TSTP Solution File: SYO630-1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SYO630-1 : TPTP v8.1.2. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 20:49:52 EDT 2023

% Result   : Unsatisfiable 0.20s 0.53s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   54
%            Number of leaves      :   16
% Syntax   : Number of clauses     :  191 (  11 unt; 153 nHn;  97 RR)
%            Number of literals    :  826 (   0 equ; 133 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   :  232 (   4 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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_8_01) ).

cnf(clause_18_04,axiom,
    iLEQ(X1,X1),
    file('/export/starexec/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_16_15) ).

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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_1_06) ).

cnf(clause_6_07,axiom,
    ~ 'LE'(f(X1),'0'),
    file('/export/starexec/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_6_07) ).

cnf(clause_13_02,axiom,
    iLEQ(X1,g(X1)),
    file('/export/starexec/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_13_02) ).

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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_3_10) ).

cnf(clause_31_05,axiom,
    ~ 'E'(f(X1),f(g(X1))),
    file('/export/starexec/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_31_05) ).

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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_30_13) ).

cnf(clause_29_24,axiom,
    ( 'E'(f(X1),f(g(X1)))
    | ~ 'E'('0',f(X1))
    | ~ 'E'('0',f(g(X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_29_24) ).

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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_12_30) ).

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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_27_12) ).

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/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p',clause_21_11) ).

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,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_26,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_27,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_25,c_0_19]) ).

cnf(c_0_28,axiom,
    ( 'E'('0',f(X2))
    | 'LE'(f(X2),'0')
    | ~ 'LE'(f(X1),s('0'))
    | ~ iLEQ(X1,X2) ),
    clause_1_06 ).

cnf(c_0_29,axiom,
    ~ 'LE'(f(X1),'0'),
    clause_6_07 ).

cnf(c_0_30,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_26,c_0_27]) ).

cnf(c_0_31,axiom,
    iLEQ(X1,g(X1)),
    clause_13_02 ).

cnf(c_0_32,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_33,axiom,
    ~ 'E'(f(X1),f(g(X1))),
    clause_31_05 ).

cnf(c_0_34,plain,
    ( 'E'('0',f(X1))
    | ~ iLEQ(X2,X1)
    | ~ 'LE'(f(X2),s('0')) ),
    inference(sr,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,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_30,c_0_31]) ).

cnf(c_0_36,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_32,c_0_33]) ).

cnf(c_0_37,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_30,c_0_19]) ).

cnf(c_0_38,axiom,
    ( 'E'(f(X1),f(g(X1)))
    | ~ 'E'(s('0'),f(X1))
    | ~ 'E'(s('0'),f(g(X1))) ),
    clause_30_13 ).

cnf(c_0_39,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_34,c_0_35]) ).

cnf(c_0_40,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_36,c_0_37]) ).

cnf(c_0_41,axiom,
    ( 'E'(f(X1),f(g(X1)))
    | ~ 'E'('0',f(X1))
    | ~ 'E'('0',f(g(X1))) ),
    clause_29_24 ).

cnf(c_0_42,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_31]) ).

cnf(c_0_43,plain,
    ( ~ 'E'(s('0'),f(g(X1)))
    | ~ 'E'(s('0'),f(X1)) ),
    inference(sr,[status(thm)],[c_0_38,c_0_33]) ).

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('0'),f(g(X1)))
    | 'E'(s(s('0')),f(X1))
    | 'E'('0',f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_39,c_0_19]) ).

cnf(c_0_45,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)
    | ~ 'E'(s(s(s(s(s('0'))))),f(X1)) ),
    inference(spm,[status(thm)],[c_0_34,c_0_40]) ).

cnf(c_0_46,plain,
    ( ~ 'E'('0',f(g(X1)))
    | ~ 'E'('0',f(X1)) ),
    inference(sr,[status(thm)],[c_0_41,c_0_33]) ).

cnf(c_0_47,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_39,c_0_31]) ).

cnf(c_0_48,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_42]) ).

cnf(c_0_49,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'('0',f(g(X1)))
    | ~ 'E'(s('0'),f(X1)) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_50,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)))
    | ~ 'E'(s(s(s(s(s('0'))))),f(X1)) ),
    inference(spm,[status(thm)],[c_0_45,c_0_31]) ).

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(s('0')),f(X1))
    | 'E'(s('0'),f(g(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_44]) ).

