%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET838-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 11:54:33 EDT 2023

% Result   : Unsatisfiable 3.69s 1.73s
% Output   : Refutation 3.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   13 (   3 unt;   4 typ;   0 def)
%            Number of atoms       :   15 (  14 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   40 (   8   ~;   6   |;   0   &;  26   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   0   ^;   6   !;   0   ?;   6   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_f_type,type,
    v_f: $i > $i ).

thf(v_g_type,type,
    v_g: $i > $i ).

thf(v_x_type,type,
    v_x: $i ).

thf(v_xa_type,type,
    v_xa: $i > $i ).

thf(1,negated_conjecture,
    ( ( v_f @ ( v_g @ v_x ) )
    = v_x ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(5,plain,
    ( ( v_f @ ( v_g @ v_x ) )
    = v_x ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ( A = v_x )
      | ( ( v_f @ ( v_g @ A ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(6,plain,
    ! [A: $i] :
      ( ( A = v_x )
      | ( ( v_f @ ( v_g @ A ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ( ( v_g @ ( v_f @ ( v_xa @ A ) ) )
        = ( v_xa @ A ) )
      | ( ( v_g @ ( v_f @ A ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(7,plain,
    ! [A: $i] :
      ( ( ( v_g @ ( v_f @ ( v_xa @ A ) ) )
        = ( v_xa @ A ) )
      | ( ( v_g @ ( v_f @ A ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,negated_conjecture,
    ! [A: $i] :
      ( ( ( v_xa @ A )
       != A )
      | ( ( v_g @ ( v_f @ A ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(8,plain,
    ! [A: $i] :
      ( ( ( v_xa @ A )
       != A )
      | ( ( v_g @ ( v_f @ A ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(18,plain,
    $false,
    inference(e,[status(thm)],[5,6,7,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET838-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n024.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 : Thu May 18 18:52:22 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.82/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.53/1.07  % [INFO] 	 Parsing done (236ms). 
% 1.90/1.08  % [INFO] 	 Running in sequential loop mode. 
% 2.32/1.28  % [INFO] 	 eprover registered as external prover. 
% 2.32/1.28  % [INFO] 	 cvc4 registered as external prover. 
% 2.32/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.78/1.39  % [INFO] 	 Found a conjecture and 1357 axioms. Running axiom selection ... 
% 2.78/1.42  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 1357 axioms). 
% 2.78/1.42  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.78/1.42  % [INFO] 	 Type checking passed. 
% 2.78/1.43  % [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 ... 
% 3.69/1.73  % External prover 'e' found a proof!
% 3.69/1.73  % [INFO] 	 Killing All external provers ... 
% 3.69/1.73  % Time passed: 1217ms (effective reasoning time: 647ms)
% 3.69/1.73  % 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)>
% 3.69/1.73  % Axioms used in derivation (0): 
% 3.69/1.73  % No. of inferences in proof: 9
% 3.69/1.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1217 ms resp. 647 ms w/o parsing
% 3.69/1.75  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.69/1.75  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------