%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO631-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:51:08 AM UTC 2026
% Result : Unsatisfiable 0.86s 0.59s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 37
% Syntax : Number of formulae : 177 ( 33 unt; 0 def)
% Number of atoms : 461 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 430 ( 146 ~; 284 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 12 ( 4 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 : 196 ( 3 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_8_03,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s(s(s('0'))))) ),
file('theBenchmark.p',clause_8_03) ).
cnf(c_1,plain,
( 'LE'(f(B),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s(s(s('0'))))) ),
inference(clausify,[status(thm)],[clause_8_03]) ).
fof(clause_3_02,axiom,
! [VAR_0] : iLEQ(VAR_0,g(VAR_0)),
file('theBenchmark.p',clause_3_02) ).
cnf(c_2,plain,
iLEQ(A,g(A)),
inference(clausify,[status(thm)],[clause_3_02]) ).
fof(clause_48_04,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
file('theBenchmark.p',clause_48_04) ).
cnf(c_3,plain,
( 'LE'(f(B),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
inference(clausify,[status(thm)],[clause_48_04]) ).
fof(clause_18_06,axiom,
! [VAR_0] : iLEQ(VAR_0,VAR_0),
file('theBenchmark.p',clause_18_06) ).
cnf(c_4,plain,
iLEQ(A,A),
inference(clausify,[status(thm)],[clause_18_06]) ).
fof(clause_21_08,axiom,
! [VAR_0] : iLEQ(VAR_0,VAR_0),
file('theBenchmark.p',clause_21_08) ).
cnf(c_5,plain,
iLEQ(A,A),
inference(clausify,[status(thm)],[clause_21_08]) ).
fof(clause_28_10,axiom,
! [VAR_0] : iLEQ(VAR_0,g(VAR_0)),
file('theBenchmark.p',clause_28_10) ).
cnf(c_6,plain,
iLEQ(A,g(A)),
inference(clausify,[status(thm)],[clause_28_10]) ).
fof(clause_5_11,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s(s(s(s(s('0'))))))) ),
file('theBenchmark.p',clause_5_11) ).
cnf(c_7,plain,
( 'LE'(f(B),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s(s(s(s(s('0'))))))) ),
inference(clausify,[status(thm)],[clause_5_11]) ).
fof(clause_10_13,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s(s(s(s(s(s(s(s('0')))))))))) ),
file('theBenchmark.p',clause_10_13) ).
cnf(c_8,plain,
( 'LE'(f(B),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s(s('0')))))))))) ),
inference(clausify,[status(thm)],[clause_10_13]) ).
fof(clause_16_18,axiom,
! [VAR_0] : iLEQ(VAR_0,g(VAR_0)),
file('theBenchmark.p',clause_16_18) ).
cnf(c_11,plain,
iLEQ(A,g(A)),
inference(clausify,[status(thm)],[clause_16_18]) ).
fof(clause_26_19,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s(s(s(s(s(s(s('0'))))))))) ),
file('theBenchmark.p',clause_26_19) ).
cnf(c_12,plain,
( 'LE'(f(B),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(clausify,[status(thm)],[clause_26_19]) ).
fof(clause_35_20,axiom,
! [VAR_0] : iLEQ(VAR_0,VAR_0),
file('theBenchmark.p',clause_35_20) ).
cnf(c_13,plain,
iLEQ(A,A),
inference(clausify,[status(thm)],[clause_35_20]) ).
fof(clause_23_21,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s('0'))
| 'E'(s('0'),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s('0'))) ),
file('theBenchmark.p',clause_23_21) ).
cnf(c_14,plain,
( 'LE'(f(B),s('0'))
| 'E'(s('0'),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s('0'))) ),
inference(clausify,[status(thm)],[clause_23_21]) ).
fof(clause_37_27,axiom,
! [VAR_0] : iLEQ(VAR_0,VAR_0),
file('theBenchmark.p',clause_37_27) ).
cnf(c_16,plain,
iLEQ(A,A),
inference(clausify,[status(thm)],[clause_37_27]) ).
fof(clause_45_29,axiom,
! [VAR_0] : iLEQ(VAR_0,g(VAR_0)),
file('theBenchmark.p',clause_45_29) ).
