%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO680-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 78 ( 10 unt; 0 def)
% Number of atoms : 281 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 399 ( 196 ~; 203 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 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 : 187 ( 187 !; 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,
! [LE,A] : 'LE'(f(A),s(s(s(s('0'))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,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(f4,axiom,
! [LE,B_60,E] :
( 'LE'(f(B_60),'0')
| 'E'('0',f(suc(B_60)))
| ~ 'LE'(f(suc(B_60)),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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(f6,axiom,
! [E,B_42,B_43,A_2] :
( ~ 'E'(s(s('0')),f(A_2))
| ~ 'E'(s(s('0')),f(B_43))
| ~ iLEQ(suc(A_2),suc(B_42))
| ~ 'E'(s(s('0')),f(suc(B_43)))
| ~ 'E'(s(s('0')),f(suc(A_2)))
| ~ iLEQ(suc(B_42),suc(B_43))
| ~ 'E'(s(s('0')),f(B_42))
| ~ 'E'(s(s('0')),f(suc(B_42))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B_24,B_25,E,A_1] :
( ~ 'E'(s(s(s('0'))),f(suc(A_1)))
| ~ 'E'(s(s(s('0'))),f(suc(B_25)))
| ~ 'E'(s(s(s('0'))),f(suc(B_24)))
| ~ 'E'(s(s(s('0'))),f(A_1))
| ~ iLEQ(suc(A_1),suc(B_24))
| ~ 'E'(s(s(s('0'))),f(B_24))
| ~ 'E'(s(s(s('0'))),f(B_25))
| ~ iLEQ(suc(B_24),suc(B_25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [LE,B_53,E] :
( 'LE'(f(B_53),s('0'))
| 'E'(s('0'),f(B_53))
| ~ 'LE'(f(B_53),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_41,E] :
( 'LE'(f(B_41),s(s('0')))
| 'E'(s(s('0')),f(suc(B_41)))
| ~ 'LE'(f(suc(B_41)),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [E,B_61,B_62,A_4] :
( ~ 'E'('0',f(A_4))
| ~ 'E'('0',f(B_62))
| ~ 'E'('0',f(suc(A_4)))
| ~ 'E'('0',f(B_61))
| ~ 'E'('0',f(suc(B_62)))
| ~ iLEQ(suc(A_4),suc(B_61))
| ~ iLEQ(suc(B_61),suc(B_62))
| ~ 'E'('0',f(suc(B_61))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [LE,B_23,E] :
( 'LE'(f(B_23),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(B_23))
| ~ 'LE'(f(B_23),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [LE,B_41,E] :
( 'LE'(f(B_41),s(s('0')))
| 'E'(s(s('0')),f(B_41))
| ~ 'LE'(f(B_41),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B_54,B_55,E,A_3] :
( ~ 'E'(s('0'),f(B_54))
| ~ 'E'(s('0'),f(suc(B_54)))
| ~ 'E'(s('0'),f(B_55))
| ~ 'E'(s('0'),f(A_3))
| ~ 'E'(s('0'),f(suc(B_55)))
| ~ iLEQ(suc(A_3),suc(B_54))
| ~ 'E'(s('0'),f(suc(A_3)))
| ~ iLEQ(suc(B_54),suc(B_55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [LE,B_23,E] :
( 'LE'(f(B_23),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(B_23)))
| ~ 'LE'(f(suc(B_23)),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,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(f17,axiom,
! [LE,B_60,E] :
( 'LE'(f(B_60),'0')
| 'E'('0',f(B_60))
| ~ 'LE'(f(B_60),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [LE,B_53,E] :
( 'LE'(f(B_53),s('0'))
| 'E'(s('0'),f(suc(B_53)))
| ~ 'LE'(f(suc(B_53)),s(s('0'))) ),
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] : 'LE'(f(A),s(s(s(s('0'))))),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f22,plain,
! [LE,X0] : 'LE'(f(X0),s(s(s(s('0'))))),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,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)],[f3]) ).
fof(f24,plain,
! [E,X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [B_60] :
( 'LE'(f(B_60),'0')
| 'E'('0',f(suc(B_60)))
| ~ 'LE'(f(suc(B_60)),s('0')) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f26,plain,
! [LE,X0,E] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s('0')) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,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)],[f5]) ).
