## TSTP Solution File: SYN367+1 by Leo-III---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Leo-III---1.7.0
% Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 22:44:48 EDT 2022

% Result   : Theorem 2.22s 1.46s
% Output   : Refutation 2.66s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :    7 (   1 unt;   3 typ;   0 def)
%            Number of atoms       :   19 (   0 equ;   0 cnn)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   32 (   5   ~;   6   |;   6   &;  12   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    9 (   0   ^   9   !;   0   ?;   9   :)

%------------------------------------------------------------------------------
thf(p_type,type,
p: \$o ).

thf(big_q_type,type,
big_q: \$i > \$o ).

thf(big_r_type,type,
big_r: \$i > \$o ).

thf(1,conjecture,
( ! [A: \$i] :
( ( p
& ( big_q @ A ) )
| ( ~ p
& ( big_r @ A ) ) )
=> ( ! [A: \$i] : ( big_q @ A )
| ! [A: \$i] : ( big_r @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2118) ).

thf(2,negated_conjecture,
~ ( ! [A: \$i] :
( ( p
& ( big_q @ A ) )
| ( ~ p
& ( big_r @ A ) ) )
=> ( ! [A: \$i] : ( big_q @ A )
| ! [A: \$i] : ( big_r @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
~ ( ! [A: \$i] :
( ( p
& ( big_q @ A ) )
| ( ~ p
& ( big_r @ A ) ) )
=> ( ! [A: \$i] : ( big_q @ A )
| ! [A: \$i] : ( big_r @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,plain,
\$false,
inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n025.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
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Sep  5 03:05:04 EDT 2022
% 0.14/0.35  % CPUTime  :
% 0.82/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.93  % [INFO] 	 Parsing done (97ms).
% 1.21/0.94  % [INFO] 	 Running in sequential loop mode.
% 1.46/1.12  % [INFO] 	 eprover registered as external prover.
% 1.46/1.12  % [INFO] 	 cvc4 registered as external prover.
% 1.46/1.12  % [INFO] 	 Scanning for conjecture ...
% 1.46/1.17  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ...
% 1.70/1.19  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.70/1.19  % [INFO] 	 Problem is first-order (TPTP FOF).
% 1.70/1.19  % [INFO] 	 Type checking passed.
% 1.70/1.19  % [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 ...
% 2.22/1.46  % External prover 'e' found a proof!
% 2.22/1.46  % [INFO] 	 Killing All external provers ...
% 2.22/1.46  % Time passed: 966ms (effective reasoning time: 518ms)
% 2.22/1.46  % 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)>
% 2.22/1.46  % Axioms used in derivation (0):
% 2.22/1.46  % No. of inferences in proof: 4
% 2.22/1.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 966 ms resp. 518 ms w/o parsing
% 2.66/1.50  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.66/1.50  % [INFO] 	 Killing All external provers ...
%------------------------------------------------------------------------------
```