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_48,c_0_19]) ).

cnf(c_0_53,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(s(s(s(s('0'))))),f(X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_49]),c_0_50]) ).

cnf(c_0_54,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(X1)) ),
    inference(spm,[status(thm)],[c_0_43,c_0_51]) ).

cnf(c_0_55,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_56,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(s(s(s(s('0'))))),f(X1))
    | ~ 'E'('0',f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_46,c_0_53]) ).

cnf(c_0_57,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(s(s(s(s('0'))))),f(X1))
    | ~ 'E'(s('0'),f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_36,c_0_54]) ).

cnf(c_0_58,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_55,c_0_19]) ).

cnf(c_0_59,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(s(s(s(s('0'))))),f(X1)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_19]),c_0_56]),c_0_57]) ).

cnf(c_0_60,plain,
    ( 'LE'(f(X1),s('0'))
    | '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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_58]),c_0_59]) ).

cnf(c_0_61,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(spm,[status(thm)],[c_0_60,c_0_19]) ).

cnf(c_0_62,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_34,c_0_61]) ).

cnf(c_0_63,plain,
    ( 'LE'(f(g(g(X1))),s('0'))
    | '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'(s(s('0')),f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_60,c_0_31]) ).

cnf(c_0_64,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_62,c_0_31]) ).

cnf(c_0_65,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(g(X1))))
    | 'E'('0',f(X2))
    | ~ iLEQ(g(g(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_63]) ).

cnf(c_0_66,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_46,c_0_64]) ).

cnf(c_0_67,plain,
    ( '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'(s(s('0')),f(g(X1)))
    | 'E'('0',f(g(g(X1)))) ),
    inference(spm,[status(thm)],[c_0_65,c_0_19]) ).

cnf(c_0_68,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_62,c_0_19]),c_0_66]) ).

cnf(c_0_69,plain,
    ( 'E'(s(s(s(s('0')))),f(g(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_65,c_0_31]) ).

cnf(c_0_70,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)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_67]),c_0_68]) ).

cnf(c_0_71,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_48,c_0_31]) ).

cnf(c_0_72,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_73,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(g(X1)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_69]),c_0_70]) ).

cnf(c_0_74,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_31]) ).

cnf(c_0_75,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_71]) ).

cnf(c_0_76,plain,
    ( ~ 'E'(s(s(s(s('0')))),f(g(X1)))
    | ~ 'E'(s(s(s(s('0')))),f(X1)) ),
    inference(sr,[status(thm)],[c_0_72,c_0_33]) ).

cnf(c_0_77,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))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_73]),c_0_68]) ).

cnf(c_0_78,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_74]) ).

cnf(c_0_79,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_75,c_0_19]) ).

cnf(c_0_80,plain,
    ( 'E'(s(s(s('0'))),f(g(X1)))
    | 'E'(s(s('0')),f(g(X1)))
    | ~ 'E'(s(s(s(s('0')))),f(X1)) ),
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_81,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_78,c_0_19]) ).

cnf(c_0_82,plain,
    ( 'LE'(f(X1),s('0'))
    | 'E'(s(s(s(s(s('0'))))),f(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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_79]),c_0_80]) ).

cnf(c_0_83,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_26,c_0_81]) ).

cnf(c_0_84,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(spm,[status(thm)],[c_0_82,c_0_19]) ).

cnf(c_0_85,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_25,c_0_31]) ).

cnf(c_0_86,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_83,c_0_19]) ).

cnf(c_0_87,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_34,c_0_84]) ).

cnf(c_0_88,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_26,c_0_85]) ).

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(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_34,c_0_86]) ).

cnf(c_0_90,plain,
    ( 'LE'(f(g(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('0'),f(g(g(g(X1)))))
    | 'E'(s(s('0')),f(g(g(X1)))) ),
    inference(spm,[status(thm)],[c_0_82,c_0_31]) ).

cnf(c_0_91,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_87,c_0_31]) ).

cnf(c_0_92,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_88,c_0_19]) ).

cnf(c_0_93,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('0'),f(g(g(X1))))
    | 'E'(s(s('0')),f(g(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_31]),c_0_80]) ).

cnf(c_0_94,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)))
    | 'E'('0',f(g(g(X1))))
    | 'E'(s('0'),f(g(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_31]),c_0_80]) ).

