## TSTP Solution File: SYN721+1 by Leo-III---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Leo-III---1.7.0
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 22:46:45 EDT 2022

% Result   : Theorem 2.53s 1.57s
% Output   : Refutation 2.53s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   1 unt;   4 typ;   0 def)
%            Number of atoms       :   22 (   0 equ;   0 cnn)
%            Maximal formula atoms :    7 (   5 avg)
%            Number of connectives :   62 (   2   ~;   0   |;   9   &;  42   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   18 (   0   ^  12   !;   6   ?;  18   :)

% Comments :
%------------------------------------------------------------------------------
thf(r_type,type,
r: \$i > \$i > \$o ).

thf(a_type,type,
a: \$i ).

thf(b_type,type,
b: \$i ).

thf(q_type,type,
q: \$i > \$i > \$o ).

thf(1,conjecture,
( ( ( r @ a @ b )
& ! [A: \$i] :
( ? [B: \$i] : ( r @ A @ B )
=> ( q @ A @ A ) )
& ! [A: \$i,B: \$i] :
( ( q @ A @ B )
=> ! [C: \$i] : ( r @ C @ B ) ) )
=> ? [A: \$i] :
( ( r @ b @ A )
& ( q @ A @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1) ).

thf(2,negated_conjecture,
~ ( ( ( r @ a @ b )
& ! [A: \$i] :
( ? [B: \$i] : ( r @ A @ B )
=> ( q @ A @ A ) )
& ! [A: \$i,B: \$i] :
( ( q @ A @ B )
=> ! [C: \$i] : ( r @ C @ B ) ) )
=> ? [A: \$i] :
( ( r @ b @ A )
& ( q @ A @ a ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
~ ( ( ( r @ a @ b )
& ! [A: \$i] :
( ? [B: \$i] : ( r @ A @ B )
=> ( q @ A @ A ) )
& ! [A: \$i,B: \$i] :
( ( q @ A @ B )
=> ! [C: \$i] : ( r @ C @ B ) ) )
=> ? [A: \$i] :
( ( r @ b @ A )
& ( q @ A @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(13,plain,
\$false,
inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n027.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  : 300
% 0.14/0.36  % DateTime : Mon Sep  5 07:00:22 EDT 2022
% 0.14/0.36  % CPUTime  :
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.12/1.00  % [INFO] 	 Parsing done (123ms).
% 1.12/1.00  % [INFO] 	 Running in sequential loop mode.
% 1.69/1.21  % [INFO] 	 eprover registered as external prover.
% 1.69/1.21  % [INFO] 	 cvc4 registered as external prover.
% 1.69/1.22  % [INFO] 	 Scanning for conjecture ...
% 1.83/1.27  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ...
% 1.83/1.29  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.83/1.29  % [INFO] 	 Problem is first-order (TPTP FOF).
% 1.83/1.29  % [INFO] 	 Type checking passed.
% 1.83/1.29  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ...
% 2.53/1.57  % External prover 'e' found a proof!
% 2.53/1.57  % [INFO] 	 Killing All external provers ...
% 2.53/1.57  % Time passed: 1064ms (effective reasoning time: 562ms)
% 2.53/1.57  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 2.53/1.57  % Axioms used in derivation (0):
% 2.53/1.57  % No. of inferences in proof: 4
% 2.53/1.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1064 ms resp. 562 ms w/o parsing
% 2.53/1.64  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.53/1.64  % [INFO] 	 Killing All external provers ...
%------------------------------------------------------------------------------
```