%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SYO630-1 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n018.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 : Thu Jul 21 19:44:39 EDT 2022
% Result : Unsatisfiable 10.46s 10.62s
% Output : Refutation 10.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of clauses : 153 ( 7 unt; 133 nHn; 22 RR)
% Number of literals : 670 ( 0 equ; 39 neg)
% Maximal clause size : 6 ( 4 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 158 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_8_01,axiom,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'LE'(f(X),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_01) ).
cnf(clause_13_02,axiom,
iLEQ(X,g(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13_02) ).
cnf(clause_18_04,axiom,
iLEQ(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18_04) ).
cnf(clause_31_05,axiom,
~ 'E'(f(X),f(g(X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31_05) ).
cnf(clause_1_06,axiom,
( ~ 'LE'(f(X),s('0'))
| ~ iLEQ(X,Y)
| 'E'('0',f(Y))
| 'LE'(f(Y),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_06) ).
cnf(clause_6_07,axiom,
~ 'LE'(f(X),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_07) ).
cnf(clause_3_10,axiom,
( ~ 'E'(s(s(s(s(s('0'))))),f(X))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(X)))
| 'E'(f(X),f(g(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_10) ).
cnf(8,plain,
( ~ 'E'(s(s(s(s(s('0'))))),f(X))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(X))) ),
inference('REWRITE',[status(thm)],[clause_3_10,clause_31_05]) ).
cnf(clause_21_11,axiom,
( ~ 'E'(s(s(s('0'))),f(X))
| ~ 'E'(s(s(s('0'))),f(g(X)))
| 'E'(f(X),f(g(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21_11) ).
cnf(10,plain,
( ~ 'E'(s(s(s('0'))),f(X))
| ~ 'E'(s(s(s('0'))),f(g(X))) ),
inference('REWRITE',[status(thm)],[clause_21_11,clause_31_05]) ).
cnf(clause_27_12,axiom,
( ~ 'E'(s(s('0')),f(X))
| ~ 'E'(s(s('0')),f(g(X)))
| 'E'(f(X),f(g(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27_12) ).
cnf(12,plain,
( ~ 'E'(s(s('0')),f(X))
| ~ 'E'(s(s('0')),f(g(X))) ),
inference('REWRITE',[status(thm)],[clause_27_12,clause_31_05]) ).
cnf(clause_30_13,axiom,
( ~ 'E'(s('0'),f(X))
| ~ 'E'(s('0'),f(g(X)))
| 'E'(f(X),f(g(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30_13) ).
cnf(14,plain,
( ~ 'E'(s('0'),f(X))
| ~ 'E'(s('0'),f(g(X))) ),
inference('REWRITE',[status(thm)],[clause_30_13,clause_31_05]) ).
cnf(clause_16_15,axiom,
( ~ 'LE'(f(X),s(s(s('0'))))
| ~ iLEQ(X,Y)
| 'E'(s(s('0')),f(Y))
| 'LE'(f(Y),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16_15) ).
cnf(clause_7_16,axiom,
( ~ 'LE'(f(X),s(s(s(s(s('0'))))))
| ~ iLEQ(X,Y)
| 'E'(s(s(s(s('0')))),f(Y))
| 'LE'(f(Y),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_16) ).
cnf(clause_26_17,axiom,
( ~ 'LE'(f(X),s(s(s(s('0')))))
| ~ iLEQ(X,Y)
| 'E'(s(s(s('0'))),f(Y))
| 'LE'(f(Y),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26_17) ).
cnf(clause_29_24,axiom,
( ~ 'E'('0',f(X))
| ~ 'E'('0',f(g(X)))
| 'E'(f(X),f(g(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29_24) ).
cnf(19,plain,
( ~ 'E'('0',f(X))
| ~ 'E'('0',f(g(X))) ),
inference('REWRITE',[status(thm)],[clause_29_24,clause_31_05]) ).