cnf(c_17,plain,
iLEQ(A,g(A)),
inference(clausify,[status(thm)],[clause_45_29]) ).
fof(clause_56_31,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),'0')
| 'E'('0',f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s('0')) ),
file('theBenchmark.p',clause_56_31) ).
cnf(c_18,plain,
( 'LE'(f(B),'0')
| 'E'('0',f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s('0')) ),
inference(clausify,[status(thm)],[clause_56_31]) ).
fof(clause_12_34,axiom,
! [VAR_0] : iLEQ(VAR_0,VAR_0),
file('theBenchmark.p',clause_12_34) ).
cnf(c_20,plain,
iLEQ(A,A),
inference(clausify,[status(thm)],[clause_12_34]) ).
fof(clause_0_36,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s(s(s(s('0')))))) ),
file('theBenchmark.p',clause_0_36) ).
cnf(c_21,plain,
( 'LE'(f(B),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s(s(s(s('0')))))) ),
inference(clausify,[status(thm)],[clause_0_36]) ).
fof(clause_4_41,axiom,
! [VAR_0] : iLEQ(VAR_0,VAR_0),
file('theBenchmark.p',clause_4_41) ).
cnf(c_24,plain,
iLEQ(A,A),
inference(clausify,[status(thm)],[clause_4_41]) ).
fof(clause_17_44,axiom,
! [VAR_0] : iLEQ(VAR_0,g(VAR_0)),
file('theBenchmark.p',clause_17_44) ).
cnf(c_26,plain,
iLEQ(A,g(A)),
inference(clausify,[status(thm)],[clause_17_44]) ).
fof(clause_54_45,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s(s(s(s(s(s('0')))))))) ),
file('theBenchmark.p',clause_54_45) ).
cnf(c_27,plain,
( 'LE'(f(B),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s(s(s(s(s(s('0')))))))) ),
inference(clausify,[status(thm)],[clause_54_45]) ).
fof(clause_39_46,axiom,
! [VAR_0] : iLEQ(VAR_0,VAR_0),
file('theBenchmark.p',clause_39_46) ).
cnf(c_28,plain,
iLEQ(A,A),
inference(clausify,[status(thm)],[clause_39_46]) ).
fof(clause_47_47,axiom,
! [VAR_0] : iLEQ(VAR_0,g(VAR_0)),
file('theBenchmark.p',clause_47_47) ).
cnf(c_29,plain,
iLEQ(A,g(A)),
inference(clausify,[status(thm)],[clause_47_47]) ).
fof(clause_51_50,axiom,
! [VAR_0,VAR_1] :
( 'LE'(f(VAR_1),s(s('0')))
| 'E'(s(s('0')),f(VAR_1))
| ~ iLEQ(VAR_0,VAR_1)
| ~ 'LE'(f(VAR_0),s(s(s('0')))) ),
file('theBenchmark.p',clause_51_50) ).
cnf(c_30,plain,
( 'LE'(f(B),s(s('0')))
| 'E'(s(s('0')),f(B))
| ~ iLEQ(A,B)
| ~ 'LE'(f(A),s(s(s('0')))) ),
inference(clausify,[status(thm)],[clause_51_50]) ).
cnf(c_33,plain,
( 'LE'(f(A),s(s('0')))
| 'E'(s(s('0')),f(A))
| ~ 'LE'(f(A),s(s(s('0')))) ),
inference(resolve,[status(thm)],[c_30,c_28]) ).
cnf(c_34,plain,
( 'LE'(f(g(A)),s(s('0')))
| 'E'(s(s('0')),f(g(A)))
| ~ 'LE'(f(A),s(s(s('0')))) ),
inference(resolve,[status(thm)],[c_30,c_29]) ).
cnf(c_35,plain,
( 'LE'(f(A),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(A))
| ~ 'LE'(f(A),s(s(s(s(s(s(s('0')))))))) ),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_36,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(A)))
| ~ 'LE'(f(A),s(s(s(s(s(s(s('0')))))))) ),
inference(resolve,[status(thm)],[c_27,c_26]) ).
