%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYO630-1 : TPTP v9.2.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 May 5 05:54:05 PM UTC 2026
% Result : Unsatisfiable 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 16
% Syntax : Number of clauses : 203 ( 13 unt; 160 nHn; 94 RR)
% Number of literals : 876 ( 0 equ; 128 neg)
% Maximal clause size : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 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 : 243 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_7_16,axiom,
( 'E'(s(s(s(s('0')))),f(X2))
| 'LE'(f(X2),s(s(s(s('0')))))
| ~ 'LE'(f(X1),s(s(s(s(s('0'))))))
| ~ iLEQ(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_16) ).
cnf(clause_8_01,axiom,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_01) ).
cnf(clause_18_04,axiom,
iLEQ(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18_04) ).
cnf(clause_26_17,axiom,
( 'E'(s(s(s('0'))),f(X2))
| 'LE'(f(X2),s(s(s('0'))))
| ~ 'LE'(f(X1),s(s(s(s('0')))))
| ~ iLEQ(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_26_17) ).
cnf(clause_16_15,axiom,
( 'E'(s(s('0')),f(X2))
| 'LE'(f(X2),s(s('0')))
| ~ 'LE'(f(X1),s(s(s('0'))))
| ~ iLEQ(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16_15) ).
cnf(clause_13_02,axiom,
iLEQ(X1,g(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_13_02) ).
cnf(clause_17_32,axiom,
( 'E'(s('0'),f(X2))
| 'LE'(f(X2),s('0'))
| ~ 'LE'(f(X1),s(s('0')))
| ~ iLEQ(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_17_32) ).
cnf(clause_1_06,axiom,
( 'E'('0',f(X2))
| 'LE'(f(X2),'0')
| ~ 'LE'(f(X1),s('0'))
| ~ iLEQ(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_06) ).
cnf(clause_6_07,axiom,
~ 'LE'(f(X1),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_07) ).
cnf(clause_29_24,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(g(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29_24) ).
cnf(clause_31_05,axiom,
~ 'E'(f(X1),f(g(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_31_05) ).
cnf(clause_27_12,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(g(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_27_12) ).
cnf(clause_3_10,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X1))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3_10) ).
cnf(clause_21_11,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(g(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21_11) ).
cnf(clause_30_13,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(g(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_30_13) ).
cnf(clause_12_30,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s(s(s(s('0')))),f(g(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_30) ).
cnf(c_0_16,axiom,
( 'E'(s(s(s(s('0')))),f(X2))
| 'LE'(f(X2),s(s(s(s('0')))))
| ~ 'LE'(f(X1),s(s(s(s(s('0'))))))
| ~ iLEQ(X1,X2) ),
clause_7_16 ).
cnf(c_0_17,axiom,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s('0')))))) ),
clause_8_01 ).
cnf(c_0_18,plain,
( 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(X1))
| ~ iLEQ(X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
iLEQ(X1,X1),
clause_18_04 ).
cnf(c_0_20,axiom,
( 'E'(s(s(s('0'))),f(X2))
| 'LE'(f(X2),s(s(s('0'))))
| ~ 'LE'(f(X1),s(s(s(s('0')))))
| ~ iLEQ(X1,X2) ),
clause_26_17 ).
cnf(c_0_21,plain,
( 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(X2))
| 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
( 'E'(s(s('0')),f(X2))
| 'LE'(f(X2),s(s('0')))
| ~ 'LE'(f(X1),s(s(s('0'))))
| ~ iLEQ(X1,X2) ),
clause_16_15 ).
cnf(c_0_24,plain,
( 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_25,axiom,
iLEQ(X1,g(X1)),
clause_13_02 ).
cnf(c_0_26,plain,
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(X2))
| 'E'(s(s(s('0'))),f(X2))
| 'E'(s(s('0')),f(X1))
| ~ iLEQ(X2,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( 'LE'(f(g(X1)),s(s(s('0'))))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_28,axiom,
( 'E'(s('0'),f(X2))
| 'LE'(f(X2),s('0'))
| ~ 'LE'(f(X1),s(s('0')))
| ~ iLEQ(X1,X2) ),
clause_17_32 ).