cnf(clause_12_30,axiom,
( ~ 'E'(s(s(s(s('0')))),f(X))
| ~ 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(f(X),f(g(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_30) ).
cnf(21,plain,
( ~ 'E'(s(s(s(s('0')))),f(X))
| ~ 'E'(s(s(s(s('0')))),f(g(X))) ),
inference('REWRITE',[status(thm)],[clause_12_30,clause_31_05]) ).
cnf(clause_17_32,axiom,
( ~ 'LE'(f(X),s(s('0')))
| ~ iLEQ(X,Y)
| 'E'(s('0'),f(Y))
| 'LE'(f(Y),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17_32) ).
cnf(23,plain,
( ~ 'LE'(f(X),s('0'))
| ~ iLEQ(X,Y)
| 'E'('0',f(Y)) ),
inference('REWRITE',[status(thm)],[clause_1_06,clause_6_07]) ).
cnf(24,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'LE'(f(X),s(s(s(s('0'))))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_7_16,clause_8_01,clause_18_04]) ).
cnf(25,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'LE'(f(g(X)),s(s(s(s('0'))))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_7_16,clause_8_01,clause_13_02]) ).
cnf(26,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'LE'(f(X),s(s(s('0')))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_26_17,24,clause_18_04]) ).
cnf(27,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'LE'(f(g(X)),s(s(s('0')))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_26_17,24,clause_13_02]) ).
cnf(28,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'LE'(f(g(X)),s(s(s('0')))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_26_17,25,clause_18_04]) ).
cnf(29,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'LE'(f(g(g(X))),s(s(s('0')))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_26_17,25,clause_13_02]) ).
cnf(30,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(X))
| 'LE'(f(X),s(s('0'))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_16_15,26,clause_18_04]) ).
cnf(31,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(g(X)))
| 'LE'(f(g(X)),s(s('0'))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_16_15,26,clause_13_02]) ).
cnf(32,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'LE'(f(g(X)),s(s('0'))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_16_15,27,clause_18_04]) ).
cnf(33,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'LE'(f(g(g(X))),s(s('0'))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_16_15,27,clause_13_02]) ).
cnf(34,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'LE'(f(g(X)),s(s('0'))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_16_15,28,clause_18_04]) ).
cnf(35,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'LE'(f(g(g(X))),s(s('0'))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_16_15,28,clause_13_02]) ).
cnf(36,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'LE'(f(g(g(X))),s(s('0'))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_16_15,29,clause_18_04]) ).
cnf(37,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'LE'(f(g(g(g(X)))),s(s('0'))) ),
inference('HYPERRESOLVE',[status(thm)],[clause_16_15,29,clause_13_02]) ).
cnf(38,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(X))
| 'E'(s('0'),f(X))
| 'LE'(f(X),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,30,clause_18_04]) ).
cnf(39,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(X))
| 'E'(s('0'),f(g(X)))
| 'LE'(f(g(X)),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,30,clause_13_02]) ).
cnf(40,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'LE'(f(g(X)),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,31,clause_18_04]) ).
cnf(41,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'LE'(f(g(g(X))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,31,clause_13_02]) ).
cnf(42,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'LE'(f(g(X)),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,32,clause_18_04]) ).
cnf(43,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'LE'(f(g(g(X))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,32,clause_13_02]) ).
cnf(44,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'LE'(f(g(X)),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,34,clause_18_04]) ).
cnf(45,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'LE'(f(g(g(X))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,34,clause_13_02]) ).
cnf(46,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(X))
| 'E'(s('0'),f(X))
| 'E'('0',f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[23,38,clause_18_04]) ).
cnf(47,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(X))
| 'E'(s('0'),f(X))
| 'E'('0',f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[23,38,clause_13_02]) ).
cnf(49,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'LE'(f(g(g(X))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,33,clause_18_04]) ).
cnf(50,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'LE'(f(g(g(g(X)))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,33,clause_13_02]) ).
cnf(51,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'LE'(f(g(g(X))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,35,clause_18_04]) ).
