TSTP Solution File: LCL550+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : LCL550+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% 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  : 600s
% DateTime : Sun Jul 17 09:26:43 EDT 2022

% Result   : Theorem 8.53s 2.38s
% Output   : CNFRefutation 8.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   32
% Syntax   : Number of clauses     :  146 (  76 unt;   4 nHn;  83 RR)
%            Number of literals    :  242 (  49 equ;  95 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   18 (  16 usr;  16 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   2 con; 0-2 aty)
%            Number of variables   :  211 (  23 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(i_0_4,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ adjunction
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_4) ).

cnf(i_0_107,plain,
    adjunction,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_107) ).

cnf(i_0_89,plain,
    ( and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2)
    | ~ op_strict_equiv ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_89) ).

cnf(i_0_117,plain,
    op_strict_equiv,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_117) ).

cnf(i_0_126,plain,
    ( X1 = X2
    | ~ substitution_strict_equiv
    | ~ is_a_theorem(strict_equiv(X1,X2)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_126) ).

cnf(i_0_119,plain,
    substitution_strict_equiv,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_119) ).

cnf(i_0_76,plain,
    ( is_a_theorem(X1)
    | ~ modus_ponens_strict_implies
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(strict_implies(X2,X1)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_76) ).

cnf(i_0_113,plain,
    modus_ponens_strict_implies,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_113) ).

cnf(i_0_30,plain,
    ( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
    | ~ axiom_m5 ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_30) ).

cnf(i_0_112,plain,
    axiom_m5,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_112) ).

cnf(i_0_22,plain,
    ( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
    | ~ axiom_m1 ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_22) ).

cnf(i_0_108,plain,
    axiom_m1,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_108) ).

cnf(i_0_24,plain,
    ( is_a_theorem(strict_implies(and(X1,X2),X1))
    | ~ axiom_m2 ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_24) ).

cnf(i_0_109,plain,
    axiom_m2,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_109) ).

cnf(i_0_26,plain,
    ( is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))
    | ~ axiom_m3 ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_26) ).

cnf(i_0_110,plain,
    axiom_m3,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_110) ).

cnf(i_0_28,plain,
    ( is_a_theorem(strict_implies(X1,and(X1,X1)))
    | ~ axiom_m4 ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_28) ).

cnf(i_0_111,plain,
    axiom_m4,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_111) ).

cnf(i_0_84,plain,
    ( not(and(X1,not(X2))) = implies(X1,X2)
    | ~ op_implies_and ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_84) ).

cnf(i_0_61,plain,
    op_implies_and,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_61) ).

cnf(i_0_90,plain,
    ( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
    | ~ op_strict_implies ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_90) ).

cnf(i_0_118,plain,
    op_strict_implies,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_118) ).

cnf(i_0_87,plain,
    ( not(and(not(X1),not(X2))) = or(X1,X2)
    | ~ op_or ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_87) ).

cnf(i_0_62,plain,
    op_or,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_62) ).

cnf(i_0_71,plain,
    ( modus_ponens
    | is_a_theorem(esk56_0) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_71) ).

cnf(i_0_59,negated_conjecture,
    ~ modus_ponens,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_59) ).

cnf(i_0_83,plain,
    ( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
    | ~ op_equiv ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_83) ).

cnf(i_0_60,plain,
    op_equiv,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_60) ).

cnf(i_0_123,plain,
    ( X1 = X2
    | ~ substitution_of_equivalents
    | ~ is_a_theorem(equiv(X1,X2)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_123) ).

cnf(i_0_120,plain,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_120) ).

cnf(i_0_70,plain,
    ( modus_ponens
    | is_a_theorem(implies(esk56_0,esk57_0)) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_70) ).

cnf(i_0_69,plain,
    ( modus_ponens
    | ~ is_a_theorem(esk57_0) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-zbmn50u7/lgb.p',i_0_69) ).

cnf(c_0_159,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ adjunction
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(X1) ),
    i_0_4 ).

cnf(c_0_160,plain,
    adjunction,
    i_0_107 ).

cnf(c_0_161,plain,
    ( and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2)
    | ~ op_strict_equiv ),
    i_0_89 ).

cnf(c_0_162,plain,
    op_strict_equiv,
    i_0_117 ).

cnf(c_0_163,plain,
    ( X1 = X2
    | ~ substitution_strict_equiv
    | ~ is_a_theorem(strict_equiv(X1,X2)) ),
    i_0_126 ).

