%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL106-1 : 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 : n009.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 : Thu Aug 31 06:52:16 EDT 2023

% Result   : Unsatisfiable 0.16s 0.56s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   21 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :   28 (   0 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    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   39 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    equivalent: ( $i * $i ) > $i ).

tff(decl_23,type,
    is_a_theorem: $i > $o ).

tff(decl_24,type,
    a: $i ).

tff(decl_25,type,
    b: $i ).

tff(decl_26,type,
    c: $i ).

cnf(condensed_detachment,axiom,
    ( is_a_theorem(X2)
    | ~ is_a_theorem(equivalent(X1,X2))
    | ~ is_a_theorem(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).

cnf(q_1,axiom,
    is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X2),X1)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_1) ).

cnf(q_4,axiom,
    is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_4) ).

cnf(prove_q_2,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_q_2) ).

cnf(c_0_4,axiom,
    ( is_a_theorem(X2)
    | ~ is_a_theorem(equivalent(X1,X2))
    | ~ is_a_theorem(X1) ),
    condensed_detachment ).

cnf(c_0_5,axiom,
    is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X2),X1)))),
    q_1 ).

cnf(c_0_6,axiom,
    is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3))),
    q_4 ).

cnf(c_0_7,plain,
    ( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_8,plain,
    ( is_a_theorem(equivalent(X1,X2))
    | ~ is_a_theorem(equivalent(equivalent(X3,X1),equivalent(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_4,c_0_6]) ).

cnf(c_0_9,plain,
    ( is_a_theorem(equivalent(equivalent(X1,X2),X3))
    | ~ is_a_theorem(equivalent(X2,X1))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_4,c_0_7]) ).

cnf(c_0_10,plain,
    ( is_a_theorem(equivalent(X1,X2))
    | ~ is_a_theorem(equivalent(X1,X3))
    | ~ is_a_theorem(equivalent(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,plain,
    ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4))
    | ~ is_a_theorem(equivalent(equivalent(X2,X3),X4)) ),
    inference(spm,[status(thm)],[c_0_10,c_0_6]) ).

cnf(c_0_12,plain,
    ( is_a_theorem(equivalent(equivalent(X1,X2),X3))
    | ~ is_a_theorem(equivalent(equivalent(X4,X2),equivalent(equivalent(X1,X4),X3))) ),
    inference(spm,[status(thm)],[c_0_8,c_0_11]) ).

cnf(c_0_13,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
    prove_q_2 ).

cnf(c_0_14,plain,
    is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))),
    inference(spm,[status(thm)],[c_0_12,c_0_5]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : LCL106-1 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.31  % Computer : n009.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri Aug 25 04:43:21 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.55  start to proof: theBenchmark
% 0.16/0.56  % Version  : CSE_E---1.5
% 0.16/0.56  % Problem  : theBenchmark.p
% 0.16/0.56  % Proof found
% 0.16/0.56  % SZS status Theorem for theBenchmark.p
% 0.16/0.56  % SZS output start Proof
% See solution above
% 0.16/0.56  % Total time : 0.003000 s
% 0.16/0.56  % SZS output end Proof
% 0.16/0.56  % Total time : 0.005000 s
%------------------------------------------------------------------------------