## TSTP Solution File: SYN721+1 by SPASS---3.9

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 12:23:54 EDT 2022

% Result   : Theorem 0.21s 0.45s
% Output   : Refutation 0.21s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   11 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

%------------------------------------------------------------------------------
cnf(1,axiom,
r(a,b),
file('SYN721+1.p',unknown),
[] ).

cnf(2,axiom,
( ~ r(u,v)
| q(u,u) ),
file('SYN721+1.p',unknown),
[] ).

cnf(3,axiom,
( ~ q(u,v)
| r(w,v) ),
file('SYN721+1.p',unknown),
[] ).

cnf(4,axiom,
( ~ q(u,a)
| ~ r(b,u) ),
file('SYN721+1.p',unknown),
[] ).

cnf(5,plain,
q(a,a),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.0')] ).

cnf(6,plain,
r(u,a),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.0,3.0')] ).

cnf(7,plain,
~ r(b,a),
inference(res,[status(thm),theory(equality)],[5,4]),
[iquote('0:Res:5.0,4.0')] ).

cnf(8,plain,
\$false,
inference(mrr,[status(thm)],[7,6]),
[iquote('0:MRR:7.0,6.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n016.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Mon Jul 11 21:13:58 EDT 2022
% 0.14/0.36  % CPUTime  :
% 0.21/0.45
% 0.21/0.45  SPASS V 3.9
% 0.21/0.45  SPASS beiseite: Proof found.
% 0.21/0.45  % SZS status Theorem
% 0.21/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 7 clauses.
% 0.21/0.45  SPASS allocated 85056 KBytes.
% 0.21/0.45  SPASS spent	0:00:00.08 on the problem.
% 0.21/0.45  		0:00:00.03 for the input.
% 0.21/0.45  		0:00:00.02 for the FLOTTER CNF translation.
% 0.21/0.45  		0:00:00.00 for inferences.
% 0.21/0.45  		0:00:00.00 for the backtracking.
% 0.21/0.45  		0:00:00.00 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45  Here is a proof with depth 2, length 8 :
% 0.21/0.45  % SZS output start Refutation
% See solution above
% 0.21/0.45  Formulae used in the proof : lx1
% 0.21/0.45
%------------------------------------------------------------------------------
```