%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT007-1 : 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 18:14:06 EDT 2023

% Result   : Unsatisfiable 0.21s 0.59s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   23 (  12 unt;   8 typ;   0 def)
%            Number of atoms       :   22 (   2 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   16 (   9   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   14 (   2 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    compose: ( $i * $i ) > $i ).

tff(decl_24,type,
    product: ( $i * $i * $i ) > $o ).

tff(decl_25,type,
    identity_map: $i > $o ).

tff(decl_26,type,
    domain: $i > $i ).

tff(decl_27,type,
    codomain: $i > $i ).

tff(decl_28,type,
    a: $i ).

tff(decl_29,type,
    b: $i ).

cnf(category_theory_axiom6,axiom,
    ( defined(X1,X3)
    | ~ defined(X1,X2)
    | ~ defined(X2,X3)
    | ~ identity_map(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).

cnf(mapping_from_codomain_of_x_to_x,axiom,
    defined(codomain(X1),X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',mapping_from_codomain_of_x_to_x) ).

cnf(codomain_is_an_identity_map,axiom,
    identity_map(codomain(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).

cnf(mapping_from_x_to_its_domain,axiom,
    defined(X1,domain(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).

cnf(domain_of_a_equals_codomain_of_b,hypothesis,
    domain(a) = codomain(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_a_equals_codomain_of_b) ).

cnf(prove_ab_is_defined,negated_conjecture,
    ~ defined(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ab_is_defined) ).

cnf(c_0_6,axiom,
    ( defined(X1,X3)
    | ~ defined(X1,X2)
    | ~ defined(X2,X3)
    | ~ identity_map(X2) ),
    category_theory_axiom6 ).

cnf(c_0_7,axiom,
    defined(codomain(X1),X1),
    mapping_from_codomain_of_x_to_x ).

cnf(c_0_8,axiom,
    identity_map(codomain(X1)),
    codomain_is_an_identity_map ).

cnf(c_0_9,axiom,
    defined(X1,domain(X1)),
    mapping_from_x_to_its_domain ).

cnf(c_0_10,hypothesis,
    domain(a) = codomain(b),
    domain_of_a_equals_codomain_of_b ).

cnf(c_0_11,plain,
    ( defined(X1,X2)
    | ~ defined(X1,codomain(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).

cnf(c_0_12,hypothesis,
    defined(a,codomain(b)),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    ~ defined(a,b),
    prove_ab_is_defined ).

cnf(c_0_14,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : CAT007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.19/0.35  % Computer : n022.cluster.edu
% 0.19/0.35  % Model    : x86_64 x86_64
% 0.19/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35  % Memory   : 8042.1875MB
% 0.19/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35  % CPULimit   : 300
% 0.19/0.35  % WCLimit    : 300
% 0.19/0.35  % DateTime   : Sun Aug 27 00:49:55 EDT 2023
% 0.19/0.35  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.59  % Version  : CSE_E---1.5
% 0.21/0.59  % Problem  : theBenchmark.p
% 0.21/0.59  % Proof found
% 0.21/0.59  % SZS status Theorem for theBenchmark.p
% 0.21/0.59  % SZS output start Proof
% See solution above
% 0.21/0.59  % Total time : 0.006000 s
% 0.21/0.59  % SZS output end Proof
% 0.21/0.59  % Total time : 0.008000 s
%------------------------------------------------------------------------------