cnf(c_37,plain,
( 'LE'(f(g(A)),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(A)))
| ~ 'LE'(f(A),s(s(s(s(s('0')))))) ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_38,plain,
( 'LE'(f(A),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(A))
| ~ 'LE'(f(A),s(s(s(s(s('0')))))) ),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_39,plain,
( 'LE'(f(A),'0')
| 'E'('0',f(A))
| ~ 'LE'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_40,plain,
( 'LE'(f(g(A)),'0')
| 'E'('0',f(g(A)))
| ~ 'LE'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_41,plain,
( 'LE'(f(g(A)),s('0'))
| 'E'(s('0'),f(g(A)))
| ~ 'LE'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_42,plain,
( 'LE'(f(A),s('0'))
| 'E'(s('0'),f(A))
| ~ 'LE'(f(A),s(s('0'))) ),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_43,plain,
( 'LE'(f(A),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(A))
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_44,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(A)))
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_45,plain,
( 'LE'(f(A),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(A))
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s(s('0')))))))))) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_46,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(A)))
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s(s('0')))))))))) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_47,plain,
( 'LE'(f(A),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(A))
| ~ 'LE'(f(A),s(s(s(s(s(s('0'))))))) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_48,plain,
( 'LE'(f(g(A)),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(A)))
| ~ 'LE'(f(A),s(s(s(s(s(s('0'))))))) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_49,plain,
( 'LE'(f(A),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(A))
| ~ 'LE'(f(A),s(s(s(s('0'))))) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_50,plain,
( 'LE'(f(A),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(A))
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_51,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A)))
| ~ 'LE'(f(A),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_52,plain,
( 'LE'(f(g(A)),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(A)))
| ~ 'LE'(f(A),s(s(s(s('0'))))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(clause_34_55,axiom,
! [VAR_0] : ~ 'E'(f(VAR_0),f(g(VAR_0))),
file('theBenchmark.p',clause_34_55) ).
cnf(c_53,plain,
~ 'E'(f(A),f(g(A))),
inference(clausify,[status(thm)],[clause_34_55]) ).
fof(clause_31_54,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(VAR_0)) ),
file('theBenchmark.p',clause_31_54) ).
cnf(c_54,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(A)) ),
inference(clausify,[status(thm)],[clause_31_54]) ).
cnf(c_55,plain,
( ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_54]) ).
fof(clause_38_52,axiom,
! [VAR_0] : ~ 'LE'(f(VAR_0),'0'),
file('theBenchmark.p',clause_38_52) ).
cnf(c_56,plain,
~ 'LE'(f(A),'0'),
inference(clausify,[status(thm)],[clause_38_52]) ).
fof(clause_55_48,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s(s(s('0')))),f(g(VAR_0)))
| ~ 'E'(s(s(s(s('0')))),f(VAR_0)) ),
file('theBenchmark.p',clause_55_48) ).
cnf(c_57,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s(s(s('0')))),f(g(A)))
| ~ 'E'(s(s(s(s('0')))),f(A)) ),
inference(clausify,[status(thm)],[clause_55_48]) ).
cnf(c_58,plain,
( ~ 'E'(s(s(s(s('0')))),f(g(A)))
| ~ 'E'(s(s(s(s('0')))),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_57]) ).
fof(clause_49_39,axiom,
! [VAR_0] :
( 'LE'(f(VAR_0),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(VAR_0)) ),
file('theBenchmark.p',clause_49_39) ).
cnf(c_59,plain,
( 'LE'(f(A),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(A)) ),
inference(clausify,[status(thm)],[clause_49_39]) ).
fof(clause_30_35,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s('0'),f(g(VAR_0)))
| ~ 'E'(s('0'),f(VAR_0)) ),
file('theBenchmark.p',clause_30_35) ).
cnf(c_60,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s('0'),f(g(A)))
| ~ 'E'(s('0'),f(A)) ),
inference(clausify,[status(thm)],[clause_30_35]) ).
cnf(c_61,plain,
( ~ 'E'(s('0'),f(g(A)))
| ~ 'E'(s('0'),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_60]) ).
fof(clause_42_32,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(VAR_0)) ),
file('theBenchmark.p',clause_42_32) ).
cnf(c_62,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(A)) ),
inference(clausify,[status(thm)],[clause_42_32]) ).
cnf(c_63,plain,
( ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_62]) ).