cnf(c_0_29,plain,
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_30,plain,
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(X2))
| 'E'(s(s(s('0'))),f(g(X2)))
| 'E'(s(s('0')),f(X1))
| ~ iLEQ(g(X2),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_31,plain,
( 'LE'(f(g(X1)),s(s('0')))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s(s(s('0'))),f(X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_32,axiom,
( 'E'('0',f(X2))
| 'LE'(f(X2),'0')
| ~ 'LE'(f(X1),s('0'))
| ~ iLEQ(X1,X2) ),
clause_1_06 ).
cnf(c_0_33,axiom,
~ 'LE'(f(X1),'0'),
clause_6_07 ).
cnf(c_0_34,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(X2))
| 'E'(s(s(s('0'))),f(X2))
| 'E'(s(s('0')),f(X2))
| 'E'(s('0'),f(X1))
| ~ iLEQ(X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( 'LE'(f(g(X1)),s(s('0')))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_36,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(X2))
| 'E'(s(s(s('0'))),f(X2))
| 'E'(s(s('0')),f(g(X2)))
| 'E'(s('0'),f(X1))
| ~ iLEQ(g(X2),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_37,plain,
( 'E'('0',f(X1))
| ~ iLEQ(X2,X1)
| ~ 'LE'(f(X2),s('0')) ),
inference(sr,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( 'LE'(f(g(X1)),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s('0'),f(g(X1)))
| 'E'(s(s('0')),f(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_39,plain,
( 'LE'(f(g(X1)),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_40,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(X2))
| 'E'(s(s(s('0'))),f(g(X2)))
| 'E'(s(s('0')),f(g(X2)))
| 'E'(s('0'),f(X1))
| ~ iLEQ(g(X2),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_41,plain,
( 'LE'(f(g(X1)),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_36,c_0_19]) ).
cnf(c_0_42,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(g(X1))) ),
clause_29_24 ).
cnf(c_0_43,axiom,
~ 'E'(f(X1),f(g(X1))),
clause_31_05 ).
cnf(c_0_44,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(X1))
| 'E'(s('0'),f(g(X1)))
| 'E'('0',f(X2))
| ~ iLEQ(g(X1),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(g(X2)))
| 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(g(X2),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_39]) ).
cnf(c_0_46,plain,
( 'LE'(f(g(X1)),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_47,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(g(X1))) ),
clause_27_12 ).
cnf(c_0_48,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1)))
| 'E'('0',f(X2))
| ~ iLEQ(g(X1),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_49,plain,
( ~ 'E'('0',f(g(X1)))
| ~ 'E'('0',f(X1)) ),
inference(sr,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'('0',f(g(g(X1))))
| 'E'(s('0'),f(g(X1)))
| 'E'(s(s('0')),f(X1)) ),
inference(spm,[status(thm)],[c_0_44,c_0_25]) ).
cnf(c_0_51,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s('0'),f(g(X1)))
| 'E'(s(s('0')),f(X1))
| 'E'('0',f(g(X1))) ),
inference(spm,[status(thm)],[c_0_44,c_0_19]) ).
cnf(c_0_52,plain,
( 'LE'(f(g(X1)),s(s(s('0'))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_45,c_0_19]) ).
cnf(c_0_53,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1)))
| 'E'('0',f(X2))
| ~ iLEQ(g(X1),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_54,plain,
( ~ 'E'(s(s('0')),f(g(X1)))
| ~ 'E'(s(s('0')),f(X1)) ),
inference(sr,[status(thm)],[c_0_47,c_0_43]) ).
cnf(c_0_55,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s('0'),f(g(X1)))
| 'E'('0',f(g(X1))) ),
inference(spm,[status(thm)],[c_0_48,c_0_19]) ).
cnf(c_0_56,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(X1))
| 'E'(s('0'),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_57,plain,
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(g(X2)))
| 'E'(s(s(s('0'))),f(g(X2)))
| 'E'(s(s('0')),f(X1))
| ~ iLEQ(g(X2),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_52]) ).
cnf(c_0_58,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X1))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(X1))) ),
clause_3_10 ).
cnf(c_0_59,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'('0',f(g(g(X1))))
| 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_53,c_0_25]) ).
cnf(c_0_60,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s(s(s('0'))),f(X1))
| 'E'('0',f(g(g(X1))))
| 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_61,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s('0'),f(g(X1)))
| 'E'('0',f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_62,plain,
( 'LE'(f(g(X1)),s(s('0')))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_57,c_0_19]) ).
