## TSTP Solution File: SYN721+1 by iProver---3.6

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : iProver---3.6
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python3 prover_driver.py --schedule_mode external --schedule fof_schedule --no_cores 8 --problem_version fof /export/starexec/sandbox2/benchmark/theBenchmark.p 300 --prover /export/starexec/sandbox2/solver/bin/res/iproveropt_no_z3

% 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  : 300s
% DateTime : Thu Sep 29 22:29:43 EDT 2022

% Result   : Theorem 1.01s 1.59s
% Output   : CNFRefutation 1.01s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   20 (   8 unt;   0 def)
%            Number of atoms       :   62 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   65 (  23   ~;  15   |;  18   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   52 (   6 sgn  36   !;   6   ?)

%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X2,X3] :
( q(X2,X3)
=> ! [X4] : r(X4,X3) )
& ! [X0] :
( ? [X1] : r(X0,X1)
=> q(X0,X0) )
& r(a,b) )
=> ? [X5] :
( q(X5,a)
& r(b,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1) ).

fof(f2,negated_conjecture,
~ ( ( ! [X2,X3] :
( q(X2,X3)
=> ! [X4] : r(X4,X3) )
& ! [X0] :
( ? [X1] : r(X0,X1)
=> q(X0,X0) )
& r(a,b) )
=> ? [X5] :
( q(X5,a)
& r(b,X5) ) ),
inference(negated_conjecture,[],[f1]) ).

fof(f3,plain,
~ ( ( ! [X0,X1] :
( q(X0,X1)
=> ! [X2] : r(X2,X1) )
& ! [X3] :
( ? [X4] : r(X3,X4)
=> q(X3,X3) )
& r(a,b) )
=> ? [X5] :
( q(X5,a)
& r(b,X5) ) ),
inference(rectify,[],[f2]) ).

fof(f4,plain,
( ! [X5] :
( ~ q(X5,a)
| ~ r(b,X5) )
& ! [X0,X1] :
( ! [X2] : r(X2,X1)
| ~ q(X0,X1) )
& ! [X3] :
( q(X3,X3)
| ! [X4] : ~ r(X3,X4) )
& r(a,b) ),
inference(ennf_transformation,[],[f3]) ).

fof(f5,plain,
( ! [X5] :
( ~ q(X5,a)
| ~ r(b,X5) )
& ! [X0,X1] :
( ! [X2] : r(X2,X1)
| ~ q(X0,X1) )
& ! [X3] :
( q(X3,X3)
| ! [X4] : ~ r(X3,X4) )
& r(a,b) ),
inference(flattening,[],[f4]) ).

fof(f6,plain,
( ! [X0] :
( ~ q(X0,a)
| ~ r(b,X0) )
& ! [X1,X2] :
( ! [X3] : r(X3,X2)
| ~ q(X1,X2) )
& ! [X4] :
( q(X4,X4)
| ! [X5] : ~ r(X4,X5) )
& r(a,b) ),
inference(rectify,[],[f5]) ).

fof(f8,plain,
! [X4,X5] :
( q(X4,X4)
| ~ r(X4,X5) ),
inference(cnf_transformation,[],[f6]) ).

fof(f7,plain,
r(a,b),
inference(cnf_transformation,[],[f6]) ).

fof(f10,plain,
! [X0] :
( ~ q(X0,a)
| ~ r(b,X0) ),
inference(cnf_transformation,[],[f6]) ).

fof(f9,plain,
! [X2,X3,X1] :
( r(X3,X2)
| ~ q(X1,X2) ),
inference(cnf_transformation,[],[f6]) ).

cnf(c_51,negated_conjecture,
( ~ r(X0,X1)
| q(X0,X0) ),
inference(cnf_transformation,[],[f8]) ).

cnf(c_52,negated_conjecture,
r(a,b),
inference(cnf_transformation,[],[f7]) ).

cnf(c_56,plain,
q(a,a),
inference(resolution,[status(thm)],[c_51,c_52]) ).

cnf(c_49,negated_conjecture,
( ~ q(X0,a)
| ~ r(b,X0) ),
inference(cnf_transformation,[],[f10]) ).

