%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO666-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Thu Sep 24 03:48:23 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.54s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 11 unt; 0 def)
% Number of atoms : 439 ( 0 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 691 ( 326 ~; 363 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 136 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_185,axiom,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_185) ).
cnf(clause_42,axiom,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_42) ).
cnf(clause_83,axiom,
'LE'(f(X1),s(s('0'))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_83) ).
cnf(clause_98,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_98) ).
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/sandbox2/benchmark/theBenchmark.p',clause_29) ).
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/sandbox2/benchmark/theBenchmark.p',clause_179) ).
cnf(clause_70,axiom,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clause_123) ).
cnf(clause_12,axiom,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
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/sandbox2/benchmark/theBenchmark.p',clause_102) ).
cnf(c_0_10,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_11,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_42]) ).
cnf(c_0_12,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
c_0_10 ).
cnf(c_0_13,axiom,
'LE'(f(X1),s(s('0'))),
clause_83 ).
cnf(c_0_14,plain,
~ 'LE'(f(z),'0'),
inference(fof_simplification,[status(thm)],[clause_98]) ).
cnf(c_0_15,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
c_0_11 ).
cnf(c_0_16,plain,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_17,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_18,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_19,plain,
~ 'LE'(f(z),'0'),
c_0_14 ).
cnf(c_0_20,plain,
( 'E'('0',f(X1))
| 'E'(s('0'),f(X1))
| 'LE'(f(X1),'0') ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
c_0_17 ).
cnf(c_0_22,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_23,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_18 ).
cnf(c_0_24,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_13])]) ).
cnf(c_0_26,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
c_0_22 ).
cnf(c_0_27,plain,
( ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X3),suc(z))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(z)))
| 'E'('0',f(z)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( 'E'('0',f(X1))
| 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_29,plain,
( ~ 'E'(s('0'),f(suc(z)))
| iLEQ(suc(z),suc(z))
| 'E'('0',f(z)) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_30,plain,
( ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X3),suc(z))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| 'E'('0',f(z)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19]) ).
cnf(c_0_31,plain,
( iLEQ(suc(z),suc(z))
| 'E'('0',f(z)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_19]) ).
cnf(c_0_32,plain,
( ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X3),suc(z))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(z)))
| 'E'('0',f(z)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24]) ).
cnf(c_0_33,plain,
( ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X3),suc(z))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| 'E'('0',f(z)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_19]) ).
cnf(c_0_34,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_35,plain,
( ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(z)))
| 'E'('0',f(z)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_24]) ).
cnf(c_0_36,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
c_0_34 ).
cnf(c_0_37,plain,
( ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| 'E'('0',f(z)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_19]) ).
cnf(c_0_38,plain,
( 'E'('0',f(suc(X1)))
| 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(spm,[status(thm)],[c_0_36,c_0_16]) ).
cnf(c_0_39,plain,
( 'E'('0',f(suc(X1)))
| 'E'(s('0'),f(suc(suc(X1))))
| 'LE'(f(X1),'0') ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_40,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(z))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(z)))
| 'E'('0',f(z)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_31]),c_0_24]) ).
cnf(c_0_41,plain,
( ~ iLEQ(suc(X6),suc(X2))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X3),suc(X6))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X4),suc(suc(X1)))
| ~ '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)))
| 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_38]),c_0_39]) ).
cnf(c_0_42,plain,
( iLEQ(suc(suc(X1)),suc(suc(X1)))
| 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_38]),c_0_39]) ).
cnf(c_0_43,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(z))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| 'E'('0',f(z)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_19]) ).
cnf(c_0_44,plain,
( ~ iLEQ(suc(X3),suc(X5))
| ~ iLEQ(suc(X5),suc(suc(X1)))
| ~ iLEQ(suc(suc(X1)),suc(X4))
| ~ iLEQ(suc(X4),suc(suc(X2)))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X3)))
| 'E'('0',f(suc(X2)))
| 'E'('0',f(suc(X1)))
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38]),c_0_39]) ).
cnf(c_0_45,plain,
( ~ iLEQ(suc(X1),suc(z))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(z)))
| 'E'('0',f(z)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_31]),c_0_24]) ).
cnf(c_0_46,plain,
( ~ iLEQ(suc(suc(X3)),suc(X4))
| ~ iLEQ(suc(X4),suc(suc(X2)))
| ~ iLEQ(suc(suc(X1)),suc(suc(X3)))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(suc(X4)))
| 'E'('0',f(suc(X3)))
| 'E'('0',f(suc(X2)))
| 'E'('0',f(suc(X1)))
| '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_44,c_0_42]),c_0_38]),c_0_39]) ).