fof(clause_2_25,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'('0',f(g(VAR_0)))
| ~ 'E'('0',f(VAR_0)) ),
file('theBenchmark.p',clause_2_25) ).
cnf(c_64,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'('0',f(g(A)))
| ~ 'E'('0',f(A)) ),
inference(clausify,[status(thm)],[clause_2_25]) ).
cnf(c_65,plain,
( ~ 'E'('0',f(g(A)))
| ~ 'E'('0',f(A)) ),
inference(resolve,[status(thm)],[c_53,c_64]) ).
fof(clause_40_23,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s('0'))))),f(VAR_0)) ),
file('theBenchmark.p',clause_40_23) ).
cnf(c_66,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(A)))
| ~ 'E'(s(s(s(s(s('0'))))),f(A)) ),
inference(clausify,[status(thm)],[clause_40_23]) ).
cnf(c_67,plain,
( ~ 'E'(s(s(s(s(s('0'))))),f(g(A)))
| ~ 'E'(s(s(s(s(s('0'))))),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_66]) ).
fof(clause_20_22,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s('0')),f(g(VAR_0)))
| ~ 'E'(s(s('0')),f(VAR_0)) ),
file('theBenchmark.p',clause_20_22) ).
cnf(c_68,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s('0')),f(g(A)))
| ~ 'E'(s(s('0')),f(A)) ),
inference(clausify,[status(thm)],[clause_20_22]) ).
cnf(c_69,plain,
( ~ 'E'(s(s('0')),f(g(A)))
| ~ 'E'(s(s('0')),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_68]) ).
fof(clause_11_16,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(VAR_0)) ),
file('theBenchmark.p',clause_11_16) ).
cnf(c_70,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(A)) ),
inference(clausify,[status(thm)],[clause_11_16]) ).
cnf(c_71,plain,
( ~ 'E'(s(s(s(s(s(s('0')))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_70]) ).
fof(clause_29_12,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s(s('0'))),f(g(VAR_0)))
| ~ 'E'(s(s(s('0'))),f(VAR_0)) ),
file('theBenchmark.p',clause_29_12) ).
cnf(c_72,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s(s('0'))),f(g(A)))
| ~ 'E'(s(s(s('0'))),f(A)) ),
inference(clausify,[status(thm)],[clause_29_12]) ).
cnf(c_73,plain,
( ~ 'E'(s(s(s('0'))),f(g(A)))
| ~ 'E'(s(s(s('0'))),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_72]) ).
fof(clause_44_07,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(VAR_0)) ),
file('theBenchmark.p',clause_44_07) ).
cnf(c_74,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(A)) ),
inference(clausify,[status(thm)],[clause_44_07]) ).
cnf(c_75,plain,
( ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_74]) ).
fof(clause_27_01,axiom,
! [VAR_0] :
( 'E'(f(VAR_0),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(VAR_0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(VAR_0)) ),
file('theBenchmark.p',clause_27_01) ).
cnf(c_76,plain,
( 'E'(f(A),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(A)) ),
inference(clausify,[status(thm)],[clause_27_01]) ).
cnf(c_77,plain,
( ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(A)) ),
inference(resolve,[status(thm)],[c_53,c_76]) ).
cnf(c_78,plain,
( 'E'('0',f(g(A)))
| ~ 'LE'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_56,c_40]) ).
cnf(c_79,plain,
( 'E'('0',f(A))
| ~ 'LE'(f(A),s('0')) ),
inference(resolve,[status(thm)],[c_56,c_39]) ).
cnf(c_80,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A)))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(A)) ),
inference(resolve,[status(thm)],[c_59,c_51]) ).
cnf(c_81,plain,
( 'LE'(f(A),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(A))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(A)) ),
inference(resolve,[status(thm)],[c_59,c_50]) ).
cnf(c_350,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(A))) ),
inference(resolve,[status(thm)],[c_63,c_80]) ).
cnf(c_351,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A)))
| 'LE'(f(g(A)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A))) ),
inference(resolve,[status(thm)],[c_350,c_81]) ).
cnf(c_352,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'LE'(f(g(A)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A))) ),
inference(copy,[status(thm)],[c_351]) ).
cnf(c_92,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A))) ),
inference(copy,[status(thm)],[c_352]) ).
