%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO674-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 03:43:07 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 25
% Syntax : Number of formulae : 107 ( 7 unt; 11 def)
% Number of atoms : 515 ( 0 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 804 ( 396 ~; 397 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 227 ( 227 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,B_233,B_232,B_230,B_231,B_229,A_2] :
( ~ iLEQ(suc(B_231),suc(B_232))
| ~ 'E'(s('0'),f(A_2))
| ~ iLEQ(suc(B_232),suc(B_233))
| ~ 'E'(s('0'),f(suc(B_230)))
| ~ 'E'(s('0'),f(B_230))
| ~ 'E'(s('0'),f(suc(B_231)))
| ~ iLEQ(suc(B_229),suc(B_230))
| ~ iLEQ(suc(A_2),suc(B_229))
| ~ 'E'(s('0'),f(B_231))
| ~ 'E'(s('0'),f(B_233))
| ~ 'E'(s('0'),f(B_232))
| ~ 'E'(s('0'),f(suc(B_229)))
| ~ 'E'(s('0'),f(suc(A_2)))
| ~ 'E'(s('0'),f(B_229))
| ~ iLEQ(suc(B_230),suc(B_231))
| ~ 'E'(s('0'),f(suc(B_232)))
| ~ 'E'(s('0'),f(suc(B_233))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [LE,B_228,E] :
( 'LE'(f(B_228),s('0'))
| 'E'(s('0'),f(B_228))
| ~ 'LE'(f(B_228),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [E,A_3] :
( iLEQ(suc(A_3),suc(A_3))
| ~ 'E'('0',f(suc(A_3)))
| ~ 'E'('0',f(A_3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [LE,B_253,E] :
( 'LE'(f(B_253),'0')
| 'E'('0',f(B_253))
| ~ 'LE'(f(B_253),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [LE,B_158,E] :
( 'LE'(f(B_158),s(s('0')))
| 'E'(s(s('0')),f(B_158))
| ~ 'LE'(f(B_158),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [E,A_1] :
( iLEQ(suc(A_1),suc(A_1))
| ~ 'E'(s(s('0')),f(suc(A_1)))
| ~ 'E'(s(s('0')),f(A_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [LE,A] : 'LE'(f(A),s(s(s('0')))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [LE] : ~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [LE,B_158,E] :
( 'LE'(f(B_158),s(s('0')))
| 'E'(s(s('0')),f(suc(B_158)))
| ~ 'LE'(f(suc(B_158)),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [E,A_1,B_163,B_159,B_160,B_161,B_162] :
( ~ iLEQ(suc(A_1),suc(B_159))
| ~ iLEQ(suc(B_162),suc(B_163))
| ~ 'E'(s(s('0')),f(suc(B_159)))
| ~ 'E'(s(s('0')),f(B_161))
| ~ iLEQ(suc(B_161),suc(B_162))
| ~ 'E'(s(s('0')),f(B_160))
| ~ 'E'(s(s('0')),f(suc(B_162)))
| ~ 'E'(s(s('0')),f(suc(B_160)))
| ~ 'E'(s(s('0')),f(suc(B_161)))
| ~ iLEQ(suc(B_159),suc(B_160))
| ~ 'E'(s(s('0')),f(B_163))
| ~ 'E'(s(s('0')),f(B_162))
| ~ 'E'(s(s('0')),f(suc(A_1)))
| ~ iLEQ(suc(B_160),suc(B_161))
| ~ 'E'(s(s('0')),f(B_159))
| ~ 'E'(s(s('0')),f(suc(B_163)))
| ~ 'E'(s(s('0')),f(A_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [LE,B_253,E] :
( 'LE'(f(B_253),'0')
| 'E'('0',f(suc(B_253)))
| ~ 'LE'(f(suc(B_253)),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [LE,B_228,E] :
( 'LE'(f(B_228),s('0'))
| 'E'(s('0'),f(suc(B_228)))
| ~ 'LE'(f(suc(B_228)),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [E,A_2] :
( iLEQ(suc(A_2),suc(A_2))
| ~ 'E'(s('0'),f(suc(A_2)))
| ~ 'E'(s('0'),f(A_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A_3,B_254,E,B_257,B_255,B_256,B_258] :
( ~ 'E'('0',f(B_257))
| ~ 'E'('0',f(B_256))
| ~ 'E'('0',f(suc(B_258)))
| ~ 'E'('0',f(suc(B_255)))
| ~ iLEQ(suc(B_257),suc(B_258))
| ~ 'E'('0',f(suc(B_256)))
| ~ 'E'('0',f(suc(A_3)))
| ~ iLEQ(suc(B_254),suc(B_255))
| ~ 'E'('0',f(suc(B_254)))
| ~ 'E'('0',f(B_255))
| ~ 'E'('0',f(A_3))
| ~ iLEQ(suc(B_256),suc(B_257))
| ~ 'E'('0',f(B_258))
| ~ iLEQ(suc(B_255),suc(B_256))
| ~ 'E'('0',f(suc(B_257)))
| ~ 'E'('0',f(B_254))
| ~ iLEQ(suc(A_3),suc(B_254)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [B_232,B_231] :
( ~ iLEQ(suc(B_231),suc(B_232))
| ! [A_2] :
( ~ 'E'(s('0'),f(A_2))
| ! [B_233] :
( ~ iLEQ(suc(B_232),suc(B_233))
