## TSTP Solution File: SYN969+1 by iProver---3.6

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : iProver---3.6
% Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python3 prover_driver.py --schedule_mode external --schedule fof_schedule --no_cores 8 --problem_version fof /export/starexec/sandbox/benchmark/theBenchmark.p 300 --prover /export/starexec/sandbox/solver/bin/res/iproveropt_no_z3

% Computer : n017.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  : 300s
% DateTime : Thu Sep 29 22:32:46 EDT 2022

% Result   : Theorem 1.10s 1.50s
% Output   : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   18 (   5 unt;   0 def)
%            Number of atoms       :   65 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :   74 (  27   ~;  18   |;  20   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   26 (   0 sgn  20   !;   4   ?)

%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( r(X0)
& ! [X1] :
( p(X1)
=> q(X1) ) )
=> ( ! [X2] :
( r(X2)
=> p(X2) )
=> q(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

fof(f2,negated_conjecture,
~ ! [X0] :
( ( r(X0)
& ! [X1] :
( p(X1)
=> q(X1) ) )
=> ( ! [X2] :
( r(X2)
=> p(X2) )
=> q(X0) ) ),
inference(negated_conjecture,[],[f1]) ).

fof(f3,plain,
? [X0] :
( ~ q(X0)
& ! [X2] :
( p(X2)
| ~ r(X2) )
& r(X0)
& ! [X1] :
( q(X1)
| ~ p(X1) ) ),
inference(ennf_transformation,[],[f2]) ).

fof(f4,plain,
? [X0] :
( ~ q(X0)
& ! [X2] :
( p(X2)
| ~ r(X2) )
& r(X0)
& ! [X1] :
( q(X1)
| ~ p(X1) ) ),
inference(flattening,[],[f3]) ).

fof(f5,plain,
? [X0] :
( ~ q(X0)
& ! [X1] :
( p(X1)
| ~ r(X1) )
& r(X0)
& ! [X2] :
( q(X2)
| ~ p(X2) ) ),
inference(rectify,[],[f4]) ).

fof(f6,plain,
( ? [X0] :
( ~ q(X0)
& ! [X1] :
( p(X1)
| ~ r(X1) )
& r(X0)
& ! [X2] :
( q(X2)
| ~ p(X2) ) )
=> ( ~ q(sK0)
& ! [X1] :
( p(X1)
| ~ r(X1) )
& r(sK0)
& ! [X2] :
( q(X2)
| ~ p(X2) ) ) ),
introduced(choice_axiom,[]) ).

fof(f7,plain,
( ~ q(sK0)
& ! [X1] :
( p(X1)
| ~ r(X1) )
& r(sK0)
& ! [X2] :
( q(X2)
| ~ p(X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f5,f6]) ).

fof(f11,plain,
~ q(sK0),
inference(cnf_transformation,[],[f7]) ).

fof(f10,plain,
! [X1] :
( p(X1)
| ~ r(X1) ),
inference(cnf_transformation,[],[f7]) ).

fof(f9,plain,
r(sK0),
inference(cnf_transformation,[],[f7]) ).

fof(f8,plain,
! [X2] :
( q(X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f7]) ).

cnf(c_49,negated_conjecture,
~ q(sK0),
inference(cnf_transformation,[],[f11]) ).

cnf(c_50,negated_conjecture,
( ~ r(X0)
| p(X0) ),
inference(cnf_transformation,[],[f10]) ).

cnf(c_54,plain,
( ~ r(sK0)
| p(sK0) ),
inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_51,negated_conjecture,
r(sK0),
inference(cnf_transformation,[],[f9]) ).

cnf(c_52,negated_conjecture,
( ~ p(X0)
| q(X0) ),
inference(cnf_transformation,[],[f8]) ).

cnf(c_53,plain,
( ~ p(sK0)
| q(sK0) ),
inference(instantiation,[status(thm)],[c_52]) ).

\$false,
inference(minisat,[status(thm)],[c_49,c_54,c_51,c_53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.14  % Command  : python3 prover_driver.py --schedule_mode external --schedule fof_schedule --no_cores 8 --problem_version fof /export/starexec/sandbox/benchmark/theBenchmark.p 300 --prover /export/starexec/sandbox/solver/bin/res/iproveropt_no_z3
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon Sep  5 09:09:41 EDT 2022
% 0.14/0.36  % CPUTime  :
% 1.10/1.50  % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.10/1.50
% 1.10/1.50  %---------------- iProver v3.6 (pre CASC-J11 2022) ----------------%
% 1.10/1.50
% 1.10/1.50  ------  iProver source info
% 1.10/1.50
% 1.10/1.50  git: date: 2022-07-26 19:47:37 +0300
% 1.10/1.50  git: sha1: 69e283425f6c8ae3fb9e67f2058d741e849b12e1
% 1.10/1.50  git: non_committed_changes: false
% 1.10/1.50  git: last_make_outside_of_git: false
% 1.10/1.50
% 1.10/1.50  ------ Parsing...
% 1.10/1.50  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.10/1.50
% 1.10/1.50  % SZS status Theorem for theBenchmark.p
% 1.10/1.50
% 1.10/1.50  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.10/1.50
% 1.10/1.50  ------                               Statistics
% 1.10/1.50
% 1.10/1.50  ------ Selected
% 1.10/1.50
% 1.10/1.50  total_time:                             0.029
% 1.10/1.50
%------------------------------------------------------------------------------
```