%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO683-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 03:43:08 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 78 ( 10 unt; 0 def)
% Number of atoms : 366 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 566 ( 278 ~; 288 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 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 : 211 ( 211 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,A_4] :
( iLEQ(suc(A_4),suc(A_4))
| ~ 'E'('0',f(suc(A_4)))
| ~ 'E'('0',f(A_4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,A_3] :
( iLEQ(suc(A_3),suc(A_3))
| ~ 'E'(s('0'),f(suc(A_3)))
| ~ 'E'(s('0'),f(A_3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [LE,A] : 'LE'(f(A),s(s(s(s('0'))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [E,A_2] :
( iLEQ(suc(A_2),suc(A_2))
| ~ 'E'(s(s('0')),f(suc(A_2)))
| ~ 'E'(s(s('0')),f(A_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [E,B_159,B_162,B_160,B_161,A_1] :
( ~ iLEQ(suc(A_1),suc(B_159))
| ~ 'E'(s(s(s('0'))),f(suc(A_1)))
| ~ 'E'(s(s(s('0'))),f(suc(B_160)))
| ~ iLEQ(suc(B_161),suc(B_162))
| ~ 'E'(s(s(s('0'))),f(suc(B_161)))
| ~ 'E'(s(s(s('0'))),f(A_1))
| ~ iLEQ(suc(B_159),suc(B_160))
| ~ 'E'(s(s(s('0'))),f(B_160))
| ~ 'E'(s(s(s('0'))),f(B_161))
| ~ 'E'(s(s(s('0'))),f(B_159))
| ~ 'E'(s(s(s('0'))),f(suc(B_162)))
| ~ iLEQ(suc(B_160),suc(B_161))
| ~ 'E'(s(s(s('0'))),f(B_162))
| ~ 'E'(s(s(s('0'))),f(suc(B_159))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [LE,B_247,E] :
( 'LE'(f(B_247),s(s('0')))
| 'E'(s(s('0')),f(suc(B_247)))
| ~ 'LE'(f(suc(B_247)),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [LE,B_247,E] :
( 'LE'(f(B_247),s(s('0')))
| 'E'(s(s('0')),f(B_247))
| ~ 'LE'(f(B_247),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [LE,B_158,E] :
( 'LE'(f(B_158),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(B_158)))
| ~ 'LE'(f(suc(B_158)),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [LE] : ~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [LE,B_309,E] :
( 'LE'(f(B_309),'0')
| 'E'('0',f(suc(B_309)))
| ~ 'LE'(f(suc(B_309)),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [E,B_249,B_250,A_2,B_248,B_251] :
( ~ iLEQ(suc(B_250),suc(B_251))
| ~ 'E'(s(s('0')),f(A_2))
| ~ 'E'(s(s('0')),f(B_249))
| ~ iLEQ(suc(B_248),suc(B_249))
| ~ 'E'(s(s('0')),f(suc(B_250)))
| ~ 'E'(s(s('0')),f(suc(B_248)))
| ~ 'E'(s(s('0')),f(B_251))
| ~ 'E'(s(s('0')),f(suc(A_2)))
| ~ iLEQ(suc(B_249),suc(B_250))
| ~ 'E'(s(s('0')),f(suc(B_251)))
| ~ 'E'(s(s('0')),f(B_248))
| ~ iLEQ(suc(A_2),suc(B_248))
| ~ 'E'(s(s('0')),f(B_250))
| ~ 'E'(s(s('0')),f(suc(B_249))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [LE,B_158,E] :
( 'LE'(f(B_158),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(B_158))
| ~ 'LE'(f(B_158),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [E,A_1] :
( iLEQ(suc(A_1),suc(A_1))
| ~ 'E'(s(s(s('0'))),f(suc(A_1)))
| ~ 'E'(s(s(s('0'))),f(A_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [LE,B_291,E] :
( 'LE'(f(B_291),s('0'))
| 'E'(s('0'),f(suc(B_291)))
| ~ 'LE'(f(suc(B_291)),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [LE,B_291,E] :
( 'LE'(f(B_291),s('0'))
| 'E'(s('0'),f(B_291))
| ~ 'LE'(f(B_291),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [E,B_310,B_311,B_313,B_312,A_4] :
( ~ 'E'('0',f(A_4))
| ~ iLEQ(suc(B_312),suc(B_313))
| ~ 'E'('0',f(suc(A_4)))
| ~ iLEQ(suc(A_4),suc(B_310))