cnf(c_0_164,plain,
    substitution_strict_equiv,
    i_0_119 ).

cnf(c_0_165,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]) ).

cnf(c_0_166,plain,
    and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_162])]) ).

cnf(c_0_167,plain,
    ( is_a_theorem(X1)
    | ~ modus_ponens_strict_implies
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(strict_implies(X2,X1)) ),
    i_0_76 ).

cnf(c_0_168,plain,
    modus_ponens_strict_implies,
    i_0_113 ).

cnf(c_0_169,plain,
    ( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
    | ~ axiom_m5 ),
    i_0_30 ).

cnf(c_0_170,plain,
    axiom_m5,
    i_0_112 ).

cnf(c_0_171,plain,
    ( X1 = X2
    | ~ is_a_theorem(strict_equiv(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]) ).

cnf(c_0_172,plain,
    ( is_a_theorem(strict_equiv(X1,X2))
    | ~ is_a_theorem(strict_implies(X2,X1))
    | ~ is_a_theorem(strict_implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_165,c_0_166]) ).

cnf(c_0_173,plain,
    ( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
    | ~ axiom_m1 ),
    i_0_22 ).

cnf(c_0_174,plain,
    axiom_m1,
    i_0_108 ).

cnf(c_0_175,plain,
    ( is_a_theorem(X1)
    | ~ is_a_theorem(strict_implies(X2,X1))
    | ~ is_a_theorem(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_168])]) ).

cnf(c_0_176,plain,
    is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170])]) ).

cnf(c_0_177,plain,
    ( is_a_theorem(strict_implies(and(X1,X2),X1))
    | ~ axiom_m2 ),
    i_0_24 ).

cnf(c_0_178,plain,
    axiom_m2,
    i_0_109 ).

cnf(c_0_179,plain,
    ( X1 = X2
    | ~ is_a_theorem(strict_implies(X2,X1))
    | ~ is_a_theorem(strict_implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_171,c_0_172]) ).

cnf(c_0_180,plain,
    is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174])]) ).

cnf(c_0_181,plain,
    ( is_a_theorem(strict_implies(X1,X2))
    | ~ is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_175,c_0_176]) ).

cnf(c_0_182,plain,
    is_a_theorem(strict_implies(and(X1,X2),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_178])]) ).

cnf(c_0_183,plain,
    and(X1,X2) = and(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_180])]) ).

cnf(c_0_184,plain,
    ( is_a_theorem(strict_implies(X1,X2))
    | ~ is_a_theorem(strict_implies(X3,X2))
    | ~ is_a_theorem(strict_implies(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_181,c_0_165]) ).

cnf(c_0_185,plain,
    is_a_theorem(strict_implies(and(X1,X2),X2)),
    inference(spm,[status(thm)],[c_0_182,c_0_183]) ).

cnf(c_0_186,plain,
    ( is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))
    | ~ axiom_m3 ),
    i_0_26 ).

cnf(c_0_187,plain,
    axiom_m3,
    i_0_110 ).

cnf(c_0_188,plain,
    ( is_a_theorem(strict_implies(X1,X2))
    | ~ is_a_theorem(strict_implies(X1,and(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_184,c_0_185]) ).

cnf(c_0_189,plain,
    is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_187])]) ).

cnf(c_0_190,plain,
    is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X2,X3))),
    inference(spm,[status(thm)],[c_0_188,c_0_189]) ).

cnf(c_0_191,plain,
    ( is_a_theorem(strict_implies(X1,and(X1,X1)))
    | ~ axiom_m4 ),
    i_0_28 ).

cnf(c_0_192,plain,
    axiom_m4,
    i_0_111 ).

cnf(c_0_193,plain,
    ( not(and(X1,not(X2))) = implies(X1,X2)
    | ~ op_implies_and ),
    i_0_84 ).

cnf(c_0_194,plain,
    op_implies_and,
    i_0_61 ).

cnf(c_0_195,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(and(and(X3,X1),X2)) ),
    inference(spm,[status(thm)],[c_0_175,c_0_190]) ).

cnf(c_0_196,plain,
    is_a_theorem(strict_implies(X1,and(X1,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_192])]) ).

cnf(c_0_197,plain,
    ( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
    | ~ op_strict_implies ),
    i_0_90 ).

cnf(c_0_198,plain,
    op_strict_implies,
    i_0_118 ).

