%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT016-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n022.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 : Wed Aug 30 18:14:11 EDT 2023

% Result   : Unsatisfiable 0.16s 0.56s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   16 (   7 unt;   6 typ;   0 def)
%            Number of atoms       :   13 (   2 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   5   ~;   3   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    7 (   2 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    equivalent: ( $i * $i ) > $o ).

tff(decl_23,type,
    there_exists: $i > $o ).

tff(decl_24,type,
    domain: $i > $i ).

tff(decl_25,type,
    codomain: $i > $i ).

tff(decl_26,type,
    compose: ( $i * $i ) > $i ).

tff(decl_27,type,
    a: $i ).

cnf(composition_implies_domain,axiom,
    ( there_exists(domain(X1))
    | ~ there_exists(compose(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).

cnf(compose_domain,axiom,
    compose(X1,domain(X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',compose_domain) ).

cnf(assume_a_exists,hypothesis,
    there_exists(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_a_exists) ).

cnf(prove_domain_of_a_exists,negated_conjecture,
    ~ there_exists(domain(a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_a_exists) ).

cnf(c_0_4,axiom,
    ( there_exists(domain(X1))
    | ~ there_exists(compose(X1,X2)) ),
    composition_implies_domain ).

cnf(c_0_5,axiom,
    compose(X1,domain(X1)) = X1,
    compose_domain ).

cnf(c_0_6,plain,
    ( there_exists(domain(X1))
    | ~ there_exists(X1) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,hypothesis,
    there_exists(a),
    assume_a_exists ).

cnf(c_0_8,negated_conjecture,
    ~ there_exists(domain(a)),
    prove_domain_of_a_exists ).

cnf(c_0_9,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : CAT016-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31  % Computer : n022.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Sun Aug 27 00:50:25 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.16/0.54  start to proof: theBenchmark
% 0.16/0.56  % Version  : CSE_E---1.5
% 0.16/0.56  % Problem  : theBenchmark.p
% 0.16/0.56  % Proof found
% 0.16/0.56  % SZS status Theorem for theBenchmark.p
% 0.16/0.56  % SZS output start Proof
% See solution above
% 0.16/0.56  % Total time : 0.003000 s
% 0.16/0.56  % SZS output end Proof
% 0.16/0.56  % Total time : 0.006000 s
%------------------------------------------------------------------------------