%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SEV565+1 : TPTP v9.1.0. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% 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 : Tue Apr 1 02:00:58 AM UTC 2025
% Result : Theorem 98.62s 13.85s
% Output : CNFRefutation 98.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 22
% Syntax : Number of clauses : 152 ( 33 unt; 66 nHn; 92 RR)
% Number of literals : 337 ( 42 equ; 93 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 254 ( 38 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_73,plain,
( X1 = X2
| ~ mem(X1,s(X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_73) ).
cnf(i_0_32,plain,
( mem(esk8_1(X1),X1)
| ~ atleast2p(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_32) ).
cnf(i_0_75,plain,
( subq(X1,X2)
| ~ mem(esk17_2(X1,X2),X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_75) ).
cnf(i_0_70,plain,
( mem(X1,p(X2))
| ~ subq(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_70) ).
cnf(i_0_76,plain,
( subq(X1,X2)
| mem(esk17_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_76) ).
cnf(i_0_72,plain,
( mem(X1,s(X2))
| X1 != X2 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_72) ).
cnf(i_0_31,plain,
( ~ atleast2p(X1)
| ~ subq(X1,p(esk8_1(X1))) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_31) ).
cnf(i_0_64,plain,
~ mem(X1,e),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_64) ).
cnf(i_0_30,plain,
( atleast2p(X1)
| subq(X1,p(X2))
| ~ mem(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_30) ).
cnf(i_0_74,plain,
( X1 = X2
| ~ subq(X2,X1)
| ~ subq(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_74) ).
cnf(i_0_71,plain,
( subq(X1,X2)
| ~ mem(X1,p(X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_71) ).
cnf(i_0_77,plain,
( mem(X1,X2)
| ~ subq(X3,X2)
| ~ mem(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_77) ).
cnf(i_0_79,plain,
( mem(X1,u(X2,X3))
| ~ mem(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_79) ).
cnf(i_0_69,negated_conjecture,
subq(u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(p(s(u(e,s(e)))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_69) ).
cnf(i_0_62,plain,
( disj(X1,X2)
| mem(esk16_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_62) ).
cnf(i_0_61,plain,
( disj(X1,X2)
| mem(esk16_2(X1,X2),X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_61) ).
cnf(i_0_80,plain,
( mem(X1,X2)
| mem(X1,X3)
| ~ mem(X1,u(X3,X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_80) ).
cnf(i_0_66,plain,
( ~ mem(X1,X2)
| ~ mem(X1,m(X3,X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_66) ).
cnf(i_0_67,plain,
( mem(X1,X2)
| ~ mem(X1,m(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_67) ).
cnf(i_0_78,plain,
( mem(X1,u(X2,X3))
| ~ mem(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_78) ).
cnf(i_0_65,plain,
( mem(X1,X2)
| mem(X1,m(X3,X2))
| ~ mem(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_65) ).
cnf(i_0_63,plain,
( ~ mem(X1,X2)
| ~ mem(X1,X3)
| ~ disj(X3,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-50rzor98/input.p',i_0_63) ).
cnf(c_0_103,plain,
( X1 = X2
| ~ mem(X1,s(X2)) ),
i_0_73 ).
cnf(c_0_104,plain,
( mem(esk8_1(X1),X1)
| ~ atleast2p(X1) ),
i_0_32 ).
cnf(c_0_105,plain,
( subq(X1,X2)
| ~ mem(esk17_2(X1,X2),X2) ),
i_0_75 ).
cnf(c_0_106,plain,
( mem(X1,p(X2))
| ~ subq(X1,X2) ),
i_0_70 ).
cnf(c_0_107,plain,
( subq(X1,X2)
| mem(esk17_2(X1,X2),X1) ),
i_0_76 ).
cnf(c_0_108,plain,
( mem(X1,s(X2))
| X1 != X2 ),
i_0_72 ).
cnf(c_0_109,plain,
( ~ atleast2p(X1)
| ~ subq(X1,p(esk8_1(X1))) ),
i_0_31 ).
cnf(c_0_110,plain,
( esk8_1(s(X1)) = X1
| ~ atleast2p(s(X1)) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,plain,
( subq(X1,p(X2))
| ~ subq(esk17_2(X1,p(X2)),X2) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,plain,
( esk17_2(s(X1),X2) = X1
| subq(s(X1),X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_107]) ).