| ~ iLEQ(suc(B_310),suc(B_311))
| ~ iLEQ(suc(B_311),suc(B_312))
| ~ 'E'('0',f(B_313))
| ~ 'E'('0',f(suc(B_312)))
| ~ 'E'('0',f(B_312))
| ~ 'E'('0',f(B_310))
| ~ 'E'('0',f(suc(B_313)))
| ~ 'E'('0',f(B_311))
| ~ 'E'('0',f(suc(B_311)))
| ~ 'E'('0',f(suc(B_310))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [LE,B_309,E] :
( 'LE'(f(B_309),'0')
| 'E'('0',f(B_309))
| ~ 'LE'(f(B_309),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [E,B_294,B_295,B_292,A_3,B_293] :
( ~ iLEQ(suc(B_292),suc(B_293))
| ~ iLEQ(suc(B_293),suc(B_294))
| ~ 'E'(s('0'),f(suc(B_293)))
| ~ 'E'(s('0'),f(A_3))
| ~ iLEQ(suc(B_294),suc(B_295))
| ~ 'E'(s('0'),f(B_293))
| ~ iLEQ(suc(A_3),suc(B_292))
| ~ 'E'(s('0'),f(B_292))
| ~ 'E'(s('0'),f(B_294))
| ~ 'E'(s('0'),f(suc(A_3)))
| ~ 'E'(s('0'),f(suc(B_292)))
| ~ 'E'(s('0'),f(suc(B_295)))
| ~ 'E'(s('0'),f(B_295))
| ~ 'E'(s('0'),f(suc(B_294))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [A_4] :
( iLEQ(suc(A_4),suc(A_4))
| ~ 'E'('0',f(suc(A_4)))
| ~ 'E'('0',f(A_4)) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f20,plain,
! [E,X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [A_3] :
( iLEQ(suc(A_3),suc(A_3))
| ~ 'E'(s('0'),f(suc(A_3)))
| ~ 'E'(s('0'),f(A_3)) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f22,plain,
! [E,X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [A] : 'LE'(f(A),s(s(s(s('0'))))),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f24,plain,
! [LE,X0] : 'LE'(f(X0),s(s(s(s('0'))))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [A_2] :
( iLEQ(suc(A_2),suc(A_2))
| ~ 'E'(s(s('0')),f(suc(A_2)))
| ~ 'E'(s(s('0')),f(A_2)) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f26,plain,
! [E,X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [B_159,A_1] :
( ~ iLEQ(suc(A_1),suc(B_159))
| ~ 'E'(s(s(s('0'))),f(suc(A_1)))
| ! [B_160] :
( ~ 'E'(s(s(s('0'))),f(suc(B_160)))
| ! [B_162,B_161] :
( ~ iLEQ(suc(B_161),suc(B_162))
| ~ 'E'(s(s(s('0'))),f(suc(B_161)))
| ~ 'E'(s(s(s('0'))),f(A_1))
| ~ iLEQ(suc(B_159),suc(B_160))
| ~ 'E'(s(s(s('0'))),f(B_160))
| ~ 'E'(s(s(s('0'))),f(B_161))
| ~ 'E'(s(s(s('0'))),f(B_159))
| ~ 'E'(s(s(s('0'))),f(suc(B_162)))
| ~ iLEQ(suc(B_160),suc(B_161))
| ~ 'E'(s(s(s('0'))),f(B_162))
| ~ 'E'(s(s(s('0'))),f(suc(B_159))) ) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f28,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ iLEQ(suc(X4),suc(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [B_247] :
( 'LE'(f(B_247),s(s('0')))
| 'E'(s(s('0')),f(suc(B_247)))
| ~ 'LE'(f(suc(B_247)),s(s(s('0')))) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f30,plain,
! [LE,X0,E] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s(s('0')))) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [B_247] :
( 'LE'(f(B_247),s(s('0')))
| 'E'(s(s('0')),f(B_247))
| ~ 'LE'(f(B_247),s(s(s('0')))) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f32,plain,
! [LE,X0,E] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0))
| ~ 'LE'(f(X0),s(s(s('0')))) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [B_158] :
( 'LE'(f(B_158),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(B_158)))
| ~ 'LE'(f(suc(B_158)),s(s(s(s('0'))))) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f34,plain,
! [LE,X0,E] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s(s(s('0'))))) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [LE] : ~ 'LE'(f(z),'0'),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