cnf(c_0_199,plain,
    ( not(and(not(X1),not(X2))) = or(X1,X2)
    | ~ op_or ),
    i_0_87 ).

cnf(c_0_200,plain,
    not(and(X1,not(X2))) = implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_194])]) ).

cnf(c_0_201,plain,
    op_or,
    i_0_62 ).

cnf(c_0_202,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(and(X3,X1))
    | ~ is_a_theorem(X2) ),
    inference(spm,[status(thm)],[c_0_195,c_0_165]) ).

cnf(c_0_203,plain,
    and(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_196]),c_0_182])]) ).

cnf(c_0_204,plain,
    necessarily(implies(X1,X2)) = strict_implies(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_198])]) ).

cnf(c_0_205,plain,
    implies(not(X1),X2) = or(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_200]),c_0_201])]) ).

cnf(c_0_206,plain,
    not(and(not(X1),X2)) = implies(X2,X1),
    inference(spm,[status(thm)],[c_0_200,c_0_183]) ).

cnf(c_0_207,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(and(and(X1,X3),X2)) ),
    inference(spm,[status(thm)],[c_0_195,c_0_183]) ).

cnf(c_0_208,plain,
    ( is_a_theorem(and(strict_implies(X1,X2),X3))
    | ~ is_a_theorem(strict_equiv(X2,X1))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_202,c_0_166]) ).

cnf(c_0_209,plain,
    strict_equiv(X1,X1) = strict_implies(X1,X1),
    inference(spm,[status(thm)],[c_0_166,c_0_203]) ).

cnf(c_0_210,plain,
    is_a_theorem(strict_implies(X1,X1)),
    inference(rw,[status(thm)],[c_0_196,c_0_203]) ).

cnf(c_0_211,plain,
    necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
    inference(spm,[status(thm)],[c_0_204,c_0_205]) ).

cnf(c_0_212,plain,
    or(X1,X2) = or(X2,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_206]),c_0_205]),c_0_205]) ).

cnf(c_0_213,plain,
    ( is_a_theorem(and(X1,X2))
    | ~ is_a_theorem(and(X2,and(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_207,c_0_183]) ).

cnf(c_0_214,plain,
    ( is_a_theorem(and(strict_implies(X1,X1),X2))
    | ~ is_a_theorem(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_210])]) ).

cnf(c_0_215,plain,
    ( is_a_theorem(strict_implies(X1,X2))
    | ~ is_a_theorem(strict_implies(X1,and(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_184,c_0_182]) ).

cnf(c_0_216,plain,
    strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_211]) ).

cnf(c_0_217,plain,
    ( is_a_theorem(and(X1,strict_implies(X2,X2)))
    | ~ is_a_theorem(and(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_213,c_0_214]) ).

cnf(c_0_218,plain,
    ( modus_ponens
    | is_a_theorem(esk56_0) ),
    i_0_71 ).

cnf(c_0_219,negated_conjecture,
    ~ modus_ponens,
    i_0_59 ).

cnf(c_0_220,plain,
    ( is_a_theorem(strict_implies(not(X1),X2))
    | ~ is_a_theorem(strict_implies(not(and(X2,X3)),X1)) ),
    inference(spm,[status(thm)],[c_0_215,c_0_216]) ).

cnf(c_0_221,plain,
    ( is_a_theorem(and(strict_implies(X1,X1),strict_implies(X2,X2)))
    | ~ is_a_theorem(X3) ),
    inference(spm,[status(thm)],[c_0_217,c_0_214]) ).

cnf(c_0_222,plain,
    is_a_theorem(esk56_0),
    inference(sr,[status(thm)],[c_0_218,c_0_219]) ).

cnf(c_0_223,plain,
    not(not(X1)) = or(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_203]),c_0_205]) ).

cnf(c_0_224,plain,
    is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_210]),c_0_216]) ).

cnf(c_0_225,plain,
    ( is_a_theorem(strict_implies(X1,X2))
    | ~ is_a_theorem(and(strict_implies(X3,X2),strict_implies(X1,X3))) ),
    inference(spm,[status(thm)],[c_0_181,c_0_183]) ).

cnf(c_0_226,plain,
    is_a_theorem(and(strict_implies(X1,X1),strict_implies(X2,X2))),
    inference(spm,[status(thm)],[c_0_221,c_0_222]) ).

cnf(c_0_227,plain,
    strict_implies(not(X1),not(X2)) = strict_implies(or(X2,X2),X1),
    inference(spm,[status(thm)],[c_0_216,c_0_223]) ).

