%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT010-1 : 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 : n010.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 18:14:07 EDT 2023

% Result   : Unsatisfiable 0.61s 0.79s
% Output   : CNFRefutation 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   37 (  16 unt;   8 typ;   0 def)
%            Number of atoms       :   50 (   5 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   44 (  23   ~;  21   |;   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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   40 (   5 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,
    b: $i ).

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

cnf(category_theory_axiom3,axiom,
    ( defined(X4,X1)
    | ~ product(X1,X2,X3)
    | ~ defined(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).

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

cnf(ba_defined,hypothesis,
    defined(b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ba_defined) ).

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

cnf(identity1,axiom,
    ( product(X1,X2,X2)
    | ~ defined(X1,X2)
    | ~ identity_map(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).

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

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

cnf(c_0_10,axiom,
    ( defined(X4,X1)
    | ~ product(X1,X2,X3)
    | ~ defined(X4,X3) ),
    category_theory_axiom3 ).

cnf(c_0_11,axiom,
    defined(codomain(X1),X1),
    mapping_from_codomain_of_x_to_x ).

cnf(c_0_12,axiom,
    ( product(X1,X2,compose(X1,X2))
    | ~ defined(X1,X2) ),
    closure_of_composition ).

cnf(c_0_13,hypothesis,
    defined(b,a),
    ba_defined ).

cnf(c_0_14,axiom,
    product(codomain(X1),X1,X1),
    product_on_codomain ).

cnf(c_0_15,plain,
    ( defined(codomain(X1),X2)
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,hypothesis,
    product(b,a,compose(b,a)),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    ( defined(X1,codomain(X2))
    | ~ defined(X1,X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_14]) ).

cnf(c_0_18,hypothesis,
    defined(codomain(compose(b,a)),b),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,axiom,
    ( product(X1,X2,X2)
    | ~ defined(X1,X2)
    | ~ identity_map(X1) ),
    identity1 ).

cnf(c_0_20,hypothesis,
    defined(codomain(compose(b,a)),codomain(b)),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,axiom,
    identity_map(codomain(X1)),
    codomain_is_an_identity_map ).

cnf(c_0_22,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    composition_is_well_defined ).

cnf(c_0_23,hypothesis,
    product(codomain(compose(b,a)),codomain(b),codomain(b)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_24,axiom,
    ( product(X1,X2,X1)
    | ~ defined(X1,X2)
    | ~ identity_map(X2) ),
    identity2 ).

cnf(c_0_25,hypothesis,
    ( X1 = codomain(b)
    | ~ product(codomain(compose(b,a)),codomain(b),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,hypothesis,
    product(codomain(compose(b,a)),codomain(b),codomain(compose(b,a))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_21])]) ).

cnf(c_0_27,negated_conjecture,
    codomain(compose(b,a)) != codomain(b),
    prove_codomain_of_ba_equals_codomain_of_b ).

cnf(c_0_28,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : CAT010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n010.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 00:02:04 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.61/0.79  % Version  : CSE_E---1.5
% 0.61/0.79  % Problem  : theBenchmark.p
% 0.61/0.79  % Proof found
% 0.61/0.79  % SZS status Theorem for theBenchmark.p
% 0.61/0.79  % SZS output start Proof
% See solution above
% 0.74/0.80  % Total time : 0.214000 s
% 0.74/0.80  % SZS output end Proof
% 0.74/0.80  % Total time : 0.217000 s
%------------------------------------------------------------------------------