cnf(52,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'LE'(f(g(g(g(X)))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,35,clause_13_02]) ).
cnf(56,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'LE'(f(g(g(X))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,36,clause_18_04]) ).
cnf(57,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'LE'(f(g(g(g(X)))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,36,clause_13_02]) ).
cnf(58,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(X))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[23,39,clause_18_04]) ).
cnf(59,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(X))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,39,clause_13_02]) ).
cnf(64,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[23,40,clause_18_04]) ).
cnf(65,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,40,clause_13_02]) ).
cnf(71,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[23,42,clause_18_04]) ).
cnf(72,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,42,clause_13_02]) ).
cnf(89,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'LE'(f(g(g(g(X)))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,37,clause_18_04]) ).
cnf(90,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'LE'(f(g(g(g(g(X))))),s('0')) ),
inference('HYPERRESOLVE',[status(thm)],[clause_17_32,37,clause_13_02]) ).
cnf(91,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[23,44,clause_18_04]) ).
cnf(92,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,44,clause_13_02]) ).
cnf(103,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[8,91,46]) ).
cnf(120,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,41,clause_18_04]) ).
cnf(121,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,41,clause_13_02]) ).
cnf(122,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(X)))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[8,92,47]) ).
cnf(158,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,43,clause_18_04]) ).
cnf(159,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,43,clause_13_02]) ).
cnf(180,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,45,clause_18_04]) ).
cnf(181,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,45,clause_13_02]) ).
cnf(226,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[8,180,58]) ).
cnf(237,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,49,clause_18_04]) ).
cnf(238,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,49,clause_13_02]) ).
cnf(369,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,51,clause_18_04]) ).
cnf(370,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,51,clause_13_02]) ).
cnf(371,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,181,59]) ).
cnf(396,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[8,369,64]) ).
cnf(413,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[23,56,clause_18_04]) ).
cnf(414,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,56,clause_13_02]) ).
cnf(451,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[8,413,71]) ).
cnf(452,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[21,451,103]) ).
cnf(453,plain,
( 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X))))
| 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[10,452,237]) ).
cnf(461,plain,
( 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(X))))
| 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[12,453,120]) ).
cnf(561,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,370,65]) ).
cnf(584,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,50,clause_18_04]) ).
cnf(585,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,50,clause_13_02]) ).
cnf(586,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,414,72]) ).
cnf(587,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[21,586,122]) ).
cnf(589,plain,
( 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X)))))
| 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[10,587,238]) ).
cnf(605,plain,
( 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(X)))))
| 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X))
| 'E'(s(s(s('0'))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[12,589,121]) ).
cnf(710,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,52,clause_18_04]) ).
cnf(711,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,52,clause_13_02]) ).
cnf(717,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,710,461]) ).
cnf(774,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,57,clause_18_04]) ).
cnf(775,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,57,clause_13_02]) ).
cnf(838,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,774,158]) ).
cnf(839,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[21,838,226]) ).
cnf(841,plain,
( 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X)))))
| 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[10,839,584]) ).
cnf(947,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,711,605]) ).
cnf(1064,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,89,clause_18_04]) ).
cnf(1065,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,89,clause_13_02]) ).
cnf(1074,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,775,159]) ).
cnf(1075,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[21,1074,371]) ).
cnf(1078,plain,
( 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[10,1075,585]) ).
cnf(1255,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[21,1064,396]) ).
cnf(1256,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[10,1255,452]) ).
cnf(1257,plain,
( 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X)))))
| 'E'(s(s(s(s('0')))),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[8,1256,453]) ).
cnf(1258,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X)))))
| 'E'(s(s(s(s('0')))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[12,1256,841]) ).
cnf(1285,plain,
( 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X)))))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[12,1257,717]) ).
cnf(1286,plain,
( 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X)))))
| 'E'(s(s(s('0'))),f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[21,1257,396]) ).
cnf(1326,plain,
( 'E'('0',f(g(g(g(X)))))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[14,1285,371]) ).
