%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO666-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 : Thu Sep 24 03:52:01 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of clauses : 57 ( 8 unt; 35 nHn; 48 RR)
% Number of literals : 384 ( 0 equ; 269 neg)
% Maximal clause size : 17 ( 6 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 163 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_29,axiom,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29) ).
cnf(clause_185,axiom,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_185) ).
cnf(clause_179,axiom,
( ~ 'E'(s('0'),f(suc(X6)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X6))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ iLEQ(suc(X3),suc(X6))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X5))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X5),suc(X2))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s('0'),f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_179) ).
cnf(clause_83,axiom,
'LE'(f(X1),s(s('0'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_83) ).
cnf(clause_70,axiom,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_70) ).
cnf(clause_123,axiom,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_123) ).
cnf(clause_42,axiom,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_42) ).
cnf(clause_102,axiom,
( ~ 'E'('0',f(X6))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(suc(X6)))
| ~ iLEQ(suc(X3),suc(X5))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(suc(X4)))
| ~ iLEQ(suc(X5),suc(X6))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X6),suc(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_102) ).
cnf(clause_12,axiom,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12) ).
cnf(clause_98,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_98) ).
cnf(c_0_10,plain,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_29]) ).
cnf(c_0_11,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_185]) ).
cnf(c_0_12,plain,
( ~ 'E'(s('0'),f(suc(X6)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X6))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ iLEQ(suc(X3),suc(X6))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X5))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X5),suc(X2))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s('0'),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_179]) ).
cnf(c_0_13,plain,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
c_0_10 ).
cnf(c_0_14,axiom,
'LE'(f(X1),s(s('0'))),
clause_83 ).
cnf(c_0_15,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
c_0_11 ).
cnf(c_0_16,plain,
( ~ 'E'(s('0'),f(suc(X6)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X6))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ iLEQ(suc(X3),suc(X6))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X5))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X5),suc(X2))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s('0'),f(X1)) ),
c_0_12 ).
cnf(c_0_17,plain,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
cnf(c_0_18,plain,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14])]) ).
cnf(c_0_19,plain,
( ~ iLEQ(suc(X6),suc(X2))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X3),suc(X6))
| ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'(s('0'),f(X6))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X6)))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_20,plain,
( ~ iLEQ(suc(X6),suc(X1))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X3),suc(X6))
| ~ iLEQ(suc(X1),suc(X5))
| ~ 'E'(s('0'),f(X6))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X6)))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X3)))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_18]) ).
cnf(c_0_21,plain,
( ~ iLEQ(suc(X6),suc(X3))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X1),suc(X6))
| ~ iLEQ(suc(X3),suc(X5))
| ~ 'E'(s('0'),f(X6))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(suc(X6)))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
( ~ iLEQ(suc(X6),suc(X2))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X4),suc(X6))
| ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'(s('0'),f(X6))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(suc(X6)))
| ~ 'E'(s('0'),f(suc(X5)))
| 'LE'(f(X4),s('0'))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_18]) ).
cnf(c_0_23,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_70]) ).
cnf(c_0_24,plain,
( ~ iLEQ(suc(X6),suc(X4))
| ~ iLEQ(suc(X1),suc(X5))
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X2),suc(X6))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s('0'),f(X6))
| ~ 'E'(s('0'),f(suc(X6)))
| 'LE'(f(X5),s('0'))
| 'LE'(f(X4),s('0'))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_18]) ).
cnf(c_0_25,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
c_0_23 ).
cnf(c_0_26,plain,
( ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X6),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X3),suc(X6))
| 'LE'(f(X6),s('0'))
| 'LE'(f(X5),s('0'))
| 'LE'(f(X4),s('0'))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_17]),c_0_18]) ).
cnf(c_0_27,plain,
( iLEQ(suc(X1),suc(X1))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_17]),c_0_18]) ).