cnf(c_0_95,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(g(X1)))))
    | 'E'('0',f(X2))
    | ~ iLEQ(g(g(g(X1))),X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_90]) ).

cnf(c_0_96,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_46,c_0_91]) ).

cnf(c_0_97,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_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(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_34,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('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_34,c_0_93]) ).

cnf(c_0_100,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)))
    | 'E'(s('0'),f(g(X1)))
    | ~ 'E'('0',f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_46,c_0_94]) ).

cnf(c_0_101,plain,
    ( 'E'(s(s(s('0'))),f(g(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'('0',f(g(g(g(X1))))) ),
    inference(spm,[status(thm)],[c_0_95,c_0_19]) ).

cnf(c_0_102,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_87,c_0_19]),c_0_96]) ).

cnf(c_0_103,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_104,plain,
    ( ~ 'E'(s(s('0')),f(g(X1)))
    | ~ 'E'(s(s('0')),f(X1)) ),
    inference(sr,[status(thm)],[c_0_97,c_0_33]) ).

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)))
    | 'E'(s(s(s('0'))),f(X1))
    | 'E'(s('0'),f(g(X1)))
    | 'E'('0',f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_98,c_0_19]) ).

cnf(c_0_106,plain,
    ( '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_99,c_0_19]) ).

cnf(c_0_107,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)))
    | 'E'(s('0'),f(g(X1))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_19]),c_0_100]),c_0_80]) ).

cnf(c_0_108,plain,
    ( 'E'(s(s(s('0'))),f(g(g(X1))))
    | '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)))) ),
    inference(spm,[status(thm)],[c_0_95,c_0_31]) ).

cnf(c_0_109,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'('0',f(g(g(g(X1))))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_101]),c_0_102]) ).

cnf(c_0_110,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_55,c_0_31]) ).

cnf(c_0_111,plain,
    ( ~ 'E'(s(s(s('0'))),f(g(X1)))
    | ~ 'E'(s(s(s('0'))),f(X1)) ),
    inference(sr,[status(thm)],[c_0_103,c_0_33]) ).

cnf(c_0_112,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_88,c_0_31]) ).

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('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_98,c_0_31]) ).

cnf(c_0_114,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_104,c_0_105]),c_0_51]) ).

cnf(c_0_115,plain,
    ( '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_99,c_0_31]) ).

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('0')),f(g(X1)))
    | 'E'('0',f(g(g(X1)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_106]),c_0_107]) ).

cnf(c_0_117,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_78,c_0_31]) ).

cnf(c_0_118,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(g(X1))))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_108]),c_0_109]) ).

cnf(c_0_119,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_26,c_0_110]) ).

cnf(c_0_120,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_111,c_0_102]) ).

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(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_34,c_0_112]) ).

cnf(c_0_122,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_46,c_0_113]),c_0_114]) ).

cnf(c_0_123,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)))
    | 'E'(s('0'),f(g(g(X1)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_115]),c_0_116]) ).

cnf(c_0_124,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_26,c_0_117]) ).

cnf(c_0_125,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)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_118]),c_0_102]) ).

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('0')),f(g(g(X1))))
    | 'E'(s('0'),f(g(g(X1)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_19]),c_0_120]) ).

cnf(c_0_127,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_121,c_0_19]) ).

cnf(c_0_128,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_104,c_0_122]),c_0_51]) ).

cnf(c_0_129,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_43,c_0_123]),c_0_107]) ).

cnf(c_0_130,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(s('0')))),f(X1))
    | 'E'(s('0'),f(g(g(X1)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_19]),c_0_120]) ).

cnf(c_0_131,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_119,c_0_31]) ).

cnf(c_0_132,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))) ),
    inference(spm,[status(thm)],[c_0_111,c_0_125]) ).

cnf(c_0_133,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(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_34,c_0_126]) ).

cnf(c_0_134,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_121,c_0_31]) ).

cnf(c_0_135,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_43,c_0_127]),c_0_128]) ).

cnf(c_0_136,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_111,c_0_129]) ).

cnf(c_0_137,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))))
    | 'E'('0',f(X2))
    | ~ iLEQ(g(g(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_130]) ).

cnf(c_0_138,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_131]),c_0_132]) ).

cnf(c_0_139,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'('0',f(g(g(g(X1)))))
    | 'E'(s('0'),f(g(g(X1)))) ),
    inference(spm,[status(thm)],[c_0_133,c_0_31]) ).

cnf(c_0_140,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('0'),f(g(g(X1))))
    | 'E'('0',f(g(g(X1)))) ),
    inference(spm,[status(thm)],[c_0_133,c_0_19]) ).

cnf(c_0_141,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(g(X1)))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_134]),c_0_135]),c_0_136]) ).

cnf(c_0_142,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(s('0')),f(g(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_137,c_0_19]) ).

