TSTP Solution File: LCL124-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL124-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 06:52:24 EDT 2023

% Result   : Unsatisfiable 246.93s 247.00s
% Output   : CNFRefutation 246.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   56
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   76 (  16 unt;   7 typ;   0 def)
%            Number of atoms       :  159 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  232 ( 142   ~;  90   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    6 (   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    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :  164 (  38 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 ).

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

tff(decl_28,type,
    f: $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(lg_2,axiom,
    is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_2) ).

cnf(prove_lg_5,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,equivalent(c,equivalent(e,f)))),equivalent(equivalent(a,equivalent(f,c)),equivalent(equivalent(b,equivalent(f,e)),f)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_5) ).

cnf(c_0_3,axiom,
    ( is_a_theorem(X2)
    | ~ is_a_theorem(equivalent(X1,X2))
    | ~ is_a_theorem(X1) ),
    condensed_detachment ).

cnf(c_0_4,axiom,
    is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),
    lg_2 ).

cnf(c_0_5,plain,
    ( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

cnf(c_0_6,plain,
    ( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3))))
    | ~ is_a_theorem(X4) ),
    inference(spm,[status(thm)],[c_0_3,c_0_5]) ).

cnf(c_0_7,plain,
    ( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
    | ~ is_a_theorem(equivalent(X1,X3))
    | ~ is_a_theorem(X4) ),
    inference(spm,[status(thm)],[c_0_3,c_0_6]) ).

cnf(c_0_8,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(a,equivalent(b,equivalent(c,equivalent(e,f)))),equivalent(equivalent(a,equivalent(f,c)),equivalent(equivalent(b,equivalent(f,e)),f)))),
    prove_lg_5 ).

cnf(c_0_9,plain,
    ( is_a_theorem(equivalent(X1,X2))
    | ~ is_a_theorem(equivalent(X3,X2))
    | ~ is_a_theorem(equivalent(X3,X1))
    | ~ is_a_theorem(X4) ),
    inference(spm,[status(thm)],[c_0_3,c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(a,equivalent(f,c)),equivalent(equivalent(b,equivalent(f,e)),f))))
    | ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(a,equivalent(f,c)),equivalent(equivalent(b,equivalent(f,e)),f))))
    | ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(b,equivalent(c,equivalent(e,f)))))) ),
    inference(spm,[status(thm)],[c_0_10,c_0_4]) ).

cnf(c_0_12,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(b,equivalent(f,e)),f)),equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(f,c))))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(b,equivalent(f,e)),f)),equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(f,c)))) ),
    inference(spm,[status(thm)],[c_0_12,c_0_4]) ).

cnf(c_0_14,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(b,equivalent(f,e)),f))))
    | ~ is_a_theorem(equivalent(X2,equivalent(a,equivalent(f,c))))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_13,c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(b,equivalent(f,e)),f))))
    | ~ is_a_theorem(equivalent(X2,equivalent(a,equivalent(f,c)))) ),
    inference(spm,[status(thm)],[c_0_14,c_0_4]) ).

cnf(c_0_16,plain,
    ( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
    | ~ is_a_theorem(equivalent(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_4]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(b,equivalent(f,e)),f)),equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(X2,equivalent(a,equivalent(f,c))))
    | ~ is_a_theorem(equivalent(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_18,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(b,equivalent(f,e)),f)),equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(f,c))))
    | ~ is_a_theorem(equivalent(X2,a)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,f),equivalent(equivalent(b,equivalent(f,e)),f)),equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(equivalent(X1,c),a))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_6]) ).

cnf(c_0_20,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,f),equivalent(equivalent(b,equivalent(f,e)),f)),equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(equivalent(X1,c),a)) ),
    inference(spm,[status(thm)],[c_0_19,c_0_4]) ).

cnf(c_0_21,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,f),equivalent(equivalent(b,equivalent(f,e)),f))))
    | ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(equivalent(X2,c),a))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_20,c_0_9]) ).

cnf(c_0_22,plain,
    is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))),
    inference(spm,[status(thm)],[c_0_6,c_0_4]) ).

