%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT019-3 : 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 : n005.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 18:14:13 EDT 2023

% Result   : Unsatisfiable 0.21s 0.59s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   24 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :   35 (  22 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   31 (  12   ~;  19   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    2 (   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    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   17 (   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 ).

cnf(indiscernibles1,axiom,
    ( there_exists(f1(X1,X2))
    | X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT003-0.ax',indiscernibles1) ).

cnf(indiscernibles2,axiom,
    ( X1 = f1(X1,X2)
    | X2 = f1(X1,X2)
    | X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT003-0.ax',indiscernibles2) ).

cnf(equality_of_a_and_b2,hypothesis,
    ( a = X1
    | ~ there_exists(X1)
    | b != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_of_a_and_b2) ).

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

cnf(equality_of_a_and_b1,hypothesis,
    ( b = X1
    | ~ there_exists(X1)
    | a != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_of_a_and_b1) ).

cnf(c_0_5,axiom,
    ( there_exists(f1(X1,X2))
    | X1 = X2 ),
    indiscernibles1 ).

cnf(c_0_6,axiom,
    ( X1 = f1(X1,X2)
    | X2 = f1(X1,X2)
    | X1 = X2 ),
    indiscernibles2 ).

cnf(c_0_7,hypothesis,
    ( a = X1
    | ~ there_exists(X1)
    | b != X1 ),
    equality_of_a_and_b2 ).

cnf(c_0_8,negated_conjecture,
    a != b,
    prove_a_equals_b ).

cnf(c_0_9,plain,
    ( f1(X1,X2) = X2
    | X1 = X2
    | there_exists(X1) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_10,hypothesis,
    ( b = X1
    | ~ there_exists(X1)
    | a != X1 ),
    equality_of_a_and_b1 ).

cnf(c_0_11,hypothesis,
    ~ there_exists(b),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_7]),c_0_8]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | there_exists(X1)
    | there_exists(X2) ),
    inference(spm,[status(thm)],[c_0_5,c_0_9]) ).

cnf(c_0_13,hypothesis,
    ~ there_exists(a),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_8]) ).

cnf(c_0_14,hypothesis,
    ( X1 = b
    | there_exists(X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_8]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : CAT019-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun Aug 27 00:29:08 EDT 2023
% 0.14/0.35  % 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 : 0.007000 s
% 0.21/0.59  % SZS output end Proof
% 0.21/0.59  % Total time : 0.010000 s
%------------------------------------------------------------------------------