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('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_138,c_0_19]) ).

cnf(c_0_144,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | '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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_139]),c_0_140]) ).

cnf(c_0_145,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(spm,[status(thm)],[c_0_43,c_0_141]) ).

cnf(c_0_146,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_124,c_0_31]) ).

cnf(c_0_147,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(s('0')),f(g(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_137,c_0_31]) ).

cnf(c_0_148,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'('0',f(g(g(X1)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_142]),c_0_141]) ).

cnf(c_0_149,plain,
    ( 'E'(s(s(s(s('0')))),f(g(X1)))
    | '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)))) ),
    inference(spm,[status(thm)],[c_0_138,c_0_31]) ).

cnf(c_0_150,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(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_43,c_0_143]),c_0_144]) ).

cnf(c_0_151,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(s(s(s('0')))),f(X1))
    | ~ 'E'(s(s('0')),f(X1))
    | ~ 'E'(s('0'),f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_104,c_0_145]) ).

cnf(c_0_152,plain,
    ( 'E'(s(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_104,c_0_136]) ).

cnf(c_0_153,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_34,c_0_146]) ).

cnf(c_0_154,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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_147]),c_0_148]) ).

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('0')),f(g(g(X1))))
    | 'E'(s('0'),f(g(g(g(X1))))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_149]),c_0_150]) ).

cnf(c_0_156,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(s(s(s('0')))),f(X1))
    | ~ 'E'(s(s('0')),f(X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_128]),c_0_152]) ).

cnf(c_0_157,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(s('0')))),f(X1))
    | 'E'('0',f(g(g(g(X1))))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_19]),c_0_132]) ).

cnf(c_0_158,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_104,c_0_154]),c_0_141]) ).

cnf(c_0_159,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_75,c_0_31]) ).

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(s('0')),f(g(g(X1)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_155]),c_0_144]) ).

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('0')),f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_36,c_0_156]) ).

cnf(c_0_162,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(s('0')))),f(X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_31]),c_0_132]) ).

cnf(c_0_163,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'('0',f(g(g(g(X1))))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_157]),c_0_158]) ).

cnf(c_0_164,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_26,c_0_159]) ).

cnf(c_0_165,plain,
    ( 'E'(s(s(s(s('0')))),f(g(X1)))
    | ~ 'E'(s(s('0')),f(g(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_160]),c_0_161]) ).

cnf(c_0_166,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(g(X1))))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_162]),c_0_163]) ).

cnf(c_0_167,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_164,c_0_31]) ).

cnf(c_0_168,plain,
    ( ~ 'E'(s(s(s(s('0')))),f(X1))
    | ~ 'E'(s(s('0')),f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_76,c_0_165]) ).

cnf(c_0_169,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(s('0')),f(g(g(X1))))
    | 'E'(s(s(s(s('0')))),f(X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_166]),c_0_158]) ).

cnf(c_0_170,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(g(X1))))))
    | 'E'('0',f(X2))
    | ~ iLEQ(g(g(g(g(X1)))),X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_167]) ).

cnf(c_0_171,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | ~ 'E'(s(s(s(s('0')))),f(g(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_76]) ).

cnf(c_0_172,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_164,c_0_19]) ).

cnf(c_0_173,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(s('0'))))),f(X1))
    | 'E'('0',f(g(g(g(g(X1)))))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_19]),c_0_171]) ).

cnf(c_0_174,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_34,c_0_172]) ).

cnf(c_0_175,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(g(X1)))))
    | 'E'('0',f(g(g(g(g(X1))))))
    | ~ 'E'(s('0'),f(g(g(g(X1))))) ),
    inference(spm,[status(thm)],[c_0_43,c_0_173]) ).

cnf(c_0_176,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)))
    | 'E'(s(s(s(s(s('0'))))),f(X1)) ),
    inference(spm,[status(thm)],[c_0_170,c_0_31]) ).