cnf(c_0_63,plain,
( ~ 'E'(s(s(s(s(s('0'))))),f(g(X1)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X1)) ),
inference(sr,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_64,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(X1))
| 'E'(s('0'),f(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_65,plain,
( 'LE'(f(g(g(X1))),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_40,c_0_25]) ).
cnf(c_0_66,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(g(X1))) ),
clause_21_11 ).
cnf(c_0_67,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1)))
| ~ 'E'('0',f(g(X1))) ),
inference(spm,[status(thm)],[c_0_49,c_0_59]) ).
cnf(c_0_68,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_60]),c_0_61]) ).
cnf(c_0_69,plain,
( 'LE'(f(g(g(X1))),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s(s(s('0'))),f(X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_70,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(g(X2)))
| 'E'(s(s(s('0'))),f(g(X2)))
| 'E'(s(s('0')),f(g(X2)))
| 'E'(s('0'),f(X1))
| ~ iLEQ(g(X2),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_71,plain,
( 'LE'(f(g(X1)),s('0'))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(g(X1))) ),
clause_30_13 ).
cnf(c_0_73,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(X1)),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_65]) ).
cnf(c_0_74,plain,
( ~ 'E'(s(s(s('0'))),f(g(X1)))
| ~ 'E'(s(s(s('0'))),f(X1)) ),
inference(sr,[status(thm)],[c_0_66,c_0_43]) ).
cnf(c_0_75,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_19]),c_0_67]) ).
cnf(c_0_76,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s('0'),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_68]),c_0_56]) ).
cnf(c_0_77,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(X1)),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_69]) ).
cnf(c_0_78,plain,
( 'LE'(f(g(X1)),s('0'))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_19]),c_0_71]) ).
cnf(c_0_79,plain,
( 'LE'(f(g(g(X1))),s(s('0')))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_80,plain,
( ~ 'E'(s('0'),f(g(X1)))
| ~ 'E'(s('0'),f(X1)) ),
inference(sr,[status(thm)],[c_0_72,c_0_43]) ).
cnf(c_0_81,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1)))
| 'E'('0',f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_73,c_0_19]) ).
cnf(c_0_82,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_83,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s(s(s('0'))),f(X1))
| 'E'('0',f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_77,c_0_19]) ).
cnf(c_0_84,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1)))
| 'E'('0',f(X2))
| ~ iLEQ(g(X1),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_78]) ).
cnf(c_0_85,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(X2))
| 'E'(s(s(s('0'))),f(g(X2)))
| 'E'(s(s('0')),f(g(g(X2))))
| 'E'(s('0'),f(X1))
| ~ iLEQ(g(g(X2)),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_79]) ).
cnf(c_0_86,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'('0',f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_73,c_0_25]) ).
cnf(c_0_87,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'('0',f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_88,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'('0',f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s(s(s('0'))),f(X1)) ),
inference(spm,[status(thm)],[c_0_77,c_0_25]) ).
cnf(c_0_89,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'('0',f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_83]),c_0_76]) ).
cnf(c_0_90,plain,
( 'LE'(f(g(g(X1))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_25]) ).
cnf(c_0_91,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'('0',f(g(g(X1))))
| 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_84,c_0_25]) ).
cnf(c_0_92,plain,
( 'LE'(f(g(g(X1))),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_85,c_0_19]) ).
cnf(c_0_93,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_86]),c_0_87]) ).
cnf(c_0_94,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_88]),c_0_89]) ).
cnf(c_0_95,plain,
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(g(X2)))
| 'E'(s(s(s('0'))),f(g(g(X2))))
| 'E'(s(s('0')),f(X1))
| ~ iLEQ(g(g(X2)),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_90]) ).
cnf(c_0_96,axiom,
( 'E'(f(X1),f(g(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s(s(s(s('0')))),f(g(X1))) ),
clause_12_30 ).
cnf(c_0_97,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1)))
| ~ 'E'('0',f(g(X1))) ),
inference(spm,[status(thm)],[c_0_49,c_0_91]) ).
cnf(c_0_98,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(X1)),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_92]) ).
cnf(c_0_99,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_93]),c_0_82]) ).
cnf(c_0_100,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s(s(s('0'))),f(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_94]),c_0_76]) ).