cnf(c_0_113,plain,
~ mem(X1,e),
i_0_64 ).
cnf(c_0_114,plain,
( atleast2p(X1)
| subq(X1,p(X2))
| ~ mem(X2,X1) ),
i_0_30 ).
cnf(c_0_115,plain,
mem(X1,s(X1)),
inference(er,[status(thm)],[c_0_108]) ).
cnf(c_0_116,plain,
( ~ atleast2p(s(X1))
| ~ subq(s(X1),p(X1)) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_117,plain,
( subq(s(X1),p(X2))
| ~ subq(X1,X2) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,plain,
subq(X1,X1),
inference(spm,[status(thm)],[c_0_105,c_0_107]) ).
cnf(c_0_119,plain,
( X1 = X2
| ~ subq(X2,X1)
| ~ subq(X1,X2) ),
i_0_74 ).
cnf(c_0_120,plain,
subq(e,X1),
inference(spm,[status(thm)],[c_0_113,c_0_107]) ).
cnf(c_0_121,plain,
( subq(X1,X2)
| ~ mem(X1,p(X2)) ),
i_0_71 ).
cnf(c_0_122,plain,
( atleast2p(s(X1))
| subq(s(X1),p(X1)) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_123,plain,
~ atleast2p(s(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118])]) ).
cnf(c_0_124,plain,
( X1 = e
| ~ subq(X1,e) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,plain,
( subq(esk17_2(p(X1),X2),X1)
| subq(p(X1),X2) ),
inference(spm,[status(thm)],[c_0_121,c_0_107]) ).
cnf(c_0_126,plain,
subq(s(X1),p(X1)),
inference(sr,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_127,plain,
( esk17_2(p(e),X1) = e
| subq(p(e),X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_128,plain,
( p(X1) = s(X1)
| ~ subq(p(X1),s(X1)) ),
inference(spm,[status(thm)],[c_0_119,c_0_126]) ).
cnf(c_0_129,plain,
( subq(p(e),X1)
| ~ mem(e,X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_127]) ).
cnf(c_0_130,plain,
( mem(X1,X2)
| ~ subq(X3,X2)
| ~ mem(X1,X3) ),
i_0_77 ).
cnf(c_0_131,plain,
( mem(X1,u(X2,X3))
| ~ mem(X1,X2) ),
i_0_79 ).
cnf(c_0_132,plain,
p(e) = s(e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_115])]) ).
cnf(c_0_133,plain,
( mem(X1,X2)
| ~ mem(X1,X3)
| ~ subq(u(X3,X4),X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_134,negated_conjecture,
subq(u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(p(s(u(e,s(e)))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
i_0_69 ).
cnf(c_0_135,plain,
( disj(X1,X2)
| mem(esk16_2(X1,X2),X1) ),
i_0_62 ).
cnf(c_0_136,plain,
( disj(X1,X2)
| mem(esk16_2(X1,X2),X2) ),
i_0_61 ).
cnf(c_0_137,plain,
( mem(X1,X2)
| mem(X1,X3)
| ~ mem(X1,u(X3,X2)) ),
i_0_80 ).
cnf(c_0_138,plain,
( mem(X1,X2)
| ~ subq(s(X1),X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_115]) ).
cnf(c_0_139,plain,
( subq(s(e),X1)
| ~ mem(e,X1) ),
inference(rw,[status(thm)],[c_0_129,c_0_132]) ).
cnf(c_0_140,negated_conjecture,
( mem(X1,u(u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(X1,m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(p(s(u(e,s(e))))))) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_141,plain,
( disj(X1,X2)
| mem(esk16_2(X1,X2),X3)
| ~ subq(X1,X3) ),
inference(spm,[status(thm)],[c_0_130,c_0_135]) ).
cnf(c_0_142,plain,
( esk16_2(X1,s(X2)) = X2
| disj(X1,s(X2)) ),
inference(spm,[status(thm)],[c_0_103,c_0_136]) ).
cnf(c_0_143,plain,
( ~ mem(X1,X2)
| ~ mem(X1,m(X3,X2)) ),
i_0_66 ).
