%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL025-1 : 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 : n025.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 06:51:50 EDT 2023

% Result   : Unsatisfiable 0.22s 0.61s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   23 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :   29 (   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    :    4 (   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    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   37 (   4 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    c: $i ).

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

cnf(c0_6,axiom,
    is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_6) ).

cnf(c0_2,axiom,
    is_a_theorem(implies(X1,implies(X2,X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_2) ).

cnf(prove_c0_1,negated_conjecture,
    ~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c0_1) ).

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

cnf(c_0_5,axiom,
    is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
    c0_6 ).

cnf(c_0_6,plain,
    ( is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))
    | ~ is_a_theorem(implies(X1,implies(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,axiom,
    is_a_theorem(implies(X1,implies(X2,X1))),
    c0_2 ).

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

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

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

cnf(c_0_11,plain,
    ( is_a_theorem(implies(X1,X2))
    | ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
    inference(spm,[status(thm)],[c_0_10,c_0_7]) ).

cnf(c_0_12,plain,
    ( is_a_theorem(implies(X1,implies(X2,X3)))
    | ~ is_a_theorem(implies(X2,implies(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_6]) ).

cnf(c_0_13,plain,
    is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
    inference(spm,[status(thm)],[c_0_11,c_0_5]) ).

cnf(c_0_14,negated_conjecture,
    ~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
    prove_c0_1 ).

cnf(c_0_15,plain,
    is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : LCL025-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Thu Aug 24 18:05:21 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.59  start to proof: theBenchmark
% 0.22/0.61  % Version  : CSE_E---1.5
% 0.22/0.61  % Problem  : theBenchmark.p
% 0.22/0.61  % Proof found
% 0.22/0.61  % SZS status Theorem for theBenchmark.p
% 0.22/0.61  % SZS output start Proof
% See solution above
% 0.22/0.61  % Total time : 0.009000 s
% 0.22/0.61  % SZS output end Proof
% 0.22/0.61  % Total time : 0.012000 s
%------------------------------------------------------------------------------