:
% 24.99/7.44  				| (52) in(all_61_0_15, all_5_4_6)
% 24.99/7.44  				| (56)  ~ in(all_61_0_15, all_5_3_5)
% 24.99/7.44  				|
% 24.99/7.44  				+-Applying beta-rule and splitting (63), into two cases.
% 24.99/7.44  				|-Branch one:
% 24.99/7.44  				| (59)  ~ in(all_61_0_15, all_5_0_2)
% 24.99/7.44  				|
% 24.99/7.44  					| From (38) and (49) follows:
% 24.99/7.44  					| (58) in(all_61_0_15, all_5_0_2)
% 24.99/7.44  					|
% 24.99/7.44  					| Using (58) and (59) yields:
% 24.99/7.44  					| (50) $false
% 24.99/7.44  					|
% 24.99/7.44  					|-The branch is then unsatisfiable
% 24.99/7.44  				|-Branch two:
% 24.99/7.44  				| (69) in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6)
% 24.99/7.44  				|
% 24.99/7.44  					| Applying alpha-rule on (69) yields:
% 24.99/7.44  					| (55) in(all_61_0_15, all_5_3_5)
% 24.99/7.44  					| (52) in(all_61_0_15, all_5_4_6)
% 24.99/7.44  					|
% 24.99/7.44  					| Using (55) and (56) yields:
% 24.99/7.44  					| (50) $false
% 24.99/7.44  					|
% 24.99/7.44  					|-The branch is then unsatisfiable
% 24.99/7.44  % SZS output end Proof for theBenchmark
% 24.99/7.44  
% 24.99/7.44  6802ms
%------------------------------------------------------------------------------