cnf(c_0_101,plain,
( 'LE'(f(g(g(X1))),s(s('0')))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_95,c_0_19]) ).
cnf(c_0_102,plain,
( ~ 'E'(s(s(s(s('0')))),f(g(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X1)) ),
inference(sr,[status(thm)],[c_0_96,c_0_43]) ).
cnf(c_0_103,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_19]),c_0_97]) ).
cnf(c_0_104,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_98,c_0_19]) ).
cnf(c_0_105,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_99]),c_0_100]) ).
cnf(c_0_106,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(g(X2)))
| 'E'(s(s(s('0'))),f(g(g(X2))))
| 'E'(s(s('0')),f(g(g(X2))))
| 'E'(s('0'),f(X1))
| ~ iLEQ(g(g(X2)),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_101]) ).
cnf(c_0_107,plain,
( 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(X1)))
| ~ 'E'(s(s(s(s('0')))),f(X1)) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,plain,
( 'LE'(f(g(g(g(X1)))),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(spm,[status(thm)],[c_0_85,c_0_25]) ).
cnf(c_0_109,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'('0',f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_98,c_0_25]) ).
cnf(c_0_110,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_104]),c_0_105]) ).
cnf(c_0_111,plain,
( 'LE'(f(g(g(X1))),s('0'))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_19]),c_0_107]) ).
cnf(c_0_112,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(g(X1))),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_108]) ).
cnf(c_0_113,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_109]),c_0_110]) ).
cnf(c_0_114,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(X1)),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_111]) ).
cnf(c_0_115,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'('0',f(g(g(g(X1))))) ),
inference(spm,[status(thm)],[c_0_112,c_0_19]) ).
cnf(c_0_116,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_113]),c_0_105]) ).
cnf(c_0_117,plain,
( 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'('0',f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_114,c_0_25]) ).
cnf(c_0_118,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'('0',f(g(g(g(g(X1))))))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(spm,[status(thm)],[c_0_112,c_0_25]) ).
cnf(c_0_119,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'('0',f(g(g(g(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_115]),c_0_116]) ).
cnf(c_0_120,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1))))
| ~ 'E'('0',f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_49,c_0_117]) ).
cnf(c_0_121,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(g(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_118]),c_0_119]) ).
cnf(c_0_122,plain,
( 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_19]),c_0_120]) ).
cnf(c_0_123,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_121]),c_0_116]) ).
cnf(c_0_124,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1))))
| ~ 'E'(s(s(s('0'))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_74,c_0_122]) ).
cnf(c_0_125,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_123]),c_0_105]) ).
cnf(c_0_126,plain,
( 'LE'(f(g(g(X1))),s('0'))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_70,c_0_25]) ).
cnf(c_0_127,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_128,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(X1)),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_126]) ).
cnf(c_0_129,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_127]),c_0_105]) ).
cnf(c_0_130,plain,
( 'LE'(f(g(g(X1))),s(s('0')))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_57,c_0_25]) ).
cnf(c_0_131,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1)))
| 'E'('0',f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_128,c_0_19]) ).
cnf(c_0_132,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_80,c_0_129]) ).
cnf(c_0_133,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X1)) ),
inference(spm,[status(thm)],[c_0_74,c_0_125]) ).
cnf(c_0_134,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(g(X2)))
| 'E'(s(s(s('0'))),f(g(X2)))
| 'E'(s(s('0')),f(g(g(X2))))
| 'E'(s('0'),f(X1))
| ~ iLEQ(g(g(X2)),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_130]) ).
cnf(c_0_135,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'('0',f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(X1))))
| 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_128,c_0_25]) ).
cnf(c_0_136,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'('0',f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_131]),c_0_103]) ).
cnf(c_0_137,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_76]),c_0_133]) ).
cnf(c_0_138,plain,
( 'LE'(f(g(g(X1))),s('0'))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_134,c_0_19]) ).
cnf(c_0_139,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1)))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_135]),c_0_136]) ).
cnf(c_0_140,plain,
( 'LE'(f(g(g(g(X1)))),s('0'))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_106,c_0_25]) ).
cnf(c_0_141,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_137]) ).
cnf(c_0_142,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(X1)),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_138]) ).
cnf(c_0_143,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_139]),c_0_103]) ).
cnf(c_0_144,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(g(X1))),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_140]),c_0_141]) ).