! [B_309] :
( 'LE'(f(B_309),'0')
| 'E'('0',f(suc(B_309)))
| ~ 'LE'(f(suc(B_309)),s('0')) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f37,plain,
! [LE,X0,E] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s('0')) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [B_250,B_251] :
( ~ iLEQ(suc(B_250),suc(B_251))
| ! [A_2] :
( ~ 'E'(s(s('0')),f(A_2))
| ! [B_249] :
( ~ 'E'(s(s('0')),f(B_249))
| ! [B_248] :
( ~ iLEQ(suc(B_248),suc(B_249))
| ~ 'E'(s(s('0')),f(suc(B_250)))
| ~ 'E'(s(s('0')),f(suc(B_248)))
| ~ 'E'(s(s('0')),f(B_251))
| ~ 'E'(s(s('0')),f(suc(A_2)))
| ~ iLEQ(suc(B_249),suc(B_250))
| ~ 'E'(s(s('0')),f(suc(B_251)))
| ~ 'E'(s(s('0')),f(B_248))
| ~ iLEQ(suc(A_2),suc(B_248))
| ~ 'E'(s(s('0')),f(B_250))
| ~ 'E'(s(s('0')),f(suc(B_249))) ) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f39,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ iLEQ(suc(X1),suc(X4))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X3),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(X3))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [B_158] :
( 'LE'(f(B_158),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(B_158))
| ~ 'LE'(f(B_158),s(s(s(s('0'))))) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f41,plain,
! [LE,X0,E] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [A_1] :
( iLEQ(suc(A_1),suc(A_1))
| ~ 'E'(s(s(s('0'))),f(suc(A_1)))
| ~ 'E'(s(s(s('0'))),f(A_1)) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f43,plain,
! [E,X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [B_291] :
( 'LE'(f(B_291),s('0'))
| 'E'(s('0'),f(suc(B_291)))
| ~ 'LE'(f(suc(B_291)),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f45,plain,
! [LE,X0,E] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s(s('0'))) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [B_291] :
( 'LE'(f(B_291),s('0'))
| 'E'(s('0'),f(B_291))
| ~ 'LE'(f(B_291),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f47,plain,
! [LE,X0,E] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| ~ 'LE'(f(X0),s(s('0'))) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [A_4] :
( ~ 'E'('0',f(A_4))
| ! [B_313,B_312] :
( ~ iLEQ(suc(B_312),suc(B_313))
| ~ 'E'('0',f(suc(A_4)))
| ! [B_310] :
( ~ iLEQ(suc(A_4),suc(B_310))
| ! [B_311] :
( ~ iLEQ(suc(B_310),suc(B_311))
| ~ iLEQ(suc(B_311),suc(B_312))
| ~ 'E'('0',f(B_313))
| ~ 'E'('0',f(suc(B_312)))
| ~ 'E'('0',f(B_312))
| ~ 'E'('0',f(B_310))
| ~ 'E'('0',f(suc(B_313)))
| ~ 'E'('0',f(B_311))
| ~ 'E'('0',f(suc(B_311)))
| ~ 'E'('0',f(suc(B_310))) ) ) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f49,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ 'E'('0',f(X4))
| ~ iLEQ(suc(X3),suc(X2))
| ~ 'E'('0',f(suc(X4)))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X0))) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [B_309] :
( 'LE'(f(B_309),'0')
| 'E'('0',f(B_309))
| ~ 'LE'(f(B_309),s('0')) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f51,plain,
! [LE,X0,E] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| ~ 'LE'(f(X0),s('0')) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [B_292,B_293] :
( ~ iLEQ(suc(B_292),suc(B_293))
| ! [B_294] :
( ~ iLEQ(suc(B_293),suc(B_294))
| ~ 'E'(s('0'),f(suc(B_293)))
| ! [A_3] :
( ~ 'E'(s('0'),f(A_3))
| ! [B_295] :
( ~ iLEQ(suc(B_294),suc(B_295))
| ~ 'E'(s('0'),f(B_293))
| ~ iLEQ(suc(A_3),suc(B_292))
| ~ 'E'(s('0'),f(B_292))