cnf(c_0_28,plain,
( ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X1),suc(X5))
| 'LE'(f(X5),s('0'))
| 'LE'(f(X4),s('0'))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,plain,
( ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| 'LE'(f(X4),s('0'))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_30,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| 'LE'(f(X3),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_31,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_123]) ).
cnf(c_0_32,plain,
( ~ iLEQ(suc(X2),suc(X1))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_33,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_42]) ).
cnf(c_0_34,plain,
( ~ 'E'('0',f(X6))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(suc(X6)))
| ~ iLEQ(suc(X3),suc(X5))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(suc(X4)))
| ~ iLEQ(suc(X5),suc(X6))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X6),suc(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(fof_simplification,[status(thm)],[clause_102]) ).
cnf(c_0_35,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
c_0_31 ).
cnf(c_0_36,plain,
'LE'(f(X1),s('0')),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_37,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
c_0_33 ).
cnf(c_0_38,plain,
( ~ 'E'('0',f(X6))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(suc(X6)))
| ~ iLEQ(suc(X3),suc(X5))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(suc(X4)))
| ~ iLEQ(suc(X5),suc(X6))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X6),suc(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X2)) ),
c_0_34 ).
cnf(c_0_39,plain,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_40,plain,
( 'E'('0',f(X1))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_36])]) ).
cnf(c_0_41,plain,
( ~ iLEQ(suc(X6),suc(X5))
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X6))
| ~ 'E'('0',f(X6))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X6)))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X2)))
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_42,plain,
( ~ iLEQ(suc(X6),suc(X5))
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X6))
| ~ 'E'('0',f(X6))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X6)))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X3)))
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_39]),c_0_40]) ).
cnf(c_0_43,plain,
( ~ iLEQ(suc(X6),suc(X5))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X6))
| ~ 'E'('0',f(X6))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(suc(X6)))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(suc(X4)))
| 'LE'(f(X3),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_40]) ).
cnf(c_0_44,plain,
( ~ iLEQ(suc(X6),suc(X5))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X6))
| ~ 'E'('0',f(X6))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(suc(X6)))
| ~ 'E'('0',f(suc(X5)))
| 'LE'(f(X4),'0')
| 'LE'(f(X3),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
( ~ iLEQ(suc(X6),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X6))
| ~ 'E'('0',f(X6))
| ~ 'E'('0',f(suc(X6)))
| 'LE'(f(X5),'0')
| 'LE'(f(X4),'0')
| 'LE'(f(X3),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_40]) ).
cnf(c_0_46,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_12]) ).
cnf(c_0_47,plain,
( ~ iLEQ(suc(X1),suc(X6))
| ~ iLEQ(suc(X6),suc(X5))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X4),suc(X1))
| 'LE'(f(X6),'0')
| 'LE'(f(X5),'0')
| 'LE'(f(X4),'0')
| 'LE'(f(X3),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_39]),c_0_40]) ).
cnf(c_0_48,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1)) ),
c_0_46 ).
cnf(c_0_49,plain,
( ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X5))
| 'LE'(f(X5),'0')
| 'LE'(f(X4),'0')
| 'LE'(f(X3),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_40]),c_0_39]) ).
cnf(c_0_50,plain,
( ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X4),'0')
| 'LE'(f(X3),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_48]),c_0_40]),c_0_39]) ).
cnf(c_0_51,plain,
( ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X3),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_48]),c_0_40]),c_0_39]) ).
cnf(c_0_52,plain,
~ 'LE'(f(z),'0'),
inference(fof_simplification,[status(thm)],[clause_98]) ).
cnf(c_0_53,plain,
( ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_48]),c_0_40]),c_0_39]) ).
cnf(c_0_54,plain,
~ 'LE'(f(z),'0'),
c_0_52 ).
cnf(c_0_55,plain,
'LE'(f(X1),'0'),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_48]),c_0_40]),c_0_39]) ).
cnf(c_0_56,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO666-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n026.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 12:11:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2228029 completed with status 0
% 0.12/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FGHNF-FFMF11-SFFFFFNN
% 0.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.45 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.12/0.45 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/0.45 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y with 136s (1) cores
% 0.12/0.45 % G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2228040 completed with status 0
% 0.12/0.45 % Result found by G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FGHNF-FFMF11-SFFFFFNN
% 0.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.45 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.12/0.45 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/0.45 % Preprocessing time : 0.001 s
% 0.12/0.45 % Presaturation interreduction done
% 0.12/0.45
% 0.12/0.45 % Proof found!
