%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT014-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 18:14:10 EDT 2023

% Result   : Unsatisfiable 0.19s 0.62s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   24 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :   27 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   22 (  12   ~;  10   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   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    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   23 (   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 ).

cnf(identity2,axiom,
    ( product(X1,X2,X1)
    | ~ defined(X1,X2)
    | ~ identity_map(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).

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

cnf(composition_is_well_defined,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).

cnf(product_on_codomain,axiom,
    product(codomain(X1),X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).

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

cnf(prove_codomain_is_idempotent,negated_conjecture,
    codomain(codomain(a)) != codomain(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_is_idempotent) ).

cnf(c_0_6,axiom,
    ( product(X1,X2,X1)
    | ~ defined(X1,X2)
    | ~ identity_map(X2) ),
    identity2 ).

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

cnf(c_0_8,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    composition_is_well_defined ).

cnf(c_0_9,axiom,
    product(codomain(X1),X1,X1),
    product_on_codomain ).

cnf(c_0_10,plain,
    ( product(codomain(X1),X1,codomain(X1))
    | ~ identity_map(X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_11,axiom,
    identity_map(codomain(X1)),
    codomain_is_an_identity_map ).

cnf(c_0_12,plain,
    ( X1 = X2
    | ~ product(codomain(X1),X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    product(codomain(codomain(X1)),codomain(X1),codomain(codomain(X1))),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    codomain(codomain(a)) != codomain(a),
    prove_codomain_is_idempotent ).

cnf(c_0_15,plain,
    codomain(codomain(X1)) = codomain(X1),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : CAT014-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n011.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   : Sun Aug 27 00:08:54 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.62  % Version  : CSE_E---1.5
% 0.19/0.62  % Problem  : theBenchmark.p
% 0.19/0.62  % Proof found
% 0.19/0.62  % SZS status Theorem for theBenchmark.p
% 0.19/0.62  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.044000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.046000 s
%------------------------------------------------------------------------------