cnf(c_0_145,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_142,c_0_19]) ).
cnf(c_0_146,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_143]),c_0_105]) ).
cnf(c_0_147,plain,
( 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'('0',f(g(g(g(X1))))) ),
inference(spm,[status(thm)],[c_0_144,c_0_19]) ).
cnf(c_0_148,plain,
( 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_141]),c_0_122]) ).
cnf(c_0_149,plain,
( 'LE'(f(g(g(g(X1)))),s('0'))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_134,c_0_25]) ).
cnf(c_0_150,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'('0',f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_142,c_0_25]) ).
cnf(c_0_151,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s('0'),f(g(g(X1))))
| 'E'('0',f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_145]),c_0_146]) ).
cnf(c_0_152,plain,
( 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'('0',f(g(g(g(g(X1))))))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_144,c_0_25]) ).
cnf(c_0_153,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'('0',f(g(g(g(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_147]),c_0_148]) ).
cnf(c_0_154,plain,
( 'LE'(f(g(g(g(X1)))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_25]) ).
cnf(c_0_155,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(g(X1))),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_149]) ).
cnf(c_0_156,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_150]),c_0_151]) ).
cnf(c_0_157,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(g(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_152]),c_0_153]) ).
cnf(c_0_158,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s(s(s(s(s('0'))))),f(X2))
| 'E'(s(s(s(s('0')))),f(g(X2)))
| 'E'(s(s(s('0'))),f(g(g(X2))))
| 'E'(s(s('0')),f(g(g(g(X2)))))
| 'E'(s('0'),f(X1))
| ~ iLEQ(g(g(g(X2))),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_154]) ).
cnf(c_0_159,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'('0',f(g(g(g(g(X1))))))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_25]),c_0_141]) ).
cnf(c_0_160,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'('0',f(g(g(g(X1))))) ),
inference(spm,[status(thm)],[c_0_155,c_0_19]) ).
cnf(c_0_161,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_156]),c_0_146]) ).
cnf(c_0_162,plain,
( 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_157]),c_0_148]) ).
cnf(c_0_163,plain,
( 'LE'(f(g(g(g(g(X1))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(X1))))))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1)) ),
inference(spm,[status(thm)],[c_0_158,c_0_25]) ).
cnf(c_0_164,plain,
( 'LE'(f(g(g(g(X1)))),s('0'))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s('0'),f(g(g(g(X1))))) ),
inference(spm,[status(thm)],[c_0_158,c_0_19]) ).
cnf(c_0_165,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(g(X1)))))
| ~ 'E'('0',f(g(g(g(X1))))) ),
inference(spm,[status(thm)],[c_0_49,c_0_159]) ).
cnf(c_0_166,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'('0',f(g(g(g(X1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_160]),c_0_161]) ).
cnf(c_0_167,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| ~ 'E'(s(s(s('0'))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_74,c_0_162]) ).
cnf(c_0_168,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(g(g(X1))))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(g(g(X1)))),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_163]),c_0_141]) ).
cnf(c_0_169,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'('0',f(X2))
| ~ iLEQ(g(g(g(X1))),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_164]) ).
cnf(c_0_170,plain,
( 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1))))
| ~ 'E'(s(s(s('0'))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_74,c_0_148]) ).
cnf(c_0_171,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s('0'),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167]),c_0_141]) ).
cnf(c_0_172,plain,
( 'E'(s('0'),f(g(g(g(g(X1))))))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'('0',f(g(g(g(g(X1)))))) ),
inference(spm,[status(thm)],[c_0_168,c_0_19]) ).
cnf(c_0_173,plain,
( 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'('0',f(g(g(g(g(X1))))))
| 'E'(s('0'),f(g(g(g(X1))))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_25]),c_0_170]),c_0_141]) ).
cnf(c_0_174,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1))))
| ~ 'E'(s('0'),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_80,c_0_171]) ).
cnf(c_0_175,plain,
( 'E'('0',f(g(g(g(g(g(X1)))))))
| 'E'(s('0'),f(g(g(g(g(X1))))))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_168,c_0_25]) ).
cnf(c_0_176,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'('0',f(g(g(g(g(X1)))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_172]),c_0_173]) ).
cnf(c_0_177,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s('0')),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_161]),c_0_167]),c_0_141]) ).