cnf(c_0_47,plain,
( ~ iLEQ(suc(X1),suc(z))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| 'E'('0',f(z)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_28]),c_0_19]) ).
cnf(c_0_48,plain,
( ~ iLEQ(suc(suc(X2)),suc(suc(X1)))
| ~ iLEQ(suc(suc(X1)),suc(suc(X3)))
| ~ iLEQ(suc(suc(X4)),suc(suc(X2)))
| 'E'('0',f(suc(X4)))
| 'E'('0',f(suc(X3)))
| 'E'('0',f(suc(X2)))
| 'E'('0',f(suc(X1)))
| '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_46,c_0_38]),c_0_39]) ).
cnf(c_0_49,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_50,plain,
( ~ 'E'(s('0'),f(suc(z)))
| 'E'('0',f(z)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_31]),c_0_24]) ).
cnf(c_0_51,plain,
( ~ iLEQ(suc(suc(X2)),suc(suc(X3)))
| ~ iLEQ(suc(suc(X3)),suc(suc(X1)))
| 'E'('0',f(suc(X3)))
| 'E'('0',f(suc(X2)))
| 'E'('0',f(suc(X1)))
| 'LE'(f(X3),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
fof(c_0_52,plain,
( ~ epred2_0
<=> ! [X5,X4,X2] :
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X5))
| ~ iLEQ(suc(z),suc(X5))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X5),suc(X4)) ) ),
introduced(definition) ).
cnf(c_0_53,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1)) ),
c_0_49 ).
cnf(c_0_54,plain,
'E'('0',f(z)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_19]) ).
cnf(c_0_55,plain,
( ~ iLEQ(suc(suc(X1)),suc(suc(X2)))
| 'E'('0',f(suc(X2)))
| 'E'('0',f(suc(X1)))
| 'LE'(f(X2),'0')
| 'LE'(f(X1),'0') ),
inference(spm,[status(thm)],[c_0_51,c_0_42]) ).
cnf(c_0_56,plain,
( ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(z),suc(X1))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
( ~ 'E'('0',f(suc(z)))
| iLEQ(suc(z),suc(z)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,plain,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(spm,[status(thm)],[c_0_55,c_0_42]) ).
cnf(c_0_59,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(z),suc(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(z)))
| epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_54]),c_0_57]) ).
cnf(c_0_60,plain,
'E'('0',f(suc(z))),
inference(spm,[status(thm)],[c_0_19,c_0_58]) ).
fof(c_0_61,plain,
( ~ epred1_0
<=> ! [X3,X1] :
( ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X3))
| ~ iLEQ(suc(X1),suc(z))
| ~ iLEQ(suc(X3),suc(X1)) ) ),
introduced(definition) ).
cnf(c_0_62,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_63,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(z),suc(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| epred2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_64,plain,
iLEQ(suc(z),suc(z)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_60])]) ).
cnf(c_0_65,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(z))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(z)))
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_61]) ).
cnf(c_0_66,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_62 ).
cnf(c_0_67,plain,
( ~ iLEQ(suc(z),suc(X1))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| epred2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_54]),c_0_60]),c_0_64])]) ).
cnf(c_0_68,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(z))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| epred1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_60])]) ).
cnf(c_0_69,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_54]),c_0_61]),c_0_52]) ).
cnf(c_0_70,plain,
epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_54]),c_0_60]),c_0_64])]) ).
cnf(c_0_71,plain,
( ~ iLEQ(suc(z),suc(X1))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| epred1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_54]),c_0_60])]) ).
cnf(c_0_72,plain,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_73,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_54]),c_0_60]),c_0_64])]),c_0_72]),
[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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n002.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 12:11:17 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.23/0.54 % Version: 3.5.1
% 0.23/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.54 % Starting sh5l with 300s (1) cores
% 0.23/0.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3243649 completed with status 0
% 0.23/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.54 % No SInE strategy applied
% 0.23/0.54 % Search class: FGHNF-FFMF11-SFFFFFNN
% 0.23/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.54 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.23/0.54 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.23/0.54 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y with 136s (1) cores
% 0.23/0.54 % G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with pid 3243660 completed with status 0
% 0.23/0.54 % Result found by G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S
% 0.23/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.54 % No SInE strategy applied
% 0.23/0.54 % Search class: FGHNF-FFMF11-SFFFFFNN
% 0.23/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.54 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.23/0.54 % Preprocessing time : 0.002 s
% 0.23/0.54 % Presaturation interreduction done
% 0.23/0.54
% 0.23/0.54 % Proof found!
