%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SYN722+1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Fri May 19 12:29:46 EDT 2023

% Result   : Theorem 2.83s 1.65s
% Output   : Refutation 2.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   11 (   1 unt;   7 typ;   0 def)
%            Number of atoms       :   31 (   0 equ;   0 cnn)
%            Maximal formula atoms :   10 (   7 avg)
%            Number of connectives :   80 (  23   ~;  18   |;   9   &;  30   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :    9 (   0   ^;   6   !;   3   ?;   9   :)

% Comments : 
%------------------------------------------------------------------------------
thf(p_type,type,
    p: $i > $o ).

thf(r_type,type,
    r: $i > $o ).

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

thf(c_type,type,
    c: $i ).

thf(d_type,type,
    d: $i ).

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

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

thf(1,conjecture,
    ~ ( ! [A: $i] :
          ( ( ( p @ A )
            | ( r @ A ) )
          & ( q @ A ) )
      & ! [A: $i] :
        ? [B: $i] :
          ( ( p @ A )
          | ~ ( q @ A )
          | ~ ( q @ B )
          | ~ ( q @ c )
          | ~ ( q @ d ) )
      & ( ~ ( p @ a )
        | ~ ( p @ b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm119) ).

thf(2,negated_conjecture,
    ~ ~ ( ! [A: $i] :
            ( ( ( p @ A )
              | ( r @ A ) )
            & ( q @ A ) )
        & ! [A: $i] :
          ? [B: $i] :
            ( ( p @ A )
            | ~ ( q @ A )
            | ~ ( q @ B )
            | ~ ( q @ c )
            | ~ ( q @ d ) )
        & ( ~ ( p @ a )
          | ~ ( p @ b ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ~ ( ! [A: $i] :
            ( ( ( p @ A )
              | ( r @ A ) )
            & ( q @ A ) )
        & ! [A: $i] :
          ? [B: $i] :
            ( ( p @ A )
            | ~ ( q @ A )
            | ~ ( q @ B )
            | ~ ( q @ c )
            | ~ ( q @ d ) )
        & ( ~ ( p @ a )
          | ~ ( p @ b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(15,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN722+1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n015.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 19:42:23 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.97/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/1.01  % [INFO] 	 Parsing done (117ms). 
% 1.24/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.59/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.59/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.28  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.82/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.82/1.30  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.82/1.30  % [INFO] 	 Type checking passed. 
% 1.82/1.31  % [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 ... 
% 2.83/1.64  % External prover 'e' found a proof!
% 2.83/1.64  % [INFO] 	 Killing All external provers ... 
% 2.83/1.65  % Time passed: 1135ms (effective reasoning time: 626ms)
% 2.83/1.65  % 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)>
% 2.83/1.65  % Axioms used in derivation (0): 
% 2.83/1.65  % No. of inferences in proof: 4
% 2.83/1.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1135 ms resp. 626 ms w/o parsing
% 2.93/1.72  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.93/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------