| ~ 'E'(s('0'),f(B_294))
| ~ 'E'(s('0'),f(suc(A_3)))
| ~ 'E'(s('0'),f(suc(B_292)))
| ~ 'E'(s('0'),f(suc(B_295)))
| ~ 'E'(s('0'),f(B_295))
| ~ 'E'(s('0'),f(suc(B_294))) ) ) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f53,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ iLEQ(suc(X2),suc(X4))
| ~ iLEQ(suc(X4),suc(X0))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X3),suc(X2))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f101,plain,
! [E,X0] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(resolution,[status(thm)],[f43,f28]) ).
fof(f109,plain,
! [E,X0] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f101]) ).
fof(f117,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f24]) ).
fof(f119,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f24]) ).
fof(f120,plain,
! [LE,X0,E] :
( ~ 'E'(s(s(s('0'))),f(X0))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(resolution,[status(thm)],[f119,f109]) ).
fof(f121,plain,
! [LE,X0] : 'LE'(f(X0),s(s(s('0')))),
inference(forward_subsumption_resolution,[status(thm)],[f120,f117]) ).
fof(f122,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[f30,f121]) ).
fof(f123,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f32,f121]) ).
fof(f128,plain,
! [E,X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[status(thm)],[f39,f26]) ).
fof(f168,plain,
! [E,X0] :
( ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f128]) ).
fof(f207,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s('0')))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[status(thm)],[f168,f122]) ).
fof(f209,plain,
! [LE,X0] : 'LE'(f(X0),s(s('0'))),
inference(forward_subsumption_resolution,[status(thm)],[f207,f123]) ).
fof(f210,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[f45,f209]) ).
fof(f211,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f47,f209]) ).
fof(f230,plain,
! [E,X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X0))) ),
inference(resolution,[status(thm)],[f49,f20]) ).
fof(f255,plain,
! [E,X0] :
( ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f230]) ).
fof(f289,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[status(thm)],[f53,f22]) ).
fof(f315,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f289]) ).
fof(f325,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[status(thm)],[f315,f210]) ).
fof(f327,plain,
! [LE,X0] : 'LE'(f(X0),s('0')),
inference(forward_subsumption_resolution,[status(thm)],[f325,f211]) ).
fof(f328,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[f37,f327]) ).
fof(f329,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f327]) ).
fof(f331,plain,
! [LE,X0,E] :
( ~ 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
inference(resolution,[status(thm)],[f328,f255]) ).
fof(f332,plain,
! [LE,X0] : 'LE'(f(X0),'0'),
inference(forward_subsumption_resolution,[status(thm)],[f331,f329]) ).
fof(f334,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f35,f332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO683-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 12:14:30 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.43 % Refutation found
% 0.12/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.085449 seconds
% 0.12/0.44 % CPU time: 0.446286 seconds
% 0.12/0.44 % Total memory used: 8.277 MB
% 0.12/0.44 % Net memory used: 7.672 MB
%------------------------------------------------------------------------------