cnf(c_0_228,plain,
    is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
    inference(spm,[status(thm)],[c_0_224,c_0_200]) ).

cnf(c_0_229,plain,
    ( is_a_theorem(strict_implies(not(X1),X2))
    | ~ is_a_theorem(and(strict_implies(X3,X2),strict_implies(not(X3),X1))) ),
    inference(spm,[status(thm)],[c_0_225,c_0_216]) ).

cnf(c_0_230,plain,
    is_a_theorem(and(strict_implies(or(X1,X1),X1),strict_implies(X2,X2))),
    inference(spm,[status(thm)],[c_0_226,c_0_227]) ).

cnf(c_0_231,plain,
    ( is_a_theorem(strict_implies(not(X1),X2))
    | ~ is_a_theorem(strict_implies(not(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_220,c_0_203]) ).

cnf(c_0_232,plain,
    is_a_theorem(strict_implies(not(not(X1)),or(X1,X2))),
    inference(spm,[status(thm)],[c_0_228,c_0_205]) ).

cnf(c_0_233,plain,
    ( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
    | ~ op_equiv ),
    i_0_83 ).

cnf(c_0_234,plain,
    op_equiv,
    i_0_60 ).

cnf(c_0_235,plain,
    ( is_a_theorem(strict_implies(X1,X2))
    | ~ is_a_theorem(and(strict_implies(not(X2),X3),strict_implies(X1,not(X3)))) ),
    inference(spm,[status(thm)],[c_0_225,c_0_216]) ).

cnf(c_0_236,plain,
    is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1))),
    inference(spm,[status(thm)],[c_0_224,c_0_206]) ).

cnf(c_0_237,plain,
    is_a_theorem(strict_implies(not(X1),not(or(X1,X1)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_216]) ).

cnf(c_0_238,plain,
    is_a_theorem(strict_implies(not(or(X1,X2)),not(X1))),
    inference(spm,[status(thm)],[c_0_231,c_0_232]) ).

cnf(c_0_239,plain,
    ( X1 = X2
    | ~ substitution_of_equivalents
    | ~ is_a_theorem(equiv(X1,X2)) ),
    i_0_123 ).

cnf(c_0_240,plain,
    substitution_of_equivalents,
    i_0_120 ).

cnf(c_0_241,plain,
    and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_233,c_0_234])]) ).

cnf(c_0_242,plain,
    ( is_a_theorem(strict_implies(X1,X2))
    | ~ is_a_theorem(strict_implies(X1,not(not(X2)))) ),
    inference(spm,[status(thm)],[c_0_235,c_0_214]) ).

cnf(c_0_243,plain,
    is_a_theorem(strict_implies(not(implies(X1,X2)),not(X2))),
    inference(spm,[status(thm)],[c_0_231,c_0_236]) ).

cnf(c_0_244,plain,
    ( X1 = not(X2)
    | ~ is_a_theorem(strict_implies(not(X1),X2))
    | ~ is_a_theorem(strict_implies(X1,not(X2))) ),
    inference(spm,[status(thm)],[c_0_179,c_0_216]) ).

cnf(c_0_245,plain,
    not(or(X1,X1)) = not(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_237]),c_0_238])]) ).

cnf(c_0_246,plain,
    ( X1 = X2
    | ~ is_a_theorem(equiv(X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_239,c_0_240])]) ).

cnf(c_0_247,plain,
    ( is_a_theorem(equiv(X1,X2))
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_165,c_0_241]) ).

cnf(c_0_248,plain,
    is_a_theorem(strict_implies(not(X1),implies(X2,not(X1)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_216]) ).

cnf(c_0_249,plain,
    ( not(not(X1)) = X1
    | ~ is_a_theorem(strict_implies(X1,not(not(X1)))) ),
    inference(spm,[status(thm)],[c_0_244,c_0_210]) ).

cnf(c_0_250,plain,
    implies(X1,or(X2,X2)) = implies(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_245]),c_0_200]) ).

cnf(c_0_251,plain,
    ( X1 = X2
    | ~ is_a_theorem(implies(X2,X1))
    | ~ is_a_theorem(implies(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_246,c_0_247]) ).

cnf(c_0_252,plain,
    ( is_a_theorem(implies(X1,not(X2)))
    | ~ is_a_theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_175,c_0_248]) ).