cnf(c_0_177,plain,
    ( 'E'(s(s('0')),f(g(g(g(X1)))))
    | 'E'(s(s(s('0'))),f(g(g(X1))))
    | 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'('0',f(g(g(g(g(X1)))))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_31]),c_0_175]),c_0_171]) ).

cnf(c_0_178,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(g(X1)))))
    | 'E'(s('0'),f(g(g(g(g(X1)))))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_176]),c_0_177]),c_0_171]) ).

cnf(c_0_179,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(g(X1)))))
    | ~ 'E'('0',f(g(g(g(X1))))) ),
    inference(spm,[status(thm)],[c_0_46,c_0_177]) ).

cnf(c_0_180,plain,
    ( 'E'(s(s('0')),f(g(g(g(X1)))))
    | 'E'(s(s(s('0'))),f(g(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_43,c_0_178]) ).

cnf(c_0_181,plain,
    ( 'E'(s(s(s('0'))),f(g(g(X1))))
    | 'E'(s(s(s(s(s('0'))))),f(X1))
    | ~ 'E'('0',f(g(g(g(X1))))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_179]),c_0_125]) ).

cnf(c_0_182,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(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_104,c_0_180]),c_0_125]) ).

cnf(c_0_183,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | ~ 'E'(s(s('0')),f(g(X1))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_169]),c_0_168]) ).

cnf(c_0_184,plain,
    ( 'E'(s(s('0')),f(g(g(g(X1)))))
    | 'E'(s(s(s('0'))),f(g(g(X1))))
    | 'E'(s(s(s(s(s('0'))))),f(X1)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_19]),c_0_181]),c_0_182]),c_0_171]) ).

cnf(c_0_185,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | ~ 'E'(s(s(s('0'))),f(X1)) ),
    inference(spm,[status(thm)],[c_0_183,c_0_136]) ).

cnf(c_0_186,plain,
    ( 'E'(s(s(s(s(s('0'))))),f(X1))
    | 'E'(s(s(s('0'))),f(g(g(X1)))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_184]),c_0_125]) ).

cnf(c_0_187,plain,
    ( ~ 'E'(s(s(s(s(s('0'))))),f(X1))
    | ~ 'E'(s(s(s('0'))),f(g(X1))) ),
    inference(spm,[status(thm)],[c_0_36,c_0_185]) ).

cnf(c_0_188,plain,
    ~ 'E'(s(s(s('0'))),f(g(X1))),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_186]),c_0_187]) ).

cnf(c_0_189,plain,
    'E'(s(s(s(s(s('0'))))),f(X1)),
    inference(sr,[status(thm)],[c_0_186,c_0_188]) ).