% 0.23/0.54 % SZS status Unsatisfiable
% 0.23/0.54 % SZS output start CNFRefutation
% See solution above
% 0.23/0.54 % Parsed axioms : 10
% 0.23/0.54 % Removed by relevancy pruning/SinE : 0
% 0.23/0.54 % Initial clauses : 10
% 0.23/0.54 % Removed in clause preprocessing : 0
% 0.23/0.54 % Initial clauses in saturation : 10
% 0.23/0.54 % Processed clauses : 82
% 0.23/0.54 % ...of these trivial : 0
% 0.23/0.54 % ...subsumed : 5
% 0.23/0.54 % ...remaining for further processing : 76
% 0.23/0.54 % Other redundant clauses eliminated : 0
% 0.23/0.54 % Clauses deleted for lack of memory : 0
% 0.23/0.54 % Backward-subsumed : 32
% 0.23/0.54 % Backward-rewritten : 10
% 0.23/0.54 % Generated clauses : 110
% 0.23/0.54 % ...of the previous two non-redundant : 113
% 0.23/0.54 % ...aggressively subsumed : 0
% 0.23/0.54 % Contextual simplify-reflections : 16
% 0.23/0.54 % Paramodulations : 104
% 0.23/0.54 % Factorizations : 0
% 0.23/0.54 % NegExts : 0
% 0.23/0.54 % Equation resolutions : 0
% 0.23/0.54 % Disequality decompositions : 0
% 0.23/0.54 % Total rewrite steps : 20
% 0.23/0.54 % ...of those cached : 14
% 0.23/0.54 % Propositional unsat checks : 0
% 0.23/0.54 % Propositional check models : 0
% 0.23/0.54 % Propositional check unsatisfiable : 0
% 0.23/0.54 % Propositional clauses : 0
% 0.23/0.54 % Propositional clauses after purity: 0
% 0.23/0.54 % Propositional unsat core size : 0
% 0.23/0.54 % Propositional preprocessing time : 0.000
% 0.23/0.54 % Propositional encoding time : 0.000
% 0.23/0.54 % Propositional solver time : 0.000
% 0.23/0.54 % Success case prop preproc time : 0.000
% 0.23/0.54 % Success case prop encoding time : 0.000
% 0.23/0.54 % Success case prop solver time : 0.000
% 0.23/0.54 % Current number of processed clauses : 22
% 0.23/0.54 % Positive orientable unit clauses : 5
% 0.23/0.54 % Positive unorientable unit clauses: 0
% 0.23/0.54 % Negative unit clauses : 2
% 0.23/0.54 % Non-unit-clauses : 15
% 0.23/0.54 % Current number of unprocessed clauses: 8
% 0.23/0.54 % ...number of literals in the above : 60
% 0.23/0.54 % Current number of archived formulas : 0
% 0.23/0.54 % Current number of archived clauses : 52
% 0.23/0.54 % Clause-clause subsumption calls (NU) : 1358
% 0.23/0.54 % Rec. Clause-clause subsumption calls : 310
% 0.23/0.54 % Non-unit clause-clause subsumptions : 53
% 0.23/0.54 % Unit Clause-clause subsumption calls : 43
% 0.23/0.54 % Rewrite failures with RHS unbound : 0
% 0.23/0.54 % BW rewrite match attempts : 9
% 0.23/0.54 % BW rewrite match successes : 3
% 0.23/0.54 % Condensation attempts : 0
% 0.23/0.54 % Condensation successes : 0
% 0.23/0.54 % Termbank termtop insertions : 10077
% 0.23/0.54 % Search garbage collected termcells : 112
% 0.23/0.54
% 0.23/0.54 % -------------------------------------------------
% 0.23/0.54 % User time : 0.022 s
% 0.23/0.54 % System time : 0.007 s
% 0.23/0.54 % Total time : 0.029 s
% 0.23/0.54 % Maximum resident set size: 3652 pages
% 0.23/0.54
% 0.23/0.54 % -------------------------------------------------
% 0.23/0.54 % User time : 0.115 s
% 0.23/0.54 % System time : 0.020 s
% 0.23/0.54 % Total time : 0.135 s
% 0.23/0.54 % Maximum resident set size: 4864 pages
% 0.23/0.54 % E exiting
%------------------------------------------------------------------------------