cnf(c_0_144,plain,
( mem(X1,X2)
| mem(X1,X3)
| ~ subq(s(X1),u(X2,X3)) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
( subq(s(e),u(u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(e,m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(p(s(u(e,s(e))))))) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_146,plain,
( disj(X1,s(X2))
| mem(X2,X3)
| ~ subq(X1,X3) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_147,plain,
subq(s(e),p(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_106]),c_0_120])]) ).
cnf(c_0_148,plain,
( subq(m(X1,X2),X3)
| ~ mem(esk17_2(m(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_143,c_0_107]) ).
cnf(c_0_149,plain,
( mem(X1,X2)
| ~ mem(X1,m(X2,X3)) ),
i_0_67 ).
cnf(c_0_150,plain,
( mem(e,u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| mem(e,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(e,m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(p(s(u(e,s(e))))))) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_151,plain,
( disj(s(e),s(X1))
| mem(X1,p(X2)) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_152,plain,
( subq(m(X1,u(X2,X3)),X4)
| ~ mem(esk17_2(m(X1,u(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_148,c_0_131]) ).
cnf(c_0_153,plain,
( mem(esk17_2(m(X1,X2),X3),X1)
| subq(m(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_149,c_0_107]) ).
cnf(c_0_154,plain,
( mem(e,u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| mem(e,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ subq(s(e),m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(p(s(u(e,s(e))))))) ),
inference(spm,[status(thm)],[c_0_150,c_0_138]) ).
cnf(c_0_155,plain,
( disj(s(e),s(X1))
| subq(X1,X2) ),
inference(spm,[status(thm)],[c_0_121,c_0_151]) ).
cnf(c_0_156,plain,
( mem(X1,u(X2,X3))
| ~ mem(X1,X3) ),
i_0_78 ).
cnf(c_0_157,plain,
( mem(X1,X2)
| mem(X1,m(X3,X2))
| ~ mem(X1,X3) ),
i_0_65 ).
cnf(c_0_158,plain,
subq(m(X1,u(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_159,plain,
( disj(s(e),s(s(e)))
| mem(e,u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| mem(e,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_160,plain,
( subq(X1,u(X2,X3))
| ~ mem(esk17_2(X1,u(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_105,c_0_156]) ).
cnf(c_0_161,plain,
( mem(X1,m(X2,X3))
| mem(X1,X3)
| ~ subq(s(X1),X2) ),
inference(spm,[status(thm)],[c_0_157,c_0_138]) ).
cnf(c_0_162,plain,
m(X1,u(X1,X2)) = e,
inference(spm,[status(thm)],[c_0_124,c_0_158]) ).
cnf(c_0_163,plain,
( disj(s(e),s(s(e)))
| mem(e,u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(e,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(e,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))) ),
inference(spm,[status(thm)],[c_0_137,c_0_159]) ).
cnf(c_0_164,plain,
( mem(esk17_2(X1,X2),X3)
| subq(X1,X2)
| ~ subq(X1,X3) ),
inference(spm,[status(thm)],[c_0_130,c_0_107]) ).
cnf(c_0_165,plain,
subq(X1,u(X2,X1)),
inference(spm,[status(thm)],[c_0_160,c_0_107]) ).
cnf(c_0_166,plain,
( mem(X1,u(X2,X3))
| ~ subq(s(X1),X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_113]) ).
cnf(c_0_167,plain,
( disj(s(e),s(s(e)))
| mem(e,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(e,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(e,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| mem(e,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(spm,[status(thm)],[c_0_137,c_0_163]) ).
cnf(c_0_168,plain,
( subq(X1,u(X2,X3))
| ~ mem(esk17_2(X1,u(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_105,c_0_131]) ).
cnf(c_0_169,plain,
( mem(esk17_2(X1,X2),u(X3,X1))
| subq(X1,X2) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_170,plain,
( subq(s(e),u(X1,X2))
| ~ subq(s(e),X1) ),
inference(spm,[status(thm)],[c_0_139,c_0_166]) ).
cnf(c_0_171,plain,
( u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = e
| disj(s(e),s(s(e)))
| mem(e,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(e,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| mem(e,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(spm,[status(thm)],[c_0_103,c_0_167]) ).
cnf(c_0_172,plain,
subq(X1,u(u(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_173,plain,
~ subq(s(X1),e),
inference(spm,[status(thm)],[c_0_113,c_0_138]) ).