cnf(1356,plain,
( 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[10,1286,452]) ).
cnf(1532,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[21,1065,561]) ).
cnf(1533,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[10,1532,587]) ).
cnf(1534,plain,
( 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s(s(s('0')))),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[8,1533,589]) ).
cnf(1535,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s(s(s('0')))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[12,1533,1078]) ).
cnf(1563,plain,
( 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[12,1534,947]) ).
cnf(1564,plain,
( 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s(s('0'))),f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[21,1534,561]) ).
cnf(1607,plain,
( 'E'(s('0'),f(g(g(g(X)))))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[19,1563,1326]) ).
cnf(1632,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'('0',f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[14,1607,226]) ).
cnf(1643,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[19,1632,1326]) ).
cnf(1647,plain,
( 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(g(X)))))))
| 'E'(s(s(s('0'))),f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[21,1643,1563]) ).
cnf(1659,plain,
( 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(X)))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[10,1564,587]) ).
cnf(1774,plain,
( 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(g(X)))))))
| 'E'(s(s('0')),f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[10,1647,1075]) ).
cnf(1879,plain,
( 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X)))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(g(X))))))) ),
inference('HYPERRESOLVE',[status(thm)],[12,1774,1659]) ).
cnf(2235,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,90,clause_18_04]) ).
cnf(2236,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(g(X))))))) ),
inference('HYPERRESOLVE',[status(thm)],[23,90,clause_13_02]) ).
cnf(2333,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,2235,1258]) ).
cnf(2334,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(g(X)))))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[21,2333,1285]) ).
cnf(2335,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[12,2334,1356]) ).
cnf(2336,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s('0')),f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[14,2335,1075]) ).
cnf(2337,plain,
( 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s('0')),f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[10,2335,839]) ).
cnf(2353,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[19,2336,587]) ).
cnf(2368,plain,
( 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(g(g(X)))))))
| 'E'(s(s('0')),f(g(g(g(X))))) ),
inference('HYPERRESOLVE',[status(thm)],[10,2353,2336]) ).
cnf(2377,plain,
( 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[12,2337,1356]) ).
cnf(2379,plain,
( 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[14,2377,1563]) ).
cnf(2380,plain,
( 'E'('0',f(g(g(g(g(g(X)))))))
| 'E'(s(s(s('0'))),f(g(X)))
| 'E'(s(s('0')),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[14,2377,1879]) ).
cnf(2382,plain,
( 'E'('0',f(g(g(g(g(X))))))
| 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(X)) ),
inference('HYPERRESOLVE',[status(thm)],[14,2377,1535]) ).
cnf(2479,plain,
( 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(g(g(X)))))))
| 'E'(s('0'),f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[12,2368,1659]) ).
cnf(2500,plain,
( 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X))))
| 'E'('0',f(g(g(g(g(g(X))))))) ),
inference('HYPERRESOLVE',[status(thm)],[14,2479,2377]) ).
cnf(3099,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'(s('0'),f(g(g(g(g(X))))))
| 'E'('0',f(g(g(g(g(g(X))))))) ),
inference('HYPERRESOLVE',[status(thm)],[12,2236,1659]) ).
cnf(3100,plain,
( 'E'(s(s(s(s(s('0'))))),f(X))
| 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'('0',f(g(g(g(g(g(X))))))) ),
inference('HYPERRESOLVE',[status(thm)],[14,3099,2377]) ).
cnf(3101,plain,
( 'E'(s(s(s(s('0')))),f(g(X)))
| 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'('0',f(g(g(g(g(g(X))))))) ),
inference('HYPERRESOLVE',[status(thm)],[8,3100,2382]) ).
cnf(3102,plain,
( 'E'(s(s(s('0'))),f(g(g(X))))
| 'E'('0',f(g(g(g(g(g(X))))))) ),
inference('HYPERRESOLVE',[status(thm)],[21,3101,2379]) ).
