TSTP Solution File: SET046-5 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET046-5 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 : Tue May 21 03:05:04 EDT 2024

% Result   : Unsatisfiable 3.12s 1.77s
% Output   : Refutation 3.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   25 (   5 unt;   3 typ;   0 def)
%            Number of atoms       :   55 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  157 (  28   ~;  25   |;   0   &; 104   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :   20 (   0   ^  20   !;   0   ?;  20   :)

% Comments : 
%------------------------------------------------------------------------------
thf(element_type,type,
    element: $i > $i > $o ).

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

thf(f_type,type,
    f: $i > $i ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ( element @ A @ ( f @ A ) )
      | ( element @ A @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).

thf(5,plain,
    ! [A: $i] :
      ( ( element @ A @ ( f @ A ) )
      | ( element @ A @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    ! [A: $i] :
      ( ( element @ A @ ( f @ A ) )
      | ( element @ A @ a ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ( element @ ( f @ A ) @ A )
      | ( element @ A @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).

thf(6,plain,
    ! [A: $i] :
      ( ( element @ ( f @ A ) @ A )
      | ( element @ A @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,plain,
    ! [A: $i] :
      ( ( element @ ( f @ A ) @ A )
      | ( element @ A @ a ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(1,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( element @ A @ a )
      | ~ ( element @ A @ B )
      | ~ ( element @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).

thf(4,plain,
    ! [B: $i,A: $i] :
      ( ~ ( element @ A @ a )
      | ~ ( element @ A @ B )
      | ~ ( element @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( element @ A @ a )
      | ~ ( element @ A @ B )
      | ~ ( element @ B @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(41,plain,
    ! [B: $i,A: $i] :
      ( ~ ( element @ A @ a )
      | ~ ( element @ B @ A )
      | ( ( element @ A @ B )
       != ( element @ A @ a ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[7]) ).

thf(44,plain,
    ! [A: $i] :
      ( ~ ( element @ A @ a )
      | ~ ( element @ a @ A ) ),
    inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( A )),bind(B,$thf( a ))]]) ).

thf(83,plain,
    ! [B: $i,A: $i] :
      ( ( element @ A @ a )
      | ~ ( element @ a @ B )
      | ( ( element @ ( f @ A ) @ A )
       != ( element @ B @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[9,44]) ).

thf(84,plain,
    ( ( element @ a @ a )
    | ~ ( element @ a @ ( f @ a ) ) ),
    inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( a )),bind(B,$thf( f @ a ))]]) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ~ ( element @ A @ a )
      | ~ ( element @ A @ B )
      | ( ( element @ B @ A )
       != ( element @ A @ a ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[7]) ).

thf(46,plain,
    ( ~ ( element @ a @ a )
    | ~ ( element @ a @ a ) ),
    inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( a )),bind(B,$thf( a ))]]) ).

thf(52,plain,
    ~ ( element @ a @ a ),
    inference(simp,[status(thm)],[46]) ).

thf(108,plain,
    ( $false
    | ~ ( element @ a @ ( f @ a ) ) ),
    inference(rewrite,[status(thm)],[84,52]) ).

thf(109,plain,
    ~ ( element @ a @ ( f @ a ) ),
    inference(simp,[status(thm)],[108]) ).

thf(112,plain,
    ! [A: $i] :
      ( ( element @ A @ a )
      | ( ( element @ A @ ( f @ A ) )
       != ( element @ a @ ( f @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,109]) ).

thf(113,plain,
    element @ a @ a,
    inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( a ))]]) ).

thf(118,plain,
    $false,
    inference(rewrite,[status(thm)],[113,52]) ).

thf(119,plain,
    $false,
    inference(simp,[status(thm)],[118]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET046-5 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n012.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May 20 12:48:54 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.96  % [INFO] 	 Parsing done (89ms). 
% 1.20/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.43/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.62/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.21  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.81/1.24  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.81/1.24  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.81/1.24  % [INFO] 	 Type checking passed. 
% 1.81/1.24  % [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 ... 
% 3.12/1.77  % [INFO] 	 Killing All external provers ... 
% 3.12/1.77  % Time passed: 1235ms (effective reasoning time: 802ms)
% 3.12/1.77  % Axioms used in derivation (0): 
% 3.12/1.77  % No. of inferences in proof: 22
% 3.12/1.77  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1235 ms resp. 802 ms w/o parsing
% 3.12/1.81  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.12/1.81  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------