cnf(c_0_174,plain,
( mem(esk17_2(u(X1,X2),X3),X1)
| mem(esk17_2(u(X1,X2),X3),X2)
| subq(u(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_137,c_0_107]) ).
cnf(c_0_175,plain,
( disj(s(e),s(s(e)))
| mem(e,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(e,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| mem(e,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_172])]),c_0_173]) ).
cnf(c_0_176,plain,
( mem(esk17_2(u(X1,X2),u(X2,X3)),X1)
| subq(u(X1,X2),u(X2,X3)) ),
inference(spm,[status(thm)],[c_0_168,c_0_174]) ).
cnf(c_0_177,plain,
( mem(esk17_2(u(X1,X2),X2),X1)
| subq(u(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_105,c_0_174]) ).
cnf(c_0_178,plain,
subq(X1,u(X1,X2)),
inference(spm,[status(thm)],[c_0_168,c_0_107]) ).
cnf(c_0_179,plain,
( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = e
| disj(s(e),s(s(e)))
| mem(e,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| mem(e,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(spm,[status(thm)],[c_0_103,c_0_175]) ).
cnf(c_0_180,plain,
subq(u(X1,X2),u(X2,X1)),
inference(spm,[status(thm)],[c_0_160,c_0_176]) ).
cnf(c_0_181,plain,
subq(u(e,X1),X1),
inference(spm,[status(thm)],[c_0_113,c_0_177]) ).
cnf(c_0_182,plain,
( mem(esk17_2(X1,X2),u(X1,X3))
| subq(X1,X2) ),
inference(spm,[status(thm)],[c_0_164,c_0_178]) ).
cnf(c_0_183,plain,
( disj(s(e),s(s(e)))
| mem(e,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| mem(e,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_179]),c_0_165])]),c_0_173]) ).
cnf(c_0_184,plain,
( mem(X1,u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| mem(X1,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X1,m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),p(p(s(u(e,s(e))))))) ),
inference(spm,[status(thm)],[c_0_137,c_0_140]) ).
cnf(c_0_185,plain,
u(X1,X2) = u(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_180]),c_0_180])]) ).
cnf(c_0_186,plain,
u(e,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_181]),c_0_165])]) ).
cnf(c_0_187,plain,
( mem(X1,m(p(X2),X3))
| mem(X1,X3)
| ~ subq(X1,X2) ),
inference(spm,[status(thm)],[c_0_157,c_0_106]) ).
cnf(c_0_188,plain,
subq(X1,u(X2,u(X1,X3))),
inference(spm,[status(thm)],[c_0_160,c_0_182]) ).
cnf(c_0_189,plain,
( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e
| disj(s(e),s(s(e)))
| mem(e,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(spm,[status(thm)],[c_0_103,c_0_183]) ).
cnf(c_0_190,plain,
( mem(X1,u(s(u(s(e),u(s(s(e)),s(s(s(e)))))),u(s(u(s(e),s(s(e)))),s(u(s(s(e)),s(s(s(e))))))))
| mem(X1,s(u(u(s(e),s(s(e))),s(u(s(e),s(s(e)))))))
| ~ mem(X1,m(p(u(s(e),u(s(s(e)),s(s(s(e)))))),p(p(s(s(e)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]),c_0_186]) ).
cnf(c_0_191,plain,
( mem(X1,m(p(u(X2,u(X1,X3))),X4))
| mem(X1,X4) ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_192,plain,
( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e
| u(u(e,s(e)),s(u(e,s(e)))) = e
| disj(s(e),s(s(e))) ),
inference(spm,[status(thm)],[c_0_103,c_0_189]) ).
cnf(c_0_193,plain,
( mem(s(s(e)),u(s(u(s(e),u(s(s(e)),s(s(s(e)))))),u(s(u(s(e),s(s(e)))),s(u(s(s(e)),s(s(s(e))))))))
| mem(s(s(e)),s(u(u(s(e),s(s(e))),s(u(s(e),s(s(e)))))))
| mem(s(s(e)),p(p(s(s(e))))) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_194,plain,
( u(u(e,s(e)),s(u(e,s(e)))) = e
| disj(s(e),s(s(e))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_192]),c_0_173]) ).