cnf(c_0_178,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s('0'),f(g(g(g(g(X1)))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_175]),c_0_176]) ).
cnf(c_0_179,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| ~ 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_54,c_0_177]) ).
cnf(c_0_180,plain,
( 'E'(s(s(s(s(s('0'))))),f(X1))
| 'E'(s(s('0')),f(g(X1)))
| ~ 'E'(s(s(s('0'))),f(X1)) ),
inference(spm,[status(thm)],[c_0_74,c_0_146]) ).
cnf(c_0_181,plain,
( 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| ~ 'E'('0',f(g(g(g(X1))))) ),
inference(spm,[status(thm)],[c_0_49,c_0_176]) ).
cnf(c_0_182,plain,
( 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1)))
| ~ 'E'(s('0'),f(g(g(g(X1))))) ),
inference(spm,[status(thm)],[c_0_80,c_0_178]) ).
cnf(c_0_183,plain,
( ~ 'E'(s(s(s(s('0')))),f(X1))
| ~ 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_102,c_0_179]) ).
cnf(c_0_184,plain,
( 'E'(s(s(s(s(s('0'))))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_180,c_0_148]) ).
cnf(c_0_185,plain,
( 'E'(s(s('0')),f(g(g(g(X1)))))
| 'E'(s(s(s('0'))),f(g(g(X1))))
| 'E'(s(s(s(s('0')))),f(g(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_19]),c_0_181]),c_0_182]),c_0_141]) ).
cnf(c_0_186,plain,
( ~ 'E'(s(s(s(s(s('0'))))),f(X1))
| ~ 'E'(s(s(s(s('0')))),f(X1)) ),
inference(spm,[status(thm)],[c_0_102,c_0_141]) ).
cnf(c_0_187,plain,
( 'E'(s(s(s(s(s('0'))))),f(g(g(X1))))
| 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_137]) ).
cnf(c_0_188,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| 'E'(s(s(s('0'))),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_185]),c_0_177]) ).
cnf(c_0_189,plain,
( 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1))))
| ~ 'E'(s(s(s(s('0')))),f(g(g(X1)))) ),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_190,plain,
( 'E'(s(s(s(s('0')))),f(g(X1)))
| ~ 'E'(s(s(s('0'))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_74,c_0_188]) ).
cnf(c_0_191,plain,
( 'E'(s(s('0')),f(g(g(X1))))
| 'E'(s('0'),f(g(g(X1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_148]) ).
cnf(c_0_192,plain,
( 'E'(s('0'),f(g(g(X1))))
| ~ 'E'(s(s(s(s('0')))),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_183,c_0_191]) ).
cnf(c_0_193,plain,
( ~ 'E'(s(s(s(s('0')))),f(g(X1)))
| ~ 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_80,c_0_192]) ).
cnf(c_0_194,plain,
( 'E'(s('0'),f(g(g(X1))))
| ~ 'E'(s(s('0')),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_54,c_0_191]) ).
cnf(c_0_195,plain,
( ~ 'E'(s(s(s('0'))),f(g(X1)))
| ~ 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_193,c_0_190]) ).
cnf(c_0_196,plain,
( ~ 'E'(s(s('0')),f(g(X1)))
| ~ 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_80,c_0_194]) ).
cnf(c_0_197,plain,
( ~ 'E'(s(s(s(s(s('0'))))),f(X1))
| ~ 'E'(s('0'),f(g(X1))) ),
inference(spm,[status(thm)],[c_0_193,c_0_141]) ).
cnf(c_0_198,plain,
~ 'E'(s('0'),f(g(X1))),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_146]),c_0_196]),c_0_197]) ).
cnf(c_0_199,plain,
~ 'E'(s(s(s(s('0')))),f(g(X1))),
inference(spm,[status(thm)],[c_0_198,c_0_192]) ).
cnf(c_0_200,plain,
~ 'E'(s(s('0')),f(g(X1))),
inference(spm,[status(thm)],[c_0_198,c_0_194]) ).
cnf(c_0_201,plain,
'E'(s(s(s('0'))),f(g(X1))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_103,c_0_198]),c_0_199]),c_0_200]) ).
cnf(c_0_202,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_201])]),c_0_199]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO630-1 : TPTP v9.2.1. Released v7.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 09:18:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------