cnf(c_0_23,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(f,e))),equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(equivalent(X1,c),a))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(f,e))),equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(equivalent(X1,c),a)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_25,plain,
    ( is_a_theorem(equivalent(X1,X2))
    | ~ is_a_theorem(equivalent(X3,X2))
    | ~ is_a_theorem(equivalent(X3,X1)) ),
    inference(spm,[status(thm)],[c_0_9,c_0_4]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(b,equivalent(c,equivalent(e,f))))))
    | ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(b,equivalent(f,e)))))
    | ~ is_a_theorem(equivalent(equivalent(X2,c),a)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_27,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(c,equivalent(e,f)))),equivalent(X2,equivalent(b,equivalent(f,e)))))
    | ~ is_a_theorem(equivalent(equivalent(X2,c),a))
    | ~ is_a_theorem(equivalent(X1,a)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_16]) ).

cnf(c_0_28,plain,
    ( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4))
    | ~ is_a_theorem(equivalent(equivalent(X1,X3),X4)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,b),equivalent(X2,equivalent(b,equivalent(f,e)))))
    | ~ is_a_theorem(equivalent(equivalent(X1,equivalent(c,equivalent(e,f))),a))
    | ~ is_a_theorem(equivalent(equivalent(X2,c),a)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(c,equivalent(e,f))),a))
    | ~ is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(f,e)),c),a)) ),
    inference(spm,[status(thm)],[c_0_29,c_0_22]) ).

cnf(c_0_31,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(c,equivalent(e,f))),a))
    | ~ is_a_theorem(equivalent(X2,equivalent(equivalent(X1,equivalent(f,e)),c)))
    | ~ is_a_theorem(equivalent(X2,a)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_25]) ).

cnf(c_0_32,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,equivalent(e,f)),equivalent(f,e)),c)))
    | ~ is_a_theorem(equivalent(equivalent(X2,c),a))
    | ~ is_a_theorem(equivalent(X1,a)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_28]) ).

cnf(c_0_33,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(e,f)),equivalent(f,e))))
    | ~ is_a_theorem(equivalent(equivalent(X2,c),a))
    | ~ is_a_theorem(equivalent(equivalent(X1,c),a)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_16]) ).

cnf(c_0_34,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(f,e)),c),a))
    | ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(e,f))))
    | ~ is_a_theorem(equivalent(equivalent(X2,c),a)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_16]) ).

cnf(c_0_35,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,e),equivalent(f,e)),c),a))
    | ~ is_a_theorem(equivalent(equivalent(equivalent(X1,f),c),a)) ),
    inference(spm,[status(thm)],[c_0_34,c_0_22]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,e),equivalent(f,e)),c)))
    | ~ is_a_theorem(equivalent(equivalent(equivalent(X2,f),c),a))
    | ~ is_a_theorem(equivalent(X1,a)) ),
    inference(spm,[status(thm)],[c_0_35,c_0_25]) ).

cnf(c_0_37,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,e),equivalent(f,e))))
    | ~ is_a_theorem(equivalent(equivalent(equivalent(X2,f),c),a))
    | ~ is_a_theorem(equivalent(equivalent(X1,c),a)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_16]) ).

cnf(c_0_38,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(equivalent(X1,f),c),a)),
    inference(spm,[status(thm)],[c_0_37,c_0_22]) ).

cnf(c_0_39,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,f),c)))
    | ~ is_a_theorem(equivalent(X1,a)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_25]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,f),c)))
    | ~ is_a_theorem(equivalent(X3,a))
    | ~ is_a_theorem(equivalent(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_39,c_0_25]) ).

cnf(c_0_41,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,c),X2))
    | ~ is_a_theorem(equivalent(X1,equivalent(X3,f)))
    | ~ is_a_theorem(equivalent(X2,a)) ),
    inference(spm,[status(thm)],[c_0_40,c_0_16]) ).

cnf(c_0_42,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,f),c),X2))
    | ~ is_a_theorem(equivalent(X2,a))
    | ~ is_a_theorem(equivalent(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_41,c_0_16]) ).

cnf(c_0_43,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,f),c),X2))
    | ~ is_a_theorem(equivalent(X2,a)) ),
    inference(spm,[status(thm)],[c_0_42,c_0_4]) ).

cnf(c_0_44,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,f),X2),equivalent(c,X2)),a)),
    inference(spm,[status(thm)],[c_0_43,c_0_22]) ).

cnf(c_0_45,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,f),X3),equivalent(c,X3))))
    | ~ is_a_theorem(equivalent(X1,a)) ),
    inference(spm,[status(thm)],[c_0_44,c_0_25]) ).

cnf(c_0_46,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(c,X2)),a))
    | ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X3,f),X2))) ),
    inference(spm,[status(thm)],[c_0_45,c_0_16]) ).

