%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT004-3 : 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 : n017.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 18:14:04 EDT 2023

% Result   : Unsatisfiable 0.21s 0.75s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   28 (   8 unt;  10 typ;   0 def)
%            Number of atoms       :   32 (  31 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   30 (  16   ~;  14   |;   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   :   29 (   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_product2,hypothesis,
    ( X1 = X3
    | compose(X1,b) != X2
    | compose(X3,b) != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product2) ).

cnf(associativity_of_compose,axiom,
    compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',associativity_of_compose) ).

cnf(h_ab_equals_g_ab,hypothesis,
    compose(h,compose(a,b)) = compose(g,compose(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_ab_equals_g_ab) ).

cnf(cancellation_for_product1,hypothesis,
    ( X1 = X3
    | compose(X1,a) != X2
    | compose(X3,a) != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product1) ).

cnf(prove_h_equals_g,negated_conjecture,
    h != g,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).

cnf(c_0_5,hypothesis,
    ( X1 = X3
    | compose(X1,b) != X2
    | compose(X3,b) != X2 ),
    cancellation_for_product2 ).

cnf(c_0_6,hypothesis,
    ( X1 = X2
    | compose(X1,b) != compose(X2,b) ),
    inference(er,[status(thm)],[c_0_5]) ).

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

cnf(c_0_8,hypothesis,
    ( compose(X1,X2) = X3
    | compose(X1,compose(X2,b)) != compose(X3,b) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,hypothesis,
    compose(h,compose(a,b)) = compose(g,compose(a,b)),
    h_ab_equals_g_ab ).

cnf(c_0_10,hypothesis,
    ( compose(g,a) = X1
    | compose(h,compose(a,b)) != compose(X1,b) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,hypothesis,
    ( X1 = X3
    | compose(X1,a) != X2
    | compose(X3,a) != X2 ),
    cancellation_for_product1 ).

cnf(c_0_12,hypothesis,
    ( compose(g,a) = compose(X1,X2)
    | compose(h,compose(a,b)) != compose(X1,compose(X2,b)) ),
    inference(spm,[status(thm)],[c_0_10,c_0_7]) ).

cnf(c_0_13,hypothesis,
    ( X1 = X2
    | compose(X1,a) != compose(X2,a) ),
    inference(er,[status(thm)],[c_0_11]) ).

cnf(c_0_14,hypothesis,
    compose(g,a) = compose(h,a),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_15,hypothesis,
    ( g = X1
    | compose(h,a) != compose(X1,a) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_16,negated_conjecture,
    h != g,
    prove_h_equals_g ).

cnf(c_0_17,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : CAT004-3 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 23:51:56 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.21/0.75  % Version  : CSE_E---1.5
% 0.21/0.75  % Problem  : theBenchmark.p
% 0.21/0.75  % Proof found
% 0.21/0.75  % SZS status Theorem for theBenchmark.p
% 0.21/0.75  % SZS output start Proof
% See solution above
% 0.21/0.75  % Total time : 0.177000 s
% 0.21/0.75  % SZS output end Proof
% 0.21/0.75  % Total time : 0.180000 s
%------------------------------------------------------------------------------