| ! [B_230] :
( ~ 'E'(s('0'),f(suc(B_230)))
| ~ 'E'(s('0'),f(B_230))
| ~ 'E'(s('0'),f(suc(B_231)))
| ! [B_229] :
( ~ iLEQ(suc(B_229),suc(B_230))
| ~ iLEQ(suc(A_2),suc(B_229))
| ~ 'E'(s('0'),f(B_231))
| ~ 'E'(s('0'),f(B_233))
| ~ 'E'(s('0'),f(B_232))
| ~ 'E'(s('0'),f(suc(B_229)))
| ~ 'E'(s('0'),f(suc(A_2)))
| ~ 'E'(s('0'),f(B_229))
| ~ iLEQ(suc(B_230),suc(B_231))
| ~ 'E'(s('0'),f(suc(B_232)))
| ~ 'E'(s('0'),f(suc(B_233))) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f16,plain,
! [E,X0,X1,X2,X3,X4,X5] :
( ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(X5))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X5),suc(X4))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [B_228] :
( 'LE'(f(B_228),s('0'))
| 'E'(s('0'),f(B_228))
| ~ 'LE'(f(B_228),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [A_3] :
( iLEQ(suc(A_3),suc(A_3))
| ~ 'E'('0',f(suc(A_3)))
| ~ 'E'('0',f(A_3)) ),
inference(miniscoping,[status(thm)],[f3]) ).
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,
! [B_253] :
( 'LE'(f(B_253),'0')
| 'E'('0',f(B_253))
| ~ 'LE'(f(B_253),s('0')) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f22,plain,
! [LE,X0,E] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| ~ 'LE'(f(X0),s('0')) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [B_158] :
( 'LE'(f(B_158),s(s('0')))
| 'E'(s(s('0')),f(B_158))
| ~ 'LE'(f(B_158),s(s(s('0')))) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f24,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)],[f23]) ).
fof(f25,plain,
! [A_1] :
( iLEQ(suc(A_1),suc(A_1))
| ~ 'E'(s(s('0')),f(suc(A_1)))
| ~ 'E'(s(s('0')),f(A_1)) ),
inference(miniscoping,[status(thm)],[f6]) ).
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,
! [A] : 'LE'(f(A),s(s(s('0')))),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f28,plain,
! [LE,X0] : 'LE'(f(X0),s(s(s('0')))),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [LE] : ~ 'LE'(f(z),'0'),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
! [B_158] :
( 'LE'(f(B_158),s(s('0')))
| 'E'(s(s('0')),f(suc(B_158)))
| ~ 'LE'(f(suc(B_158)),s(s(s('0')))) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f31,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)],[f30]) ).
fof(f32,plain,
! [A_1,B_159] :
( ~ iLEQ(suc(A_1),suc(B_159))
| ! [B_163,B_162] :
( ~ iLEQ(suc(B_162),suc(B_163))
| ~ 'E'(s(s('0')),f(suc(B_159)))
| ! [B_161] :
( ~ 'E'(s(s('0')),f(B_161))
| ~ iLEQ(suc(B_161),suc(B_162))
| ! [B_160] :
( ~ 'E'(s(s('0')),f(B_160))
| ~ 'E'(s(s('0')),f(suc(B_162)))
| ~ 'E'(s(s('0')),f(suc(B_160)))
| ~ 'E'(s(s('0')),f(suc(B_161)))
| ~ iLEQ(suc(B_159),suc(B_160))
| ~ 'E'(s(s('0')),f(B_163))
| ~ 'E'(s(s('0')),f(B_162))
| ~ 'E'(s(s('0')),f(suc(A_1)))
| ~ iLEQ(suc(B_160),suc(B_161))
| ~ 'E'(s(s('0')),f(B_159))
| ~ 'E'(s(s('0')),f(suc(B_163)))
| ~ 'E'(s(s('0')),f(A_1)) ) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f33,plain,
! [E,X0,X1,X2,X3,X4,X5] :
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X5),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X4))
| ~ iLEQ(suc(X4),suc(X5))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(suc(X5)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X5))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [B_253] :
( 'LE'(f(B_253),'0')
| 'E'('0',f(suc(B_253)))
| ~ 'LE'(f(suc(B_253)),s('0')) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f35,plain,
! [LE,X0,E] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s('0')) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [B_228] :
( 'LE'(f(B_228),s('0'))
| 'E'(s('0'),f(suc(B_228)))
| ~ 'LE'(f(suc(B_228)),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f37,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)],[f36]) ).
