%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO683-1 : 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 : n015.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 03:48:26 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of clauses : 87 ( 10 unt; 40 nHn; 72 RR)
% Number of literals : 452 ( 0 equ; 343 neg)
% Maximal clause size : 14 ( 5 avg)
% Maximal term depth : 5 ( 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 : 175 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_443,axiom,
( ~ 'LE'(f(suc(X1)),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_443) ).
cnf(clause_539,axiom,
( ~ 'LE'(f(X1),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_539) ).
cnf(clause_560,axiom,
( ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(X5))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_560) ).
cnf(clause_451,axiom,
'LE'(f(X1),s(s(s(s('0'))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_451) ).
cnf(clause_59,axiom,
( ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_59) ).
cnf(clause_563,axiom,
( ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(X5))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X5)))
| ~ 'E'(s(s('0')),f(X4))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_563) ).
cnf(clause_29,axiom,
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29) ).
cnf(clause_151,axiom,
( ~ iLEQ(suc(X3),suc(X5))
| ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'(s('0'),f(X3))
| ~ '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(X2))
| ~ 'E'(s('0'),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_151) ).
cnf(clause_398,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_398) ).
cnf(clause_476,axiom,
( ~ 'LE'(f(suc(X1)),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_476) ).
cnf(clause_97,axiom,
( ~ 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_97) ).
cnf(clause_442,axiom,
( ~ 'E'('0',f(X5))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'('0',f(suc(X5)))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_442) ).
cnf(clause_469,axiom,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_469) ).
cnf(clause_222,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_222) ).
cnf(clause_44,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_44) ).
cnf(clause_547,axiom,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_547) ).
cnf(clause_89,axiom,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_89) ).
cnf(clause_287,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_287) ).
cnf(c_0_18,plain,
( ~ 'LE'(f(suc(X1)),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_443]) ).
cnf(c_0_19,plain,
( ~ 'LE'(f(X1),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_539]) ).
cnf(c_0_20,plain,
( ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(X5))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_560]) ).
cnf(c_0_21,plain,
( ~ 'LE'(f(suc(X1)),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X1))) ),
c_0_18 ).
cnf(c_0_22,axiom,
'LE'(f(X1),s(s(s(s('0'))))),
clause_451 ).
cnf(c_0_23,plain,
( ~ 'LE'(f(X1),s(s(s(s('0')))))
| 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1)) ),
c_0_19 ).
cnf(c_0_24,plain,
( ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(X5))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
c_0_20 ).
cnf(c_0_25,plain,
( 'E'(s(s(s('0'))),f(suc(X1)))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_26,plain,
( 'E'(s(s(s('0'))),f(X1))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_22])]) ).
cnf(c_0_27,plain,
( ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(X5))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ iLEQ(suc(X2),suc(X5))
| ~ iLEQ(suc(X5),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,plain,
( ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(X5))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ iLEQ(suc(X3),suc(X5))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X1),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
( ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(X5))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ iLEQ(suc(X4),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X3),suc(X5))
| ~ iLEQ(suc(X2),suc(X4))
| 'LE'(f(X3),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
( ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_59]) ).
cnf(c_0_31,plain,
( ~ 'E'(s(s(s('0'))),f(X5))
| ~ 'E'(s(s(s('0'))),f(suc(X5)))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X3),suc(X5))
| 'LE'(f(X4),s(s(s('0'))))
| 'LE'(f(X3),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_26]) ).
cnf(c_0_32,plain,
( ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
c_0_30 ).
cnf(c_0_33,plain,
( ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(X5))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X5)))
| ~ 'E'(s(s('0')),f(X4))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_563]) ).
cnf(c_0_34,plain,
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_29]) ).
cnf(c_0_35,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X3),suc(X1))
| 'LE'(f(X5),s(s(s('0'))))
| 'LE'(f(X4),s(s(s('0'))))
| 'LE'(f(X3),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_26]) ).
cnf(c_0_36,plain,
( iLEQ(suc(X1),suc(X1))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_26]) ).
cnf(c_0_37,plain,
( ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(X5))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X5)))
| ~ 'E'(s(s('0')),f(X4))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
c_0_33 ).
cnf(c_0_38,plain,
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
c_0_34 ).
cnf(c_0_39,plain,
( ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X2),suc(X1))
| 'LE'(f(X4),s(s(s('0'))))
| 'LE'(f(X3),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( ~ iLEQ(suc(X3),suc(X5))
| ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'(s('0'),f(X3))
| ~ '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(X2))
| ~ 'E'(s('0'),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_151]) ).
cnf(c_0_41,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_398]) ).
cnf(c_0_42,plain,
( ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| 'LE'(f(X3),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(spm,[status(thm)],[c_0_39,c_0_36]) ).
cnf(c_0_44,plain,
( ~ iLEQ(suc(X3),suc(X5))
| ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'(s('0'),f(X3))
| ~ '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(X2))
| ~ 'E'(s('0'),f(suc(X1))) ),
c_0_40 ).
cnf(c_0_45,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1)) ),
c_0_41 ).