cnf(3104,plain,
( 'E'('0',f(g(g(g(g(g(X)))))))
| 'E'(s(s('0')),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[10,3102,2380]) ).
cnf(3132,plain,
( 'E'(s(s('0')),f(g(X)))
| 'E'(s(s('0')),f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[19,3104,3104]) ).
cnf(3133,plain,
( 'E'(s(s('0')),f(g(g(X))))
| 'E'(s('0'),f(g(g(X)))) ),
inference('HYPERRESOLVE',[status(thm)],[19,3104,2500]) ).
cnf(3145,plain,
( 'E'(s('0'),f(g(g(g(X)))))
| 'E'(s(s('0')),f(g(X))) ),
inference('HYPERRESOLVE',[status(thm)],[12,3133,3132]) ).
cnf(3149,plain,
( 'E'(s(s('0')),f(g(X)))
| 'E'('0',f(g(g(g(g(X)))))) ),
inference('HYPERRESOLVE',[status(thm)],[14,3145,2377]) ).
cnf(3166,plain,
'E'(s(s('0')),f(g(X))),
inference('HYPERRESOLVE',[status(thm)],[19,3149,3104]) ).
cnf(3167,plain,
~ 'E'(s(s('0')),f(X)),
inference('REWRITE',[status(thm)],[12,3166]) ).
cnf(3168,plain,
$false,
inference('REWRITE',[status(thm)],[3166,3167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO630-1 : TPTP v8.1.0. Released v7.1.0.
% 0.12/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 23:04:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-08T23:04:26
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-07-08T23:04:26
% 10.46/10.62
% 10.46/10.62
% 10.46/10.62 #||
% 10.46/10.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.46/10.62 % SZS output start Refutation
% See solution above
% 10.46/10.65 ||#
% 10.46/10.65
% 10.46/10.65 ; Summary of computation:
% 10.46/10.65 ; 24992 formulas have been input or derived (from 397 formulas).
% 10.46/10.65 ; 3168 (13%) were retained. Of these,
% 10.46/10.65 ; 3072 (97%) were simplified or subsumed later,
% 10.46/10.65 ; 96 ( 3%) are still being kept.
% 10.46/10.65 ;
% 10.46/10.65 ; Run time in seconds excluding printing time:
% 10.46/10.65 ; 0.006 0% Read assertion file (1 call)
% 10.46/10.65 ; 0.001 0% Assert (32 calls)
% 10.46/10.65 ; 0.453 4% Process new row (24,544 calls)
% 10.46/10.65 ; 0.560 6% Resolution (792 calls)
% 10.46/10.65 ; 0.007 0% Paramodulation (396 calls)
% 10.46/10.65 ; 0.006 0% Factoring (381 calls)
% 10.46/10.65 ; 0.287 3% Condensing (18,117 calls)
% 10.46/10.65 ; 4.520 45% Forward subsumption (18,117 calls)
% 10.46/10.65 ; 0.676 7% Backward subsumption (3,155 calls)
% 10.46/10.65 ; 2.380 23% Clause clause subsumption (596,809 calls)
% 10.46/10.65 ; 0.573 6% Forward simplification (18,140 calls)
% 10.46/10.65 ; 0.008 0% Backward simplification (3,162 calls)
% 10.46/10.65 ; 0.558 5% Ordering (120,152 calls)
% 10.46/10.65 ; 0.000 0% Sortal reasoning (32 calls)
% 10.46/10.65 ; 0.000 0% Purity testing (1 call)
% 10.46/10.65 ; 0.117 1% Other
% 10.46/10.65 ; 10.152 Total
% 10.46/10.65 ; 10.184 Real time
% 10.46/10.65 ;
% 10.46/10.65 ; Term-hash-array has 140 terms in all.
% 10.46/10.65 ; Feature-vector-row-index has 90 entries (555 at peak, 3,155 added, 3,065 deleted).
% 10.46/10.65 ; Feature-vector-row-index has 751 nodes (3,882 at peak, 21,048 added, 20,297 deleted).