cnf(c_0_190,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_189]),c_0_189])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SYO630-1 : TPTP v8.1.2. Released v7.1.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 2400
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Oct  2 15:54:52 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  Running first-order model finding
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.kqw07Uej5o/E---3.1_22862.p
% 0.20/0.53  # Version: 3.1pre001
% 0.20/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53  # Starting sh5l with 300s (1) cores
% 0.20/0.53  # new_bool_3 with pid 23016 completed with status 8
% 0.20/0.53  # new_bool_1 with pid 23017 completed with status 8
% 0.20/0.53  # sh5l with pid 23018 completed with status 8
% 0.20/0.53  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 23014 completed with status 0
% 0.20/0.53  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.20/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.53  # No SInE strategy applied
% 0.20/0.53  # Search class: FGUNM-FFMF11-MFFFFFNN
% 0.20/0.53  # partial match(1): FGUNM-FFMF21-MFFFFFNN
% 0.20/0.53  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.53  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 0.20/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.20/0.53  # Starting new_bool_3 with 136s (1) cores
% 0.20/0.53  # Starting new_bool_1 with 136s (1) cores
% 0.20/0.53  # Starting sh5l with 136s (1) cores
% 0.20/0.53  # SAT001_MinMin_p005000_rr_RG with pid 23023 completed with status 0
% 0.20/0.53  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.20/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.53  # No SInE strategy applied
% 0.20/0.53  # Search class: FGUNM-FFMF11-MFFFFFNN
% 0.20/0.53  # partial match(1): FGUNM-FFMF21-MFFFFFNN
% 0.20/0.53  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.53  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 0.20/0.53  # Preprocessing time       : 0.001 s
% 0.20/0.53  # Presaturation interreduction done
% 0.20/0.53  
% 0.20/0.53  # Proof found!
% 0.20/0.53  # SZS status Unsatisfiable
% 0.20/0.53  # SZS output start CNFRefutation
% See solution above
% 0.20/0.53  # Parsed axioms                        : 32
% 0.20/0.53  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.53  # Initial clauses                      : 32
% 0.20/0.53  # Removed in clause preprocessing      : 0
% 0.20/0.53  # Initial clauses in saturation        : 32
% 0.20/0.53  # Processed clauses                    : 350
% 0.20/0.53  # ...of these trivial                  : 10
% 0.20/0.53  # ...subsumed                          : 59
% 0.20/0.53  # ...remaining for further processing  : 281
% 0.20/0.53  # Other redundant clauses eliminated   : 0
% 0.20/0.53  # Clauses deleted for lack of memory   : 0
% 0.20/0.53  # Backward-subsumed                    : 221
% 0.20/0.53  # Backward-rewritten                   : 20
% 0.20/0.53  # Generated clauses                    : 475
% 0.20/0.53  # ...of the previous two non-redundant : 357
% 0.20/0.53  # ...aggressively subsumed             : 0
% 0.20/0.53  # Contextual simplify-reflections      : 74
% 0.20/0.53  # Paramodulations                      : 470
% 0.20/0.53  # Factorizations                       : 0
% 0.20/0.53  # NegExts                              : 0
% 0.20/0.53  # Equation resolutions                 : 0
% 0.20/0.53  # Total rewrite steps                  : 32
% 0.20/0.53  # Propositional unsat checks           : 0
% 0.20/0.53  #    Propositional check models        : 0
% 0.20/0.53  #    Propositional check unsatisfiable : 0
% 0.20/0.53  #    Propositional clauses             : 0
% 0.20/0.53  #    Propositional clauses after purity: 0
% 0.20/0.53  #    Propositional unsat core size     : 0
% 0.20/0.53  #    Propositional preprocessing time  : 0.000
% 0.20/0.53  #    Propositional encoding time       : 0.000
% 0.20/0.53  #    Propositional solver time         : 0.000
% 0.20/0.53  #    Success case prop preproc time    : 0.000
% 0.20/0.53  #    Success case prop encoding time   : 0.000
% 0.20/0.53  #    Success case prop solver time     : 0.000
% 0.20/0.53  # Current number of processed clauses  : 19
% 0.20/0.53  #    Positive orientable unit clauses  : 3
% 0.20/0.53  #    Positive unorientable unit clauses: 0
% 0.20/0.53  #    Negative unit clauses             : 3
% 0.20/0.53  #    Non-unit-clauses                  : 13
% 0.20/0.53  # Current number of unprocessed clauses: 13
% 0.20/0.53  # ...number of literals in the above   : 46
% 0.20/0.53  # Current number of archived formulas  : 0
% 0.20/0.53  # Current number of archived clauses   : 262
% 0.20/0.53  # Clause-clause subsumption calls (NU) : 6398
% 0.20/0.53  # Rec. Clause-clause subsumption calls : 2493
% 0.20/0.53  # Non-unit clause-clause subsumptions  : 341
% 0.20/0.53  # Unit Clause-clause subsumption calls : 17
% 0.20/0.53  # Rewrite failures with RHS unbound    : 0
% 0.20/0.53  # BW rewrite match attempts            : 13
% 0.20/0.53  # BW rewrite match successes           : 3
% 0.20/0.53  # Condensation attempts                : 0
% 0.20/0.53  # Condensation successes               : 0
% 0.20/0.53  # Termbank termtop insertions          : 25620
% 0.20/0.53  
% 0.20/0.53  # -------------------------------------------------
% 0.20/0.53  # User time                : 0.047 s
% 0.20/0.53  # System time              : 0.004 s
% 0.20/0.53  # Total time               : 0.051 s
% 0.20/0.53  # Maximum resident set size: 1684 pages
% 0.20/0.53  
% 0.20/0.53  # -------------------------------------------------
% 0.20/0.53  # User time                : 0.279 s
% 0.20/0.53  # System time              : 0.028 s
% 0.20/0.53  # Total time               : 0.307 s
% 0.20/0.53  # Maximum resident set size: 1692 pages
% 0.20/0.53  % E---3.1 exiting
%------------------------------------------------------------------------------