%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV431^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n001.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 : Mon Jun 24 15:59:00 EDT 2024

% Result   : Theorem 2.84s 1.61s
% Output   : Refutation 2.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   13 (   8 unt;   0 typ;   0 def)
%            Number of atoms       :   18 (  17 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   46 (   9   ~;   3   |;   0   &;  32   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   2 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   19 (   0   ^  16   !;   3   ?;  19   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

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

thf(f_type,type,
    f: a > b ).

thf(sk1_type,type,
    sk1: ( b > a ) > a ).

thf(sk2_type,type,
    sk2: b > a ).

thf(3,axiom,
    ! [A: a,B: a] :
      ( ( ( f @ A )
        = ( f @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finj) ).

thf(7,plain,
    ! [A: a,B: a] :
      ( ( ( f @ A )
        = ( f @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,plain,
    ! [B: a,A: a] :
      ( ( ( f @ A )
       != ( f @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(9,plain,
    ! [B: a,A: a] :
      ( ( ( f @ A )
       != ( f @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(10,plain,
    ! [A: a] :
      ( ( sk2 @ ( f @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse(f),[sk2])]) ).

thf(1,conjecture,
    ? [A: b > a] :
    ! [B: a] :
      ( ( A @ ( f @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',invexists) ).

thf(2,negated_conjecture,
    ~ ? [A: b > a] :
      ! [B: a] :
        ( ( A @ ( f @ B ) )
        = B ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ~ ? [A: b > a] :
      ! [B: a] :
        ( ( A @ ( f @ B ) )
        = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ! [A: b > a] :
      ( ( A @ ( f @ ( sk1 @ A ) ) )
     != ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(6,plain,
    ! [A: b > a] :
      ( ( A @ ( f @ ( sk1 @ A ) ) )
     != ( sk1 @ A ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(11,plain,
    ! [B: b > a,A: a] :
      ( ( A
       != ( sk1 @ B ) )
      | ( ( sk2 @ ( f @ A ) )
       != ( B @ ( f @ ( sk1 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,6]) ).

thf(13,plain,
    ( ( sk1 @ sk2 )
   != ( sk1 @ sk2 ) ),
    inference(pre_uni,[status(thm)],[11:[bind(A,$thf( sk1 @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(14,plain,
    $false,
    inference(pattern_uni,[status(thm)],[13:[]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEV431^1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.34  % Computer : n001.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Jun 21 19:06:24 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.88/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.95  % [INFO] 	 Parsing done (97ms). 
% 1.19/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.51/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.51/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.83/1.24  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.83/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.83/1.24  % [INFO] 	 Type checking passed. 
% 1.83/1.24  % [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 ... 
% 2.60/1.61  % [INFO] 	 Killing All external provers ... 
% 2.60/1.61  % Time passed: 1083ms (effective reasoning time: 647ms)
% 2.60/1.61  % 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)>
% 2.60/1.61  % Axioms used in derivation (1): finj
% 2.60/1.61  % No. of inferences in proof: 13
% 2.84/1.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1083 ms resp. 647 ms w/o parsing
% 2.84/1.63  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.84/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------