% 10.46/10.65 ; Retrieved 782,174 possibly forward subsuming rows in 18,117 calls.
% 10.46/10.65 ; Retrieved 95,607 possibly backward subsumed rows in 3,155 calls.
% 10.46/10.65 ; Path-index has 93 entries (136 at peak, 188 added, 95 deleted).
% 10.46/10.65 ; Path-index has 137 nodes (151 at peak, 171 added, 34 deleted).
% 10.46/10.65 ; Trie-index has 93 entries (136 at peak, 188 added, 95 deleted).
% 10.46/10.66 ; Trie-index has 202 nodes (284 at peak, 377 added, 175 deleted).
% 10.46/10.66 ; Retrieved 28 generalization terms in 123,727 calls.
% 10.46/10.66 ; Retrieved 14 instance terms in 6 calls.
% 10.46/10.66 ; Retrieved 15,278 unifiable terms in 7,248 calls.
% 10.46/10.66 ;
% 10.46/10.66 ; The agenda of backward simplifiable rows to process has 1 entry:
% 10.46/10.66 ; 1 with value 0
% 10.46/10.66 ; The agenda of rows to process has 31 entries:
% 10.46/10.66 ; 1 with value 36 1 with value 49 1 with value 57
% 10.46/10.66 ; 1 with value 38 1 with value 51 1 with value 58
% 10.46/10.66 ; 1 with value 40 2 with value 52 1 with value 61
% 10.46/10.66 ; 2 with value 46 3 with value 53 3 with value 62
% 10.46/10.66 ; 1 with value 47 2 with value 54 2 with value 64
% 10.46/10.66 ; 4 with value 48 2 with value 56 2 with value 68
% 10.46/10.66 ; The agenda of input rows to give has 1 entry:
% 10.46/10.66 ; 1 with value 9
% 10.46/10.66 ; The agenda of rows to give has 49 entries:
% 10.46/10.66 ; 2 with value (4 48) 1 with value (4 93) 2 with value (4 119)
% 10.46/10.66 ; 2 with value (4 49) 1 with value (4 94) 1 with value (4 121)
% 10.46/10.66 ; 1 with value (4 51) 1 with value (4 95) 1 with value (4 122)
% 10.46/10.66 ; 2 with value (4 53) 1 with value (4 97) 1 with value (4 123)
% 10.46/10.66 ; 1 with value (4 54) 2 with value (4 98) 2 with value (4 125)
% 10.46/10.66 ; 1 with value (4 58) 2 with value (4 101) 1 with value (4 126)
% 10.46/10.66 ; 1 with value (4 59) 1 with value (4 102) 2 with value (4 128)
% 10.46/10.66 ; 1 with value (4 60) 2 with value (4 105) 2 with value (4 132)
% 10.46/10.66 ; 1 with value (4 61) 1 with value (4 109) 1 with value (4 137)
% 10.46/10.66 ; 1 with value (4 62) 1 with value (4 110) 1 with value (4 140)
% 10.46/10.66 ; 1 with value (4 69) 1 with value (4 114) 1 with value (4 141)
% 10.46/10.66 ; 1 with value (4 91) 1 with value (4 117) 1 with value (4 145)
% 10.46/10.66 ; 1 with value (4 92) 1 with value (4 118) 1 with value (4 153)
% 10.46/10.66 Evaluation took:
% 10.46/10.66 10.184 seconds of real time
% 10.46/10.66 9.262357 seconds of user run time
% 10.46/10.66 0.920968 seconds of system run time
% 10.46/10.66 [Run times include 0.421 seconds GC run time.]
% 10.46/10.66 0 calls to %EVAL
% 10.46/10.66 0 page faults and
% 10.46/10.66 1,607,914,920 bytes consed.
% 10.46/10.66 :PROOF-FOUND
% 10.46/10.66 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-08T23:04:36
% 10.46/10.66 :PROOF-FOUND
% 10.46/10.66 *
%------------------------------------------------------------------------------