cnf(c_0_195,plain,
( mem(s(s(e)),u(s(u(s(e),s(s(e)))),s(u(s(s(e)),s(s(s(e)))))))
| mem(s(s(e)),s(u(u(s(e),s(s(e))),s(u(s(e),s(s(e)))))))
| mem(s(s(e)),s(u(s(e),u(s(s(e)),s(s(s(e)))))))
| mem(s(s(e)),p(p(s(s(e))))) ),
inference(spm,[status(thm)],[c_0_137,c_0_193]) ).
cnf(c_0_196,plain,
( ~ mem(X1,X2)
| ~ mem(X1,X3)
| ~ disj(X3,X2) ),
i_0_63 ).
cnf(c_0_197,plain,
disj(s(e),s(s(e))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_194]),c_0_165])]),c_0_173]) ).
cnf(c_0_198,plain,
( mem(s(s(e)),s(u(u(s(e),s(s(e))),s(u(s(e),s(s(e)))))))
| mem(s(s(e)),s(u(s(e),u(s(s(e)),s(s(s(e)))))))
| mem(s(s(e)),s(u(s(s(e)),s(s(s(e))))))
| mem(s(s(e)),s(u(s(e),s(s(e)))))
| mem(s(s(e)),p(p(s(s(e))))) ),
inference(spm,[status(thm)],[c_0_137,c_0_195]) ).
cnf(c_0_199,plain,
( ~ mem(X1,s(s(e)))
| ~ mem(X1,s(e)) ),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_200,plain,
( atleast2p(X1)
| subq(X1,p(X2))
| ~ subq(s(X2),X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_138]) ).
cnf(c_0_201,plain,
subq(X1,u(u(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_168,c_0_182]) ).
cnf(c_0_202,plain,
( u(u(s(e),s(s(e))),s(u(s(e),s(s(e))))) = s(s(e))
| mem(s(s(e)),s(u(s(e),u(s(s(e)),s(s(s(e)))))))
| mem(s(s(e)),s(u(s(s(e)),s(s(s(e))))))
| mem(s(s(e)),s(u(s(e),s(s(e)))))
| mem(s(s(e)),p(p(s(s(e))))) ),
inference(spm,[status(thm)],[c_0_103,c_0_198]) ).
cnf(c_0_203,plain,
~ mem(s(e),s(e)),
inference(spm,[status(thm)],[c_0_199,c_0_115]) ).
cnf(c_0_204,plain,
( atleast2p(u(u(s(X1),X2),X3))
| subq(u(u(s(X1),X2),X3),p(X1)) ),
inference(spm,[status(thm)],[c_0_200,c_0_201]) ).
cnf(c_0_205,plain,
( u(u(s(e),s(s(e))),s(u(s(e),s(s(e))))) = s(s(e))
| u(s(e),u(s(s(e)),s(s(s(e))))) = s(s(e))
| mem(s(s(e)),s(u(s(s(e)),s(s(s(e))))))
| mem(s(s(e)),s(u(s(e),s(s(e)))))
| mem(s(s(e)),p(p(s(s(e))))) ),
inference(spm,[status(thm)],[c_0_103,c_0_202]) ).
cnf(c_0_206,plain,
~ subq(s(s(e)),s(e)),
inference(spm,[status(thm)],[c_0_203,c_0_138]) ).
cnf(c_0_207,plain,
( u(s(e),u(s(s(e)),s(s(s(e))))) = s(s(e))
| mem(s(s(e)),s(u(s(s(e)),s(s(s(e))))))
| mem(s(s(e)),s(u(s(e),s(s(e)))))
| mem(s(s(e)),p(p(s(s(e))))) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_132]),c_0_123]),c_0_206]) ).
cnf(c_0_208,plain,
( mem(X1,X2)
| ~ mem(X1,u(X2,X2)) ),
inference(ef,[status(thm)],[c_0_137]) ).
cnf(c_0_209,plain,
( u(s(e),u(s(s(e)),s(s(s(e))))) = s(s(e))
| u(s(s(e)),s(s(s(e)))) = s(s(e))
| mem(s(s(e)),s(u(s(e),s(s(e)))))
| mem(s(s(e)),p(p(s(s(e))))) ),
inference(spm,[status(thm)],[c_0_103,c_0_207]) ).