cnf(c_95,plain,
( 'LE'(f(g(g(A))),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(A))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A))) ),
inference(resolve,[status(thm)],[c_92,c_46]) ).
cnf(c_96,plain,
( 'LE'(f(g(A)),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(A)))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(A))) ),
inference(resolve,[status(thm)],[c_92,c_45]) ).
cnf(c_103,plain,
( ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(A))
| 'LE'(f(g(A)),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(A))) ),
inference(resolve,[status(thm)],[c_96,c_77]) ).
cnf(c_353,plain,
( 'LE'(f(g(g(A))),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(A))))
| 'LE'(f(g(g(A))),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(A)))) ),
inference(resolve,[status(thm)],[c_95,c_103]) ).
cnf(c_354,plain,
( 'LE'(f(g(g(A))),s(s(s(s(s(s(s(s('0')))))))))
| 'LE'(f(g(g(A))),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(A)))) ),
inference(copy,[status(thm)],[c_353]) ).
cnf(c_106,plain,
( 'LE'(f(g(g(A))),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(A)))) ),
inference(copy,[status(thm)],[c_354]) ).
cnf(c_111,plain,
( 'LE'(f(g(g(g(A)))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(A)))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(A)))) ),
inference(resolve,[status(thm)],[c_106,c_44]) ).
cnf(c_112,plain,
( 'LE'(f(g(g(A))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(A))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(A)))) ),
inference(resolve,[status(thm)],[c_106,c_43]) ).
cnf(c_119,plain,
( ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(A)))
| 'LE'(f(g(g(A))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(A)))) ),
inference(resolve,[status(thm)],[c_112,c_55]) ).
cnf(c_355,plain,
( 'LE'(f(g(g(g(A)))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(A)))))
| 'LE'(f(g(g(g(A)))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(A))))) ),
inference(resolve,[status(thm)],[c_111,c_119]) ).
cnf(c_356,plain,
( 'LE'(f(g(g(g(A)))),s(s(s(s(s(s(s('0'))))))))
| 'LE'(f(g(g(g(A)))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(A))))) ),
inference(copy,[status(thm)],[c_355]) ).
cnf(c_122,plain,
( 'LE'(f(g(g(g(A)))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(A))))) ),
inference(copy,[status(thm)],[c_356]) ).
cnf(c_127,plain,
( 'LE'(f(g(g(g(g(A))))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(A))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(A))))) ),
inference(resolve,[status(thm)],[c_122,c_36]) ).
cnf(c_128,plain,
( 'LE'(f(g(g(g(A)))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(A)))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(A))))) ),
inference(resolve,[status(thm)],[c_122,c_35]) ).
cnf(c_134,plain,
( ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(A))))
| 'LE'(f(g(g(g(A)))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(A))))) ),
inference(resolve,[status(thm)],[c_128,c_75]) ).
cnf(c_357,plain,
( 'LE'(f(g(g(g(g(A))))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(A))))))
| 'LE'(f(g(g(g(g(A))))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(A)))))) ),
inference(resolve,[status(thm)],[c_127,c_134]) ).
cnf(c_358,plain,
( 'LE'(f(g(g(g(g(A))))),s(s(s(s(s(s('0')))))))
| 'LE'(f(g(g(g(g(A))))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(A)))))) ),
inference(copy,[status(thm)],[c_357]) ).
cnf(c_139,plain,
( 'LE'(f(g(g(g(g(A))))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(A)))))) ),
inference(copy,[status(thm)],[c_358]) ).
cnf(c_144,plain,
( 'LE'(f(g(g(g(g(g(A)))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(A)))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(A)))))) ),
inference(resolve,[status(thm)],[c_139,c_48]) ).
cnf(c_145,plain,
( 'LE'(f(g(g(g(g(A))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(A))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(A)))))) ),
inference(resolve,[status(thm)],[c_139,c_47]) ).
cnf(c_151,plain,
( ~ 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(A)))))
| 'LE'(f(g(g(g(g(A))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(A)))))) ),
inference(resolve,[status(thm)],[c_145,c_71]) ).
cnf(c_359,plain,
( 'LE'(f(g(g(g(g(g(A)))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(A)))))))
| 'LE'(f(g(g(g(g(g(A)))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(A))))))) ),
inference(resolve,[status(thm)],[c_144,c_151]) ).
