## TSTP Solution File: SYN721+1 by CSE_E---1.4

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : CSE_E---1.4
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n015.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 21:12:48 EDT 2022

% Result   : Theorem 0.62s 0.69s
% Output   : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   11 (   5 unt;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   31 (  10   ~;   6   |;   9   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   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   :   25 (   4 sgn  14   !;   4   ?)

%------------------------------------------------------------------------------
fof(lx1,conjecture,
( ( r(a,b)
& ! [X1] :
( ? [X2] : r(X1,X2)
=> q(X1,X1) )
& ! [X3,X4] :
( q(X3,X4)
=> ! [X5] : r(X5,X4) ) )
=> ? [X6] :
( r(b,X6)
& q(X6,a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1) ).

fof(c_0_1,negated_conjecture,
~ ( ( r(a,b)
& ! [X1] :
( ? [X2] : r(X1,X2)
=> q(X1,X1) )
& ! [X3,X4] :
( q(X3,X4)
=> ! [X5] : r(X5,X4) ) )
=> ? [X6] :
( r(b,X6)
& q(X6,a) ) ),
inference(assume_negation,[status(cth)],[lx1]) ).

fof(c_0_2,negated_conjecture,
! [X13,X14,X15,X16,X17,X18] :
( r(a,b)
& ( ~ r(X13,X14)
| q(X13,X13) )
& ( ~ q(X15,X16)
| r(X17,X16) )
& ( ~ r(b,X18)
| ~ q(X18,a) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).

cnf(c_0_3,negated_conjecture,
( q(X1,X1)
| ~ r(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
r(a,b),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_5,negated_conjecture,
( ~ r(b,X1)
| ~ q(X1,a) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_6,negated_conjecture,
q(a,a),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

cnf(c_0_7,negated_conjecture,
( r(X3,X2)
| ~ q(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_8,negated_conjecture,
~ r(b,a),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,negated_conjecture,
r(X1,a),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).

cnf(c_0_10,negated_conjecture,
\$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]),
[proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12  % Command   : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n015.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Sep  5 06:56:42 EDT 2022
% 0.13/0.33  % CPUTime  :
% 0.20/0.44  openjdk version "1.8.0_171"
% 0.20/0.44  OpenJDK Runtime Environment (build 1.8.0_171-b10)
% 0.20/0.44  OpenJDK 64-Bit Server VM (build 25.171-b10, mixed mode)
% 0.20/0.44  file=/export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/0.66  start to proof: theBenchmark
% 0.62/0.69  % Version  : CSE_E---1.4
% 0.62/0.69  % Problem  : theBenchmark.p
% 0.62/0.69  % Proof found
% 0.62/0.69  % SZS status Theorem for theBenchmark.p
% 0.62/0.69  % SZS output start Proof
% See solution above
% 0.62/0.69  % Total time : 0.019000 s
%------------------------------------------------------------------------------
```