cnf(c_0_210,plain,
( atleast2p(u(X1,X2))
| subq(u(X1,X2),p(X3))
| ~ mem(X3,X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_156]) ).
cnf(c_0_211,plain,
( mem(esk17_2(u(X1,X1),X2),X1)
| subq(u(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_208,c_0_107]) ).
cnf(c_0_212,plain,
( subq(m(X1,u(X2,X3)),X4)
| ~ mem(esk17_2(m(X1,u(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_148,c_0_156]) ).
cnf(c_0_213,plain,
( u(s(e),u(s(s(e)),s(s(s(e))))) = s(s(e))
| u(s(s(e)),s(s(s(e)))) = s(s(e))
| mem(s(s(e)),s(u(s(e),s(s(e)))))
| subq(s(s(e)),p(s(s(e)))) ),
inference(spm,[status(thm)],[c_0_121,c_0_209]) ).
cnf(c_0_214,plain,
( atleast2p(u(X1,s(X2)))
| subq(u(X1,s(X2)),p(X2)) ),
inference(spm,[status(thm)],[c_0_210,c_0_115]) ).
cnf(c_0_215,plain,
subq(u(X1,X1),X1),
inference(spm,[status(thm)],[c_0_105,c_0_211]) ).
cnf(c_0_216,plain,
subq(m(X1,u(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_212,c_0_153]) ).
cnf(c_0_217,plain,
( u(X1,X2) = X2
| ~ subq(u(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_119,c_0_165]) ).
cnf(c_0_218,plain,
( u(s(e),u(s(s(e)),s(s(s(e))))) = s(s(e))
| u(s(s(e)),s(s(s(e)))) = s(s(e))
| u(s(e),s(s(e))) = s(s(e))
| subq(s(s(e)),p(s(s(e)))) ),
inference(spm,[status(thm)],[c_0_103,c_0_213]) ).
cnf(c_0_219,plain,
( atleast2p(u(X1,s(X2)))
| mem(X3,p(X2))
| ~ mem(X3,X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_214]) ).
cnf(c_0_220,plain,
u(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_215]),c_0_178])]) ).
cnf(c_0_221,plain,
( mem(X1,m(s(X1),X2))
| mem(X1,X2) ),
inference(spm,[status(thm)],[c_0_157,c_0_115]) ).
cnf(c_0_222,plain,
m(X1,u(X2,X1)) = e,
inference(spm,[status(thm)],[c_0_124,c_0_216]) ).
cnf(c_0_223,plain,
( subq(X1,X2)
| ~ subq(s(X1),p(X2)) ),
inference(spm,[status(thm)],[c_0_121,c_0_138]) ).
cnf(c_0_224,plain,
( u(s(s(e)),s(s(s(e)))) = s(s(e))
| u(s(e),s(s(e))) = s(s(e))
| subq(s(s(e)),p(s(s(e)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_178])]) ).
cnf(c_0_225,plain,
( mem(X1,p(X2))
| ~ mem(X1,s(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_123]) ).
cnf(c_0_226,plain,
mem(X1,u(X2,s(X1))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_113]) ).
cnf(c_0_227,plain,
( u(s(s(e)),s(s(s(e)))) = s(s(e))
| u(s(e),s(s(e))) = s(s(e))
| subq(s(e),s(s(e))) ),
inference(spm,[status(thm)],[c_0_223,c_0_224]) ).
cnf(c_0_228,plain,
( subq(X1,X2)
| ~ mem(X1,s(X2)) ),
inference(spm,[status(thm)],[c_0_121,c_0_225]) ).
cnf(c_0_229,plain,
( u(s(e),s(s(e))) = s(s(e))
| mem(s(s(e)),s(s(e)))
| subq(s(e),s(s(e))) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_230,plain,
( u(s(e),s(s(e))) = s(s(e))
| subq(s(e),s(s(e))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_229]),c_0_206]) ).
cnf(c_0_231,plain,
subq(s(e),s(s(e))),
inference(spm,[status(thm)],[c_0_178,c_0_230]) ).
cnf(c_0_232,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_231]),c_0_132]),c_0_123]),c_0_206]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV565+1 : TPTP v9.1.0. Released v9.1.0.