cnf(c_0_253,plain,
    ( or(X1,X1) = X1
    | ~ is_a_theorem(strict_implies(X1,or(X1,X1))) ),
    inference(spm,[status(thm)],[c_0_249,c_0_223]) ).

cnf(c_0_254,plain,
    strict_implies(X1,or(X2,X2)) = strict_implies(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_250]),c_0_204]) ).

cnf(c_0_255,plain,
    ( not(X1) = X2
    | ~ is_a_theorem(or(X1,X2))
    | ~ is_a_theorem(not(X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_205]) ).

cnf(c_0_256,plain,
    ( is_a_theorem(or(X1,not(X2)))
    | ~ is_a_theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_252,c_0_205]) ).

cnf(c_0_257,plain,
    or(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_253,c_0_254]),c_0_210])]) ).

cnf(c_0_258,plain,
    ( not(X1) = not(X2)
    | ~ is_a_theorem(not(X1))
    | ~ is_a_theorem(not(X2)) ),
    inference(spm,[status(thm)],[c_0_255,c_0_256]) ).

cnf(c_0_259,plain,
    not(not(X1)) = X1,
    inference(rw,[status(thm)],[c_0_223,c_0_257]) ).

cnf(c_0_260,plain,
    ( X1 = not(X2)
    | ~ is_a_theorem(not(X2))
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_258,c_0_259]) ).

cnf(c_0_261,plain,
    ( X1 = X2
    | ~ is_a_theorem(X2)
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_260,c_0_259]) ).

cnf(c_0_262,plain,
    ( modus_ponens
    | is_a_theorem(implies(esk56_0,esk57_0)) ),
    i_0_70 ).

cnf(c_0_263,plain,
    ( X1 = esk56_0
    | ~ is_a_theorem(X1) ),
    inference(spm,[status(thm)],[c_0_261,c_0_222]) ).

cnf(c_0_264,plain,
    is_a_theorem(implies(esk56_0,esk57_0)),
    inference(sr,[status(thm)],[c_0_262,c_0_219]) ).

cnf(c_0_265,plain,
    implies(esk56_0,esk57_0) = esk56_0,
    inference(spm,[status(thm)],[c_0_263,c_0_264]) ).

cnf(c_0_266,plain,
    strict_implies(not(X1),X1) = necessarily(X1),
    inference(spm,[status(thm)],[c_0_211,c_0_257]) ).

cnf(c_0_267,plain,
    is_a_theorem(necessarily(esk56_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_265]),c_0_266]) ).

cnf(c_0_268,plain,
    necessarily(esk56_0) = esk56_0,
    inference(spm,[status(thm)],[c_0_263,c_0_267]) ).

cnf(c_0_269,plain,
    ( modus_ponens
    | ~ is_a_theorem(esk57_0) ),
    i_0_69 ).

cnf(c_0_270,plain,
    strict_implies(esk56_0,esk57_0) = esk56_0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_265]),c_0_268]) ).

cnf(c_0_271,plain,
    ~ is_a_theorem(esk57_0),
    inference(sr,[status(thm)],[c_0_269,c_0_219]) ).

cnf(c_0_272,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_270]),c_0_222])]),c_0_271]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL550+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  2 17:22:52 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  # ENIGMATIC: Selected SinE mode:
% 0.18/0.45  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.18/0.45  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.18/0.45  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 8.53/2.38  # ENIGMATIC: Solved by autoschedule-lgb:
% 8.53/2.38  # No SInE strategy applied
% 8.53/2.38  # Trying AutoSched0 for 150 seconds
% 8.53/2.38  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 8.53/2.38  # and selection function SelectComplexExceptUniqMaxHorn.
% 8.53/2.38  #
% 8.53/2.38  # Preprocessing time       : 0.023 s
% 8.53/2.38  # Presaturation interreduction done
% 8.53/2.38  
% 8.53/2.38  # Proof found!
% 8.53/2.38  # SZS status Theorem
% 8.53/2.38  # SZS output start CNFRefutation
% See solution above
% 8.53/2.38  # Training examples: 0 positive, 0 negative
% 8.53/2.38  
% 8.53/2.38  # -------------------------------------------------
% 8.53/2.38  # User time                : 0.202 s
% 8.53/2.38  # System time              : 0.012 s
% 8.53/2.38  # Total time               : 0.214 s
% 8.53/2.38  # Maximum resident set size: 7124 pages
% 8.53/2.38  
%------------------------------------------------------------------------------