## TSTP Solution File: SYN969+1 by ePrincess---1.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Thu Jul 21 05:06:10 EDT 2022

% Result   : Theorem 1.38s 0.98s
% Output   : Proof 1.93s
% Verified :
% SZS Type : -

%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n020.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 : Mon Jul 11 12:51:42 EDT 2022
% 0.12/0.33  % CPUTime  :
% 0.18/0.58          ____       _
% 0.18/0.58    ___  / __ \_____(_)___  ________  __________
% 0.18/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  )
% 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 RÃ¼mmer, 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
% 0.67/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.87  Prover 0: Preprocessing ...
% 1.33/0.92  Prover 0: Constructing countermodel ...
% 1.38/0.98  Prover 0: proved (353ms)
% 1.38/0.98
% 1.38/0.98  No countermodel exists, formula is valid
% 1.38/0.98  % SZS status Theorem for theBenchmark
% 1.38/0.98
% 1.38/0.98  Generating proof ... found it (size 5)
% 1.66/1.07
% 1.66/1.07  % SZS output start Proof for theBenchmark
% 1.66/1.07  Assumed formulas after preprocessing and simplification:
% 1.66/1.07  | (0)  ? [v0] : (r(v0) &  ~ q(v0) &  ! [v1] : ( ~ r(v1) | p(v1)) &  ! [v1] : ( ~ p(v1) | q(v1)))
% 1.66/1.08  | Instantiating (0) with all_0_0_0 yields:
% 1.66/1.08  | (1) r(all_0_0_0) &  ~ q(all_0_0_0) &  ! [v0] : ( ~ r(v0) | p(v0)) &  ! [v0] : ( ~ p(v0) | q(v0))
% 1.66/1.08  |
% 1.66/1.08  | Applying alpha-rule on (1) yields:
% 1.66/1.08  | (2) r(all_0_0_0)
% 1.66/1.08  | (3)  ~ q(all_0_0_0)
% 1.93/1.08  | (4)  ! [v0] : ( ~ r(v0) | p(v0))
% 1.93/1.09  | (5)  ! [v0] : ( ~ p(v0) | q(v0))
% 1.93/1.09  |
% 1.93/1.09  | Instantiating formula (4) with all_0_0_0 and discharging atoms r(all_0_0_0), yields:
% 1.93/1.09  | (6) p(all_0_0_0)
% 1.93/1.09  |
% 1.93/1.09  | Instantiating formula (5) with all_0_0_0 and discharging atoms p(all_0_0_0),  ~ q(all_0_0_0), yields:
% 1.93/1.09  | (7) \$false
% 1.93/1.09  |
% 1.93/1.09  |-The branch is then unsatisfiable
% 1.93/1.09  % SZS output end Proof for theBenchmark
% 1.93/1.09
% 1.93/1.09  502ms
%------------------------------------------------------------------------------
```