%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT002-3 : 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 : n020.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 18:14:02 EDT 2023

% Result   : Unsatisfiable 0.18s 0.55s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   27 (   9 unt;  10 typ;   0 def)
%            Number of atoms       :   29 (  28 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   26 (  14   ~;  12   |;   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  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (   0 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,
    f1: ( $i * $i ) > $i ).

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

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

tff(decl_30,type,
    h: $i ).

tff(decl_31,type,
    g: $i ).

cnf(cancellation_for_compose1,hypothesis,
    ( X1 = X3
    | compose(a,X1) != X2
    | compose(a,X3) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_compose1) ).

cnf(ab_h_equals_ab_g,hypothesis,
    compose(compose(a,b),h) = compose(compose(a,b),g),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).

cnf(associativity_of_compose,axiom,
    compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT003-0.ax',associativity_of_compose) ).

cnf(cancellation_for_compose2,hypothesis,
    ( X1 = X3
    | compose(b,X1) != X2
    | compose(b,X3) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_compose2) ).

cnf(prove_g_equals_h,negated_conjecture,
    g != h,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_equals_h) ).

cnf(c_0_5,hypothesis,
    ( X1 = X3
    | compose(a,X1) != X2
    | compose(a,X3) != X2 ),
    cancellation_for_compose1 ).

cnf(c_0_6,hypothesis,
    compose(compose(a,b),h) = compose(compose(a,b),g),
    ab_h_equals_ab_g ).

cnf(c_0_7,axiom,
    compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
    associativity_of_compose ).

cnf(c_0_8,hypothesis,
    ( X1 = X2
    | compose(a,X1) != compose(a,X2) ),
    inference(er,[status(thm)],[c_0_5]) ).

cnf(c_0_9,hypothesis,
    compose(a,compose(b,g)) = compose(a,compose(b,h)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).

cnf(c_0_10,hypothesis,
    ( X1 = X3
    | compose(b,X1) != X2
    | compose(b,X3) != X2 ),
    cancellation_for_compose2 ).

cnf(c_0_11,hypothesis,
    ( compose(b,g) = X1
    | compose(a,compose(b,h)) != compose(a,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,hypothesis,
    ( X1 = X2
    | compose(b,X1) != compose(b,X2) ),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_13,hypothesis,
    compose(b,g) = compose(b,h),
    inference(er,[status(thm)],[c_0_11]) ).

cnf(c_0_14,hypothesis,
    ( g = X1
    | compose(b,h) != compose(b,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,negated_conjecture,
    g != h,
    prove_g_equals_h ).

cnf(c_0_16,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_14]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : CAT002-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n020.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 00:28:14 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.18/0.53  start to proof: theBenchmark
% 0.18/0.55  % Version  : CSE_E---1.5
% 0.18/0.55  % Problem  : theBenchmark.p
% 0.18/0.55  % Proof found
% 0.18/0.55  % SZS status Theorem for theBenchmark.p
% 0.18/0.55  % SZS output start Proof
% See solution above
% 0.18/0.55  % Total time : 0.008000 s
% 0.18/0.55  % SZS output end Proof
% 0.18/0.55  % Total time : 0.009000 s
%------------------------------------------------------------------------------