fof(f38,plain,
! [A_2] :
( iLEQ(suc(A_2),suc(A_2))
| ~ 'E'(s('0'),f(suc(A_2)))
| ~ 'E'(s('0'),f(A_2)) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f39,plain,
! [E,X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [B_257] :
( ~ 'E'('0',f(B_257))
| ! [B_256] :
( ~ 'E'('0',f(B_256))
| ! [B_258] :
( ~ 'E'('0',f(suc(B_258)))
| ! [B_255] :
( ~ 'E'('0',f(suc(B_255)))
| ~ iLEQ(suc(B_257),suc(B_258))
| ~ 'E'('0',f(suc(B_256)))
| ! [A_3] :
( ~ 'E'('0',f(suc(A_3)))
| ! [B_254] :
( ~ iLEQ(suc(B_254),suc(B_255))
| ~ 'E'('0',f(suc(B_254)))
| ~ 'E'('0',f(B_255))
| ~ 'E'('0',f(A_3))
| ~ iLEQ(suc(B_256),suc(B_257))
| ~ 'E'('0',f(B_258))
| ~ iLEQ(suc(B_255),suc(B_256))
| ~ 'E'('0',f(suc(B_257)))
| ~ 'E'('0',f(B_254))
| ~ iLEQ(suc(A_3),suc(B_254)) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f41,plain,
! [X0,X1,E,X2,X3,X4,X5] :
( ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X4),suc(X2))
| ~ 'E'('0',f(X5))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f24,f28]) ).
fof(f43,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f28]) ).
fof(f44,plain,
! [E,X0,X1,X2,X3] :
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f47,plain,
! [E,X0,X1,X2,X3] :
( ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f44]) ).
fof(f50,plain,
! [E,X0,X1,X2] :
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[status(thm)],[f47,f26]) ).
fof(f51,plain,
! [E,X0,X1,X2] :
( ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f50]) ).
fof(f52,plain,
! [E,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[status(thm)],[f51,f26]) ).
fof(f53,plain,
! [E,X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f52]) ).
fof(f54,plain,
! [E,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(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[status(thm)],[f53,f26]) ).
fof(f55,plain,
! [E,X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f54]) ).
fof(f56,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s('0')))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[status(thm)],[f55,f43]) ).
fof(f58,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[f37,f60]) ).
fof(f59,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f18,f60]) ).
fof(f60,plain,
! [LE,X0] : 'LE'(f(X0),s(s('0'))),
inference(forward_subsumption_resolution,[status(thm)],[f56,f42]) ).
fof(f61,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[status(thm)],[f58,f35]) ).
fof(f62,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[status(thm)],[f58,f22]) ).
fof(f63,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[status(thm)],[f59,f35]) ).
fof(f64,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[status(thm)],[f59,f22]) ).
fof(f65,plain,
! [E] :
( 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(resolution,[status(thm)],[f64,f29]) ).
fof(f66,definition,
! [E] :
( sQ0_spl
<=> 'E'(s('0'),f(z)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f69,definition,
! [E] :
( sQ1_spl
<=> 'E'('0',f(z)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f70,plain,
! [E] :
( ~ sQ1_spl
| 'E'('0',f(z)) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f66,f69]) ).
fof(f73,plain,
! [E] :
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[status(thm)],[f61,f29]) ).
fof(f74,definition,
! [E] :
( sQ2_spl
<=> 'E'(s('0'),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f75,plain,
! [E] :
( ~ sQ2_spl
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
! [E] :
( sQ3_spl
<=> 'E'('0',f(suc(z))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f78,plain,
! [E] :
( ~ sQ3_spl
| 'E'('0',f(suc(z))) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f73,f74,f77]) ).
fof(f81,plain,
! [E] :
( 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[status(thm)],[f62,f29]) ).
fof(f82,definition,
! [E] :
( sQ4_spl
<=> 'E'(s('0'),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f83,plain,
! [E] :
( ~ sQ4_spl
| 'E'(s('0'),f(suc(z))) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f81,f82,f69]) ).
fof(f86,plain,
! [X0,X1,E] :
( ~ sQ1_spl
| ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(suc(z)))
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(z),suc(z))
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[f70,f41]) ).
fof(f94,definition,
! [X0,X1,E] :
( sQ5_spl
<=> ( ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f95,plain,
! [X0,X1,E] :
( ~ sQ5_spl
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ6_spl
<=> iLEQ(suc(z),suc(z)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f86,f94,f77,f97,f69]) ).