cnf(c_0_47,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(c,equivalent(X2,f))),a)),
    inference(spm,[status(thm)],[c_0_46,c_0_22]) ).

cnf(c_0_48,negated_conjecture,
    ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(c,equivalent(X3,f)))))
    | ~ is_a_theorem(equivalent(X1,a)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_25]) ).

cnf(c_0_49,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(c,equivalent(X2,f))),a))
    | ~ is_a_theorem(equivalent(X1,equivalent(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_48,c_0_16]) ).

cnf(c_0_50,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(X2,f)),equivalent(X3,X2)))
    | ~ is_a_theorem(equivalent(equivalent(X1,c),a)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_28]) ).

cnf(c_0_51,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(equivalent(X2,X1))
    | ~ is_a_theorem(equivalent(X2,X3))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_3,c_0_25]) ).

cnf(c_0_52,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(X1,c),a)),
    inference(spm,[status(thm)],[c_0_50,c_0_4]) ).

cnf(c_0_53,plain,
    ( is_a_theorem(equivalent(X1,X2))
    | ~ is_a_theorem(equivalent(equivalent(X3,X2),X4))
    | ~ is_a_theorem(equivalent(X3,X1))
    | ~ is_a_theorem(X4) ),
    inference(spm,[status(thm)],[c_0_51,c_0_16]) ).

cnf(c_0_54,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,a),X2))
    | ~ is_a_theorem(equivalent(X1,equivalent(X3,c)))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_55,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,c),a),X2))
    | ~ is_a_theorem(equivalent(X1,X3))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_54,c_0_16]) ).

cnf(c_0_56,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,c),a),X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_55,c_0_4]) ).

cnf(c_0_57,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(equivalent(X1,c),X2),equivalent(a,X2))),
    inference(spm,[status(thm)],[c_0_56,c_0_22]) ).

cnf(c_0_58,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(a,equivalent(X2,c)))),
    inference(spm,[status(thm)],[c_0_57,c_0_28]) ).

cnf(c_0_59,plain,
    ( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
    | ~ is_a_theorem(equivalent(equivalent(X4,X3),X1))
    | ~ is_a_theorem(equivalent(X4,X2)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_16]) ).

cnf(c_0_60,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(X2,c)),equivalent(X3,X2)))
    | ~ is_a_theorem(equivalent(X1,a)) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,negated_conjecture,
    ~ is_a_theorem(equivalent(X1,a)),
    inference(spm,[status(thm)],[c_0_60,c_0_4]) ).

cnf(c_0_62,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,a),X2))
    | ~ is_a_theorem(equivalent(X1,X3))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_61,c_0_53]) ).

cnf(c_0_63,negated_conjecture,
    ( ~ is_a_theorem(equivalent(equivalent(X1,a),X2))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_62,c_0_4]) ).

cnf(c_0_64,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(a,X2))),
    inference(spm,[status(thm)],[c_0_63,c_0_22]) ).

cnf(c_0_65,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(a,equivalent(X2,X3)))),
    inference(spm,[status(thm)],[c_0_64,c_0_28]) ).

cnf(c_0_66,plain,
    ( is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X3,X5),equivalent(X4,X5))))))
    | ~ is_a_theorem(equivalent(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_4]) ).

cnf(c_0_67,negated_conjecture,
    ~ is_a_theorem(equivalent(a,equivalent(X1,equivalent(X2,X3)))),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_68,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_67,c_0_4]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem    : LCL124-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.09/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.34  % Computer : n011.cluster.edu
% 0.10/0.34  % Model    : x86_64 x86_64
% 0.10/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34  % Memory   : 8042.1875MB
% 0.10/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34  % CPULimit   : 300
% 0.10/0.34  % WCLimit    : 300
% 0.10/0.34  % DateTime   : Thu Aug 24 19:25:52 EDT 2023
% 0.10/0.34  % CPUTime  : 
% 0.15/0.58  start to proof: theBenchmark
% 246.93/247.00  % Version  : CSE_E---1.5
% 246.93/247.00  % Problem  : theBenchmark.p
% 246.93/247.00  % Proof found
% 246.93/247.00  % SZS status Theorem for theBenchmark.p
% 246.93/247.00  % SZS output start Proof
% See solution above
% 246.93/247.00  % Total time : 246.400000 s
% 246.93/247.00  % SZS output end Proof
% 246.93/247.00  % Total time : 246.413000 s
%------------------------------------------------------------------------------