% 0.03/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.33 % Computer : n009.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 : 300
% 0.12/0.33 % DateTime : Mon Mar 31 12:30:14 EDT 2025
% 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
% 98.62/13.85 # ENIGMATIC: Solved by G_E___302_C18_F1_URBAN_S5PRR_RG_S04BN:
% 98.62/13.85 # Version: 2.1pre011
% 98.62/13.85 # Preprocessing time : 0.099 s
% 98.62/13.85
% 98.62/13.85 # Proof found!
% 98.62/13.85 # SZS status Theorem
% 98.62/13.85 # SZS output start CNFRefutation
% See solution above
% 98.62/13.85 # Proof object total steps : 152
% 98.62/13.85 # Proof object clause steps : 130
% 98.62/13.85 # Proof object formula steps : 22
% 98.62/13.85 # Proof object conjectures : 4
% 98.62/13.85 # Proof object clause conjectures : 3
% 98.62/13.85 # Proof object formula conjectures : 1
% 98.62/13.85 # Proof object initial clauses used : 22
% 98.62/13.85 # Proof object initial formulas used : 22
% 98.62/13.85 # Proof object generating inferences : 104
% 98.62/13.85 # Proof object simplifying inferences : 53
% 98.62/13.85 # Training examples: 0 positive, 0 negative
% 98.62/13.85 # Parsed axioms : 78
% 98.62/13.85 # Removed by relevancy pruning/SinE : 0
% 98.62/13.85 # Initial clauses : 78
% 98.62/13.85 # Removed in clause preprocessing : 0
% 98.62/13.85 # Initial clauses in saturation : 78
% 98.62/13.85 # Processed clauses : 15932
% 98.62/13.85 # ...of these trivial : 182
% 98.62/13.85 # ...subsumed : 9411
% 98.62/13.85 # ...remaining for further processing : 6339
% 98.62/13.85 # Other redundant clauses eliminated : 1
% 98.62/13.85 # Clauses deleted for lack of memory : 0
% 98.62/13.85 # Backward-subsumed : 408
% 98.62/13.85 # Backward-rewritten : 1019
% 98.62/13.85 # Generated clauses : 437905
% 98.62/13.85 # ...of the previous two non-trivial : 395979
% 98.62/13.85 # Contextual simplify-reflections : 1950
% 98.62/13.85 # Paramodulations : 437635
% 98.62/13.85 # Factorizations : 242
% 98.62/13.85 # Equation resolutions : 1
% 98.62/13.85 # Propositional unsat checks : 1
% 98.62/13.85 # Propositional unsat check successes : 0
% 98.62/13.85 # Current number of processed clauses : 4884
% 98.62/13.85 # Positive orientable unit clauses : 168
% 98.62/13.85 # Positive unorientable unit clauses: 1
% 98.62/13.85 # Negative unit clauses : 54
% 98.62/13.85 # Non-unit-clauses : 4661
% 98.62/13.85 # Current number of unprocessed clauses: 261437
% 98.62/13.85 # ...number of literals in the above : 920319
% 98.62/13.85 # Current number of archived formulas : 0
% 98.62/13.85 # Current number of archived clauses : 1454
% 98.62/13.85 # Clause-clause subsumption calls (NU) : 5799730
% 98.62/13.85 # Rec. Clause-clause subsumption calls : 1629845
% 98.62/13.85 # Non-unit clause-clause subsumptions : 5904
% 98.62/13.85 # Unit Clause-clause subsumption calls : 71138
% 98.62/13.85 # Rewrite failures with RHS unbound : 0
% 98.62/13.85 # BW rewrite match attempts : 2704
% 98.62/13.85 # BW rewrite match successes : 801
% 98.62/13.85 # Condensation attempts : 0
% 98.62/13.85 # Condensation successes : 0
% 98.62/13.85 # Termbank termtop insertions : 17497370
% 98.62/13.85
% 98.62/13.85 # -------------------------------------------------
% 98.62/13.85 # User time : 11.165 s
% 98.62/13.85 # System time : 0.255 s
% 98.62/13.85 # Total time : 11.420 s
% 98.62/13.85 # ...preprocessing : 0.099 s
% 98.62/13.85 # ...main loop : 11.320 s
% 98.62/13.85 # Maximum resident set size: 325260 pages
% 98.62/13.85
%------------------------------------------------------------------------------