cnf(c_360,plain,
( 'LE'(f(g(g(g(g(g(A)))))),s(s(s(s(s('0'))))))
| 'LE'(f(g(g(g(g(g(A)))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(A))))))) ),
inference(copy,[status(thm)],[c_359]) ).
cnf(c_157,plain,
( 'LE'(f(g(g(g(g(g(A)))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(A))))))) ),
inference(copy,[status(thm)],[c_360]) ).
cnf(c_162,plain,
( 'LE'(f(g(g(g(g(g(A)))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(A)))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(A))))))) ),
inference(resolve,[status(thm)],[c_157,c_38]) ).
cnf(c_163,plain,
( 'LE'(f(g(g(g(g(g(g(A))))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(A))))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(A))))))) ),
inference(resolve,[status(thm)],[c_157,c_37]) ).
cnf(c_170,plain,
( ~ 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(A))))))
| 'LE'(f(g(g(g(g(g(A)))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(A))))))) ),
inference(resolve,[status(thm)],[c_162,c_67]) ).
cnf(c_361,plain,
( 'LE'(f(g(g(g(g(g(g(A))))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(A))))))))
| 'LE'(f(g(g(g(g(g(g(A))))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(A)))))))) ),
inference(resolve,[status(thm)],[c_163,c_170]) ).
cnf(c_362,plain,
( 'LE'(f(g(g(g(g(g(g(A))))))),s(s(s(s('0')))))
| 'LE'(f(g(g(g(g(g(g(A))))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(A)))))))) ),
inference(copy,[status(thm)],[c_361]) ).
cnf(c_173,plain,
( 'LE'(f(g(g(g(g(g(g(A))))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(A)))))))) ),
inference(copy,[status(thm)],[c_362]) ).
cnf(c_178,plain,
( 'LE'(f(g(g(g(g(g(g(g(A)))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(A)))))))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(A)))))))) ),
inference(resolve,[status(thm)],[c_173,c_52]) ).
cnf(c_179,plain,
( 'LE'(f(g(g(g(g(g(g(A))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(A))))))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(A)))))))) ),
inference(resolve,[status(thm)],[c_173,c_49]) ).
cnf(c_185,plain,
( ~ 'E'(s(s(s(s('0')))),f(g(g(g(g(g(A)))))))
| 'LE'(f(g(g(g(g(g(g(A))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(A)))))))) ),
inference(resolve,[status(thm)],[c_179,c_58]) ).
cnf(c_363,plain,
( 'LE'(f(g(g(g(g(g(g(g(A)))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(A)))))))))
| 'LE'(f(g(g(g(g(g(g(g(A)))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(A))))))))) ),
inference(resolve,[status(thm)],[c_178,c_185]) ).
cnf(c_364,plain,
( 'LE'(f(g(g(g(g(g(g(g(A)))))))),s(s(s('0'))))
| 'LE'(f(g(g(g(g(g(g(g(A)))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(A))))))))) ),
inference(copy,[status(thm)],[c_363]) ).
cnf(c_190,plain,
( 'LE'(f(g(g(g(g(g(g(g(A)))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(A))))))))) ),
inference(copy,[status(thm)],[c_364]) ).
cnf(c_195,plain,
( 'LE'(f(g(g(g(g(g(g(g(g(A))))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(A))))))))) ),
inference(resolve,[status(thm)],[c_190,c_34]) ).
cnf(c_196,plain,
( 'LE'(f(g(g(g(g(g(g(g(A)))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(A)))))))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(A))))))))) ),
inference(resolve,[status(thm)],[c_190,c_33]) ).
cnf(c_202,plain,
( ~ 'E'(s(s(s('0'))),f(g(g(g(g(g(g(A))))))))
| 'LE'(f(g(g(g(g(g(g(g(A)))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(A))))))))) ),
inference(resolve,[status(thm)],[c_196,c_73]) ).
cnf(c_365,plain,
( 'LE'(f(g(g(g(g(g(g(g(g(A))))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A))))))))))
| 'LE'(f(g(g(g(g(g(g(g(g(A))))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_195,c_202]) ).