cnf(c_57,plain,
~ r(b,a),
inference(resolution,[status(thm)],[c_56,c_49]) ).

cnf(c_50,negated_conjecture,
( ~ q(X0,X1)
| r(X2,X1) ),
inference(cnf_transformation,[],[f9]) ).

cnf(c_58,plain,
r(X0,a),
inference(resolution,[status(thm)],[c_56,c_50]) ).

cnf(c_60,plain,
q(X0,X0),
inference(resolution,[status(thm)],[c_58,c_51]) ).

cnf(c_62,plain,
r(X0,X1),
inference(resolution,[status(thm)],[c_60,c_50]) ).

cnf(c_64,plain,
\$false,
inference(resolution,[status(thm)],[c_57,c_62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.14  % Command  : python3 prover_driver.py --schedule_mode external --schedule fof_schedule --no_cores 8 --problem_version fof /export/starexec/sandbox2/benchmark/theBenchmark.p 300 --prover /export/starexec/sandbox2/solver/bin/res/iproveropt_no_z3
% 0.13/0.36  % Computer : n029.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Mon Sep  5 06:55:16 EDT 2022
% 0.13/0.36  % CPUTime  :
% 1.01/1.59  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.01/1.59
% 1.01/1.59  %---------------- iProver v3.6 (pre CASC-J11 2022) ----------------%
% 1.01/1.59
% 1.01/1.59  ------  iProver source info
% 1.01/1.59
% 1.01/1.59  git: date: 2022-07-26 19:47:37 +0300
% 1.01/1.59  git: sha1: 69e283425f6c8ae3fb9e67f2058d741e849b12e1
% 1.01/1.59  git: non_committed_changes: false
% 1.01/1.59  git: last_make_outside_of_git: false
% 1.01/1.59
% 1.01/1.59  ------ Parsing...
% 1.01/1.59  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Option_epr_horn
% 1.01/1.59
% 1.01/1.59
% 1.01/1.59  ------ Preprocessing... sf_s  rm: 0 0s  sf_e
% 1.01/1.59
% 1.01/1.59  ------ Preprocessing...------  preprocesses with Option_epr_horn
% 1.01/1.59   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e
% 1.01/1.59  ------ Proving...
% 1.01/1.59  ------ Problem Properties
% 1.01/1.59
% 1.01/1.59
% 1.01/1.59  clauses                                 4
% 1.01/1.59  conjectures                             4
% 1.01/1.59  EPR                                     4
% 1.01/1.59  Horn                                    4
% 1.01/1.59  unary                                   1
% 1.01/1.59  binary                                  3
% 1.01/1.59  lits                                    7
% 1.01/1.59  lits eq                                 0
% 1.01/1.59  fd_pure                                 0
% 1.01/1.59  fd_pseudo                               0
% 1.01/1.59  fd_cond                                 0
% 1.01/1.59  fd_pseudo_cond                          0
% 1.01/1.59  AC symbols                              0
% 1.01/1.59
% 1.01/1.59  ------ Schedule EPR Horn non eq is on
% 1.01/1.59
% 1.01/1.59  ------ no equalities: superposition off
% 1.01/1.59
% 1.01/1.59  ------ Option_epr_horn Time Limit: Unbounded
% 1.01/1.59
% 1.01/1.59
% 1.01/1.59  ------
% 1.01/1.59  Current options:
% 1.01/1.59  ------
% 1.01/1.59
% 1.01/1.59
% 1.01/1.59
% 1.01/1.59
% 1.01/1.59  ------ Proving...
% 1.01/1.59
% 1.01/1.59
% 1.01/1.59  % SZS status Theorem for theBenchmark.p
% 1.01/1.59
% 1.01/1.59  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.01/1.59
% 1.01/1.59  ------                               Statistics
% 1.01/1.59
% 1.01/1.59  ------ Selected
% 1.01/1.59
% 1.01/1.59  total_time:                             0.032
% 1.01/1.59
%------------------------------------------------------------------------------
```