% 0.12/0.45 % SZS status Unsatisfiable
% 0.12/0.45 % SZS output start CNFRefutation
% See solution above
% 0.12/0.45 % Parsed axioms : 10
% 0.12/0.45 % Removed by relevancy pruning/SinE : 0
% 0.12/0.45 % Initial clauses : 10
% 0.12/0.45 % Removed in clause preprocessing : 0
% 0.12/0.45 % Initial clauses in saturation : 10
% 0.12/0.45 % Processed clauses : 51
% 0.12/0.45 % ...of these trivial : 0
% 0.12/0.45 % ...subsumed : 1
% 0.12/0.45 % ...remaining for further processing : 50
% 0.12/0.45 % Other redundant clauses eliminated : 0
% 0.12/0.45 % Clauses deleted for lack of memory : 0
% 0.12/0.45 % Backward-subsumed : 14
% 0.12/0.45 % Backward-rewritten : 19
% 0.12/0.45 % Generated clauses : 54
% 0.12/0.45 % ...of the previous two non-redundant : 56
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 23
% 0.12/0.45 % Paramodulations : 54
% 0.12/0.45 % Factorizations : 0
% 0.12/0.45 % NegExts : 0
% 0.12/0.45 % Equation resolutions : 0
% 0.12/0.45 % Disequality decompositions : 0
% 0.12/0.45 % Total rewrite steps : 28
% 0.12/0.45 % ...of those cached : 16
% 0.12/0.45 % Propositional unsat checks : 0
% 0.12/0.45 % Propositional check models : 0
% 0.12/0.45 % Propositional check unsatisfiable : 0
% 0.12/0.45 % Propositional clauses : 0
% 0.12/0.45 % Propositional clauses after purity: 0
% 0.12/0.45 % Propositional unsat core size : 0
% 0.12/0.45 % Propositional preprocessing time : 0.000
% 0.12/0.45 % Propositional encoding time : 0.000
% 0.12/0.45 % Propositional solver time : 0.000
% 0.12/0.45 % Success case prop preproc time : 0.000
% 0.12/0.45 % Success case prop encoding time : 0.000
% 0.12/0.45 % Success case prop solver time : 0.000
% 0.12/0.45 % Current number of processed clauses : 7
% 0.12/0.45 % Positive orientable unit clauses : 3
% 0.12/0.45 % Positive unorientable unit clauses: 0
% 0.12/0.45 % Negative unit clauses : 0
% 0.12/0.45 % Non-unit-clauses : 4
% 0.12/0.45 % Current number of unprocessed clauses: 8
% 0.12/0.45 % ...number of literals in the above : 121
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 43
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 451
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 229
% 0.12/0.45 % Non-unit clause-clause subsumptions : 38
% 0.12/0.45 % Unit Clause-clause subsumption calls : 0
% 0.12/0.45 % Rewrite failures with RHS unbound : 0
% 0.12/0.45 % BW rewrite match attempts : 10
% 0.12/0.45 % BW rewrite match successes : 10
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 6378
% 0.12/0.45 % Search garbage collected termcells : 112
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.009 s
% 0.12/0.45 % System time : 0.002 s
% 0.12/0.45 % Total time : 0.011 s
% 0.12/0.45 % Maximum resident set size: 3600 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.037 s
% 0.12/0.45 % System time : 0.012 s
% 0.12/0.45 % Total time : 0.049 s
% 0.12/0.45 % Maximum resident set size: 4608 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------