cnf(c_366,plain,
( 'LE'(f(g(g(g(g(g(g(g(g(A))))))))),s(s('0')))
| 'LE'(f(g(g(g(g(g(g(g(g(A))))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(copy,[status(thm)],[c_365]) ).
cnf(c_208,plain,
( 'LE'(f(g(g(g(g(g(g(g(g(A))))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(copy,[status(thm)],[c_366]) ).
cnf(c_213,plain,
( 'LE'(f(g(g(g(g(g(g(g(g(A))))))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_208,c_42]) ).
cnf(c_214,plain,
( 'LE'(f(g(g(g(g(g(g(g(g(g(A)))))))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A)))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_208,c_41]) ).
cnf(c_223,plain,
( 'E'('0',f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_213,c_79]) ).
cnf(c_224,plain,
( 'E'('0',f(g(g(g(g(g(g(g(g(g(A)))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_213,c_78]) ).
cnf(c_367,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A))))))))))
| ~ 'E'('0',f(g(g(g(g(g(g(g(g(g(A))))))))))) ),
inference(resolve,[status(thm)],[c_65,c_223]) ).
cnf(c_368,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_367,c_224]) ).
cnf(c_369,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(copy,[status(thm)],[c_368]) ).
cnf(c_238,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(copy,[status(thm)],[c_369]) ).
cnf(c_370,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| ~ 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(g(A))))))))))) ),
inference(resolve,[status(thm)],[c_69,c_238]) ).
cnf(c_244,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A)))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_370,c_238]) ).
cnf(c_371,plain,
( 'LE'(f(g(g(g(g(g(g(g(g(g(A)))))))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A)))))))))))
| ~ 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(g(A))))))))))) ),
inference(resolve,[status(thm)],[c_69,c_214]) ).
cnf(c_372,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A)))))))))))
| 'LE'(f(g(g(g(g(g(g(g(g(g(A)))))))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A))))))))))) ),
inference(resolve,[status(thm)],[c_371,c_238]) ).
cnf(c_254,plain,
( 'LE'(f(g(g(g(g(g(g(g(g(g(A)))))))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A))))))))))) ),
inference(copy,[status(thm)],[c_372]) ).
cnf(c_272,plain,
( 'E'('0',f(g(g(g(g(g(g(g(g(g(A)))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A))))))))))) ),
inference(resolve,[status(thm)],[c_254,c_79]) ).
cnf(c_273,plain,
( 'E'('0',f(g(g(g(g(g(g(g(g(g(g(A))))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A))))))))))) ),
inference(resolve,[status(thm)],[c_254,c_78]) ).
cnf(c_373,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(A))))))))))
| ~ 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(g(A)))))))))))) ),
inference(resolve,[status(thm)],[c_61,c_244]) ).
cnf(c_294,plain,
( 'E'('0',f(g(g(g(g(g(g(g(g(g(g(A))))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_373,c_272]) ).
cnf(c_297,plain,
( ~ 'E'('0',f(g(g(g(g(g(g(g(g(g(A)))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(A)))))))))) ),
inference(resolve,[status(thm)],[c_294,c_65]) ).
cnf(c_374,plain,
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A)))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A))))))))))) ),
inference(resolve,[status(thm)],[c_273,c_297]) ).
cnf(c_342,plain,
'E'(s('0'),f(g(g(g(g(g(g(g(g(g(A))))))))))),
inference(copy,[status(thm)],[c_374]) ).
cnf(c_348,plain,
~ 'E'(s('0'),f(g(g(g(g(g(g(g(g(A)))))))))),
inference(resolve,[status(thm)],[c_342,c_61]) ).
cnf(c_349,plain,
$false,
inference(resolve,[status(thm)],[c_348,c_342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO631-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 19:43:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2532578 was started by sandbox2 on n002,
% 0.10/0.36 % Sat Sep 26 19:43:20 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.86/0.59
% 0.86/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.86/0.59
% 0.86/0.59 % Proof 1 at 0.12 (+ 0.04) seconds.
% 0.86/0.59 % Length of proof is 115.
% 0.86/0.59 % Level of proof is 34.
% 0.86/0.59 % Maximum clause weight is 92.000.
% 0.86/0.59 % Given clauses 172.
% 0.86/0.59
% 0.86/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------