%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO657-1 : 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 : n012.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 03:48:21 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of clauses : 80 ( 8 unt; 38 nHn; 69 RR)
% Number of literals : 383 ( 0 equ; 277 neg)
% Maximal clause size : 9 ( 4 avg)
% Maximal term depth : 4 ( 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 : 108 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_38,axiom,
( ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_38) ).
cnf(clause_52,axiom,
( ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_52) ).
cnf(clause_56,axiom,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_56) ).
cnf(clause_33,axiom,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_33) ).
cnf(clause_45,axiom,
( ~ 'LE'(f(suc(suc(X1))),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(suc(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_45) ).
cnf(clause_9,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_9) ).
cnf(clause_32,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_32) ).
cnf(clause_17,axiom,
'LE'(f(X1),s(s('0'))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
cnf(clause_5,axiom,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
cnf(clause_23,axiom,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
cnf(clause_31,axiom,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
cnf(clause_10,axiom,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
cnf(clause_15,axiom,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
cnf(clause_43,axiom,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_43) ).
cnf(clause_41,axiom,
( ~ 'E'('0',f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_41) ).
cnf(clause_26,axiom,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
cnf(clause_51,axiom,
( ~ 'LE'(f(suc(suc(X1))),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(suc(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_51) ).
cnf(clause_34,axiom,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
cnf(clause_40,axiom,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_40) ).
cnf(clause_24,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
cnf(c_0_20,plain,
( ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_38]) ).
cnf(c_0_21,plain,
( ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_52]) ).
cnf(c_0_22,plain,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2))) ),
inference(fof_simplification,[status(thm)],[clause_56]) ).
cnf(c_0_23,plain,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(fof_simplification,[status(thm)],[clause_33]) ).
cnf(c_0_24,plain,
( ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X1),f(suc(X1))) ),
c_0_20 ).
cnf(c_0_25,plain,
( ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
c_0_21 ).
cnf(c_0_26,plain,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X2),f(suc(X2))) ),
c_0_22 ).
cnf(c_0_27,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(suc(X1)))) ),
inference(fof_simplification,[status(thm)],[clause_45]) ).
cnf(c_0_28,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_9]) ).
cnf(c_0_29,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_32]) ).
cnf(c_0_30,plain,
( ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ iLEQ(suc(X1),suc(X2)) ),
c_0_23 ).
cnf(c_0_31,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X1),f(suc(X1))) ),
inference(csr,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( ~ '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(suc(X2))))
| ~ iLEQ(suc(X2),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(csr,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_33,plain,
( ~ 'LE'(f(suc(suc(X1))),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(suc(X1)))) ),
c_0_27 ).
cnf(c_0_34,axiom,
'LE'(f(X1),s(s('0'))),
clause_17 ).
cnf(c_0_35,plain,
( ~ 'LE'(f(X1),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
c_0_28 ).
cnf(c_0_36,plain,
( ~ 'LE'(f(suc(X1)),s(s('0')))
| 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
c_0_29 ).
cnf(c_0_37,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_5]) ).
cnf(c_0_38,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_23]) ).
cnf(c_0_39,plain,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_31]) ).
cnf(c_0_40,plain,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_10]) ).
cnf(c_0_41,plain,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
inference(fof_simplification,[status(thm)],[clause_15]) ).
cnf(c_0_42,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_43,plain,
( 'E'(s('0'),f(suc(suc(X1))))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_44,plain,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_34])]) ).
cnf(c_0_45,plain,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0')) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_34])]) ).
cnf(c_0_46,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
c_0_37 ).
cnf(c_0_47,plain,
( ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
c_0_38 ).
cnf(c_0_48,plain,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_43]) ).
cnf(c_0_49,plain,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X1),f(suc(X1))) ),
c_0_39 ).
cnf(c_0_50,plain,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
c_0_40 ).
cnf(c_0_51,plain,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X2),f(suc(X2))) ),
c_0_41 ).
cnf(c_0_52,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(fof_simplification,[status(thm)],[clause_41]) ).
cnf(c_0_53,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_26]) ).
cnf(c_0_54,plain,
( ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ iLEQ(suc(X2),suc(X1))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_55,plain,
( ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(csr,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,plain,
( ~ 'E'('0',f(suc(X2)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'('0',f(suc(X1))) ),
c_0_48 ).