cnf(c_0_46,plain,
( ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_47,plain,
( ~ 'LE'(f(suc(X1)),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_476]) ).
cnf(c_0_48,plain,
( ~ iLEQ(suc(X2),suc(X1))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(spm,[status(thm)],[c_0_43,c_0_36]) ).
cnf(c_0_49,plain,
( ~ 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_97]) ).
cnf(c_0_50,plain,
( ~ 'E'('0',f(X5))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'('0',f(suc(X5)))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_442]) ).
cnf(c_0_51,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_469]) ).
cnf(c_0_52,plain,
( ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,plain,
( ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_46,c_0_38]) ).
cnf(c_0_54,plain,
( ~ 'LE'(f(suc(X1)),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(X1))) ),
c_0_47 ).
cnf(c_0_55,plain,
'LE'(f(X1),s(s(s('0')))),
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
cnf(c_0_56,plain,
( ~ 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1)) ),
c_0_49 ).
cnf(c_0_57,plain,
( ~ 'E'('0',f(X5))
| ~ iLEQ(suc(X4),suc(X3))
| ~ 'E'('0',f(suc(X5)))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1))) ),
c_0_50 ).
cnf(c_0_58,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1)) ),
c_0_51 ).
cnf(c_0_59,plain,
( ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_45]) ).
cnf(c_0_60,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_222]) ).
cnf(c_0_61,plain,
( ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
inference(spm,[status(thm)],[c_0_53,c_0_38]) ).
cnf(c_0_62,plain,
( 'E'(s(s('0')),f(suc(X1)))
| 'LE'(f(X1),s(s('0'))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_63,plain,
( 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_55])]) ).
cnf(c_0_64,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_44]) ).
cnf(c_0_65,plain,
( ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X4)))
| ~ iLEQ(suc(X4),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
( ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_45]) ).
cnf(c_0_67,plain,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
c_0_60 ).
cnf(c_0_68,plain,
'LE'(f(X1),s(s('0'))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_69,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
c_0_64 ).
cnf(c_0_70,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_58]) ).
cnf(c_0_71,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_547]) ).
cnf(c_0_72,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1))) ),
inference(spm,[status(thm)],[c_0_66,c_0_45]) ).
cnf(c_0_73,plain,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_74,plain,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_68])]) ).
cnf(c_0_75,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_89]) ).
cnf(c_0_76,plain,
( ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_58]) ).
cnf(c_0_77,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
c_0_71 ).
cnf(c_0_78,plain,
'LE'(f(X1),s('0')),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_79,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
c_0_75 ).
cnf(c_0_80,plain,
~ 'LE'(f(z),'0'),
inference(fof_simplification,[status(thm)],[clause_287]) ).
cnf(c_0_81,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1))) ),
inference(spm,[status(thm)],[c_0_76,c_0_58]) ).
cnf(c_0_82,plain,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_83,plain,
( 'E'('0',f(X1))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_78])]) ).
cnf(c_0_84,plain,
~ 'LE'(f(z),'0'),
c_0_80 ).
cnf(c_0_85,plain,
'LE'(f(X1),'0'),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_86,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO683-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 12:12:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1421274 completed with status 0
% 0.14/0.44 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FGHNF-FFMF11-MFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 1421281 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FGHNF-FFMF11-MFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Preprocessing time : 0.002 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 18
% 0.14/0.44 % Removed by relevancy pruning/SinE : 0
% 0.14/0.44 % Initial clauses : 18
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 18
% 0.14/0.44 % Processed clauses : 68
% 0.14/0.44 % ...of these trivial : 0
% 0.14/0.44 % ...subsumed : 0
% 0.14/0.44 % ...remaining for further processing : 68
% 0.14/0.44 % Other redundant clauses eliminated : 0
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 42
% 0.14/0.44 % Backward-rewritten : 15
% 0.14/0.44 % Generated clauses : 233
% 0.14/0.44 % ...of the previous two non-redundant : 176
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 9
% 0.14/0.44 % Paramodulations : 233
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 0
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 19
% 0.14/0.44 % ...of those cached : 8
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 11
% 0.14/0.44 % Positive orientable unit clauses : 6
% 0.14/0.44 % Positive unorientable unit clauses: 0
% 0.14/0.44 % Negative unit clauses : 0
% 0.14/0.44 % Non-unit-clauses : 5
% 0.14/0.44 % Current number of unprocessed clauses: 62
% 0.14/0.44 % ...number of literals in the above : 682
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 57
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 1200
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 191
% 0.14/0.44 % Non-unit clause-clause subsumptions : 46
% 0.14/0.44 % Unit Clause-clause subsumption calls : 42
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 14
% 0.14/0.44 % BW rewrite match successes : 9
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 18161
% 0.14/0.44 % Search garbage collected termcells : 174
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.016 s
% 0.14/0.44 % System time : 0.005 s
% 0.14/0.44 % Total time : 0.021 s
% 0.14/0.44 % Maximum resident set size: 3664 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.086 s
% 0.14/0.44 % System time : 0.011 s
% 0.14/0.44 % Total time : 0.097 s
% 0.14/0.44 % Maximum resident set size: 4608 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------