fof(f126,plain,
! [E] :
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[status(thm)],[f63,f29]) ).
fof(f127,plain,
( sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f126,f82,f77]) ).
fof(f128,plain,
! [E] :
( ~ sQ4_spl
| iLEQ(suc(z),suc(z))
| ~ 'E'(s('0'),f(z)) ),
inference(resolution,[status(thm)],[f83,f39]) ).
fof(f129,plain,
! [E,X0] :
( ~ sQ4_spl
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'(s('0'),f(z))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'(s('0'),f(z))
| ~ iLEQ(suc(z),suc(z))
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'(s('0'),f(z))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(z))
| ~ 'E'(s('0'),f(z))
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[status(thm)],[f83,f16]) ).
fof(f139,plain,
( ~ sQ4_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f128,f66,f97,f82]) ).
fof(f140,definition,
! [E,X0] :
( sQ13_spl
<=> ( ~ iLEQ(suc(z),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f141,plain,
! [E,X0] :
( ~ sQ13_spl
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f129,f140,f97,f66,f82]) ).
fof(f189,plain,
! [E] :
( ~ sQ3_spl
| iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(z)) ),
inference(resolution,[status(thm)],[f78,f20]) ).
fof(f219,definition,
! [X0,E] :
( sQ26_spl
<=> ( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(z)) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f220,plain,
! [X0,E] :
( ~ sQ26_spl
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X0),suc(z)) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f228,plain,
( ~ sQ3_spl
| sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f189,f69,f97,f77]) ).
fof(f229,definition,
( sQ28_spl
<=> iLEQ(suc(suc(z)),suc(suc(z))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f261,plain,
! [E] :
( ~ sQ4_spl
| ~ sQ13_spl
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'(s('0'),f(z)) ),
inference(resolution,[status(thm)],[f141,f83]) ).
fof(f262,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f261,f66,f97,f140,f82]) ).
fof(f263,plain,
! [E] :
( ~ sQ2_spl
| iLEQ(suc(suc(z)),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(z))) ),
inference(resolution,[status(thm)],[f75,f39]) ).
fof(f264,plain,
! [E,X0] :
( ~ sQ2_spl
| ~ iLEQ(suc(suc(z)),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(z)))
| ~ iLEQ(suc(suc(z)),suc(X0))
| ~ 'E'(s('0'),f(suc(z)))
| ~ iLEQ(suc(suc(z)),suc(suc(z)))
| ~ iLEQ(suc(suc(z)),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s('0'),f(suc(z)))
| ~ iLEQ(suc(suc(z)),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[status(thm)],[f75,f16]) ).
fof(f274,plain,
( ~ sQ2_spl
| sQ28_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f263,f82,f229,f74]) ).
fof(f275,definition,
! [E,X0] :
( sQ36_spl
<=> ( ~ iLEQ(suc(suc(z)),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f276,plain,
! [E,X0] :
( ~ sQ36_spl
| ~ iLEQ(suc(suc(z)),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ28_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f264,f275,f229,f82,f74]) ).
fof(f328,plain,
! [E] :
( ~ sQ3_spl
| ~ sQ26_spl
| ~ 'E'('0',f(z))
| ~ iLEQ(suc(z),suc(z)) ),
inference(resolution,[status(thm)],[f220,f78]) ).
fof(f329,plain,
( ~ sQ3_spl
| ~ sQ26_spl
| ~ sQ1_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f328,f97,f69,f219,f77]) ).
fof(f332,plain,
! [X0,E] :
( ~ sQ3_spl
| ~ sQ5_spl
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(z))
| ~ iLEQ(suc(X0),suc(z)) ),
inference(resolution,[status(thm)],[f95,f78]) ).
fof(f333,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f332,f219,f69,f97,f94,f77]) ).
fof(f358,plain,
! [E] :
( ~ sQ36_spl
| ~ sQ2_spl
| ~ iLEQ(suc(suc(z)),suc(suc(z)))
| ~ 'E'(s('0'),f(suc(z))) ),
inference(resolution,[status(thm)],[f75,f276]) ).
fof(f370,plain,
( ~ sQ36_spl
| ~ sQ2_spl
| ~ sQ28_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f358,f82,f229,f74,f275]) ).
fof(f382,plain,
$false,
inference(sat_refutation,[status(thm)],[f72,f80,f85,f100,f127,f139,f143,f228,f262,f274,f278,f329,f333,f370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO674-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.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 12:08:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.043407 seconds
% 0.12/0.40 % CPU time: 0.164990 seconds
% 0.12/0.40 % Total memory used: 4.766 MB
% 0.12/0.40 % Net memory used: 4.432 MB
%------------------------------------------------------------------------------