TSTP Solution File: SEU161+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU161+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jul 19 08:47:08 EDT 2022

% Result   : Theorem 1.88s 1.27s
% Output   : Proof 2.64s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU161+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 19 12:47:00 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.63/0.63          ____       _                          
% 0.63/0.63    ___  / __ \_____(_)___  ________  __________
% 0.63/0.63   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.63  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.63/0.63  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.63/0.63  
% 0.63/0.63  A Theorem Prover for First-Order Logic
% 0.63/0.63  (ePrincess v.1.0)
% 0.63/0.63  
% 0.63/0.63  (c) Philipp Rümmer, 2009-2015
% 0.63/0.63  (c) Peter Backeman, 2014-2015
% 0.63/0.63  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.63  Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.63  Bug reports to peter@backeman.se
% 0.63/0.63  
% 0.63/0.63  For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.63  
% 0.63/0.64  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.70  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/1.00  Prover 0: Preprocessing ...
% 1.56/1.16  Prover 0: Constructing countermodel ...
% 1.88/1.27  Prover 0: proved (567ms)
% 1.88/1.27  
% 1.88/1.27  No countermodel exists, formula is valid
% 1.88/1.27  % SZS status Theorem for theBenchmark
% 1.88/1.27  
% 1.88/1.27  Generating proof ... found it (size 5)
% 2.49/1.41  
% 2.49/1.41  % SZS output start Proof for theBenchmark
% 2.49/1.41  Assumed formulas after preprocessing and simplification: 
% 2.49/1.41  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v3 = v1) & singleton(v0) = v2 & set_union2(v2, v1) = v3 & in(v0, v1) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v5 |  ~ (singleton(v4) = v6) |  ~ (set_union2(v6, v5) = v7) |  ~ in(v4, v5)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (set_union2(v7, v6) = v5) |  ~ (set_union2(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (singleton(v6) = v5) |  ~ (singleton(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_union2(v5, v4) = v6) | set_union2(v4, v5) = v6) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_union2(v4, v5) = v6) | set_union2(v5, v4) = v6) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (set_union2(v4, v4) = v5)) &  ! [v4] :  ! [v5] : ( ~ in(v5, v4) |  ~ in(v4, v5)))
% 2.64/1.47  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.64/1.47  | (1)  ~ (all_0_0_0 = all_0_2_2) & singleton(all_0_3_3) = all_0_1_1 & set_union2(all_0_1_1, all_0_2_2) = all_0_0_0 & in(all_0_3_3, all_0_2_2) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (singleton(v0) = v2) |  ~ (set_union2(v2, v1) = v3) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 2.64/1.47  |
% 2.64/1.47  | Applying alpha-rule on (1) yields:
% 2.64/1.47  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 2.64/1.47  | (3) singleton(all_0_3_3) = all_0_1_1
% 2.64/1.47  | (4)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 2.64/1.47  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (singleton(v0) = v2) |  ~ (set_union2(v2, v1) = v3) |  ~ in(v0, v1))
% 2.64/1.48  | (6)  ~ (all_0_0_0 = all_0_2_2)
% 2.64/1.48  | (7) in(all_0_3_3, all_0_2_2)
% 2.64/1.48  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 2.64/1.48  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 2.64/1.48  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 2.64/1.48  | (11)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 2.64/1.48  | (12) set_union2(all_0_1_1, all_0_2_2) = all_0_0_0
% 2.64/1.48  |
% 2.64/1.48  | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms singleton(all_0_3_3) = all_0_1_1, set_union2(all_0_1_1, all_0_2_2) = all_0_0_0, in(all_0_3_3, all_0_2_2), yields:
% 2.64/1.48  | (13) all_0_0_0 = all_0_2_2
% 2.64/1.48  |
% 2.64/1.48  | Equations (13) can reduce 6 to:
% 2.64/1.48  | (14) $false
% 2.64/1.48  |
% 2.64/1.48  |-The branch is then unsatisfiable
% 2.64/1.48  % SZS output end Proof for theBenchmark
% 2.64/1.48  
% 2.64/1.48  834ms
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