cnf(c_0_57,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ iLEQ(suc(X1),suc(X2))
| 'E'(f(X1),f(suc(X1))) ),
inference(csr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,plain,
( ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ iLEQ(suc(X2),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
inference(csr,[status(thm)],[c_0_51,c_0_50]) ).
cnf(c_0_59,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
c_0_52 ).
cnf(c_0_60,plain,
( ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| iLEQ(suc(X1),suc(X1))
| 'E'(f(X1),f(suc(X1))) ),
c_0_53 ).
cnf(c_0_61,plain,
( ~ 'LE'(f(suc(suc(X1))),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(suc(X1)))) ),
inference(fof_simplification,[status(thm)],[clause_51]) ).
cnf(c_0_62,plain,
( ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_63,plain,
( iLEQ(suc(X1),suc(X1))
| 'LE'(f(X1),s('0')) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_64,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
inference(fof_simplification,[status(thm)],[clause_34]) ).
cnf(c_0_65,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
inference(fof_simplification,[status(thm)],[clause_40]) ).
cnf(c_0_66,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ iLEQ(suc(X1),suc(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_67,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1))))
| iLEQ(suc(X1),suc(X1)) ),
inference(csr,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
( ~ 'LE'(f(suc(suc(X1))),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(suc(X1)))) ),
c_0_61 ).
cnf(c_0_69,plain,
'LE'(f(X1),s('0')),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,plain,
( ~ 'LE'(f(X1),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
c_0_64 ).
cnf(c_0_71,plain,
( ~ 'LE'(f(suc(X1)),s('0'))
| 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
c_0_65 ).
cnf(c_0_72,plain,
~ 'LE'(f(z),'0'),
inference(fof_simplification,[status(thm)],[clause_24]) ).
cnf(c_0_73,plain,
( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X1)))) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,plain,
( 'E'('0',f(suc(suc(X1))))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
cnf(c_0_75,plain,
( 'E'('0',f(X1))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_69])]) ).
cnf(c_0_76,plain,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0') ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_69])]) ).
cnf(c_0_77,plain,
~ 'LE'(f(z),'0'),
c_0_72 ).
cnf(c_0_78,plain,
'LE'(f(X1),'0'),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_76]) ).
cnf(c_0_79,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO657-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 12:07:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S 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--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2318435 completed with status 0
% 0.12/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.12/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S 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-MFFFFFNN
% 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--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.45 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2318438 completed with status 0
% 0.12/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S 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-MFFFFFNN
% 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--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_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 : 20
% 0.12/0.45 % Removed by relevancy pruning/SinE : 0
% 0.12/0.45 % Initial clauses : 20
% 0.12/0.45 % Removed in clause preprocessing : 0
% 0.12/0.45 % Initial clauses in saturation : 20
% 0.12/0.45 % Processed clauses : 54
% 0.12/0.45 % ...of these trivial : 0
% 0.12/0.45 % ...subsumed : 1
% 0.12/0.45 % ...remaining for further processing : 53
% 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 : 11
% 0.12/0.45 % Backward-rewritten : 11
% 0.12/0.45 % Generated clauses : 47
% 0.12/0.45 % ...of the previous two non-redundant : 50
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 20
% 0.12/0.45 % Paramodulations : 47
% 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 : 17
% 0.12/0.45 % ...of those cached : 7
% 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 : 11
% 0.12/0.45 % Positive orientable unit clauses : 5
% 0.12/0.45 % Positive unorientable unit clauses: 0
% 0.12/0.45 % Negative unit clauses : 0
% 0.12/0.45 % Non-unit-clauses : 6
% 0.12/0.45 % Current number of unprocessed clauses: 36
% 0.12/0.45 % ...number of literals in the above : 200
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 42
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 224
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 85
% 0.12/0.45 % Non-unit clause-clause subsumptions : 27
% 0.12/0.45 % Unit Clause-clause subsumption calls : 13
% 0.12/0.45 % Rewrite failures with RHS unbound : 0
% 0.12/0.45 % BW rewrite match attempts : 9
% 0.12/0.45 % BW rewrite match successes : 6
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 4395
% 0.12/0.45 % Search garbage collected termcells : 106
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.007 s
% 0.12/0.45 % System time : 0.003 s
% 0.12/0.45 % Total time : 0.010 s
% 0.12/0.45 % Maximum resident set size: 3652 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.034 s
% 0.12/0.45 % System time : 0.010 s
% 0.12/0.45 % Total time : 0.045 s
% 0.12/0.45 % Maximum resident set size: 4864 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------