fof(f28,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)],[f27]) ).
fof(f29,plain,
! [A_2] :
( ~ 'E'(s(s('0')),f(A_2))
| ! [B_43] :
( ~ 'E'(s(s('0')),f(B_43))
| ! [B_42] :
( ~ iLEQ(suc(A_2),suc(B_42))
| ~ 'E'(s(s('0')),f(suc(B_43)))
| ~ 'E'(s(s('0')),f(suc(A_2)))
| ~ iLEQ(suc(B_42),suc(B_43))
| ~ 'E'(s(s('0')),f(B_42))
| ~ 'E'(s(s('0')),f(suc(B_42))) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f30,plain,
! [E,X0,X1,X2] :
( ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [A_1] :
( ~ 'E'(s(s(s('0'))),f(suc(A_1)))
| ! [B_25] :
( ~ 'E'(s(s(s('0'))),f(suc(B_25)))
| ! [B_24] :
( ~ 'E'(s(s(s('0'))),f(suc(B_24)))
| ~ 'E'(s(s(s('0'))),f(A_1))
| ~ iLEQ(suc(A_1),suc(B_24))
| ~ 'E'(s(s(s('0'))),f(B_24))
| ~ 'E'(s(s(s('0'))),f(B_25))
| ~ iLEQ(suc(B_24),suc(B_25)) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f32,plain,
! [X0,X1,E,X2] :
( ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [B_53] :
( 'LE'(f(B_53),s('0'))
| 'E'(s('0'),f(B_53))
| ~ 'LE'(f(B_53),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f34,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)],[f33]) ).
fof(f35,plain,
! [LE] : ~ 'LE'(f(z),'0'),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
! [B_41] :
( 'LE'(f(B_41),s(s('0')))
| 'E'(s(s('0')),f(suc(B_41)))
| ~ 'LE'(f(suc(B_41)),s(s(s('0')))) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f37,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)],[f36]) ).
fof(f38,plain,
! [A_4] :
( ~ 'E'('0',f(A_4))
| ! [B_62] :
( ~ 'E'('0',f(B_62))
| ~ 'E'('0',f(suc(A_4)))
| ! [B_61] :
( ~ 'E'('0',f(B_61))
| ~ 'E'('0',f(suc(B_62)))
| ~ iLEQ(suc(A_4),suc(B_61))
| ~ iLEQ(suc(B_61),suc(B_62))
| ~ 'E'('0',f(suc(B_61))) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f39,plain,
! [E,X0,X1,X2] :
( ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X0))) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [B_23] :
( 'LE'(f(B_23),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(B_23))
| ~ 'LE'(f(B_23),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,
! [B_41] :
( 'LE'(f(B_41),s(s('0')))
| 'E'(s(s('0')),f(B_41))
| ~ 'LE'(f(B_41),s(s(s('0')))) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f43,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)],[f42]) ).
fof(f44,plain,
! [B_54] :
( ~ 'E'(s('0'),f(B_54))
| ~ 'E'(s('0'),f(suc(B_54)))
| ! [B_55] :
( ~ 'E'(s('0'),f(B_55))
| ! [A_3] :
( ~ 'E'(s('0'),f(A_3))
| ~ 'E'(s('0'),f(suc(B_55)))
| ~ iLEQ(suc(A_3),suc(B_54))
| ~ 'E'(s('0'),f(suc(A_3)))
| ~ iLEQ(suc(B_54),suc(B_55)) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f45,plain,
! [X0,X1,E,X2] :
( ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [B_23] :
( 'LE'(f(B_23),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(B_23)))
| ~ 'LE'(f(suc(B_23)),s(s(s(s('0'))))) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f47,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)],[f46]) ).
fof(f48,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)],[f16]) ).
fof(f49,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)],[f48]) ).
fof(f50,plain,
! [B_60] :
( 'LE'(f(B_60),'0')
| 'E'('0',f(B_60))
| ~ 'LE'(f(B_60),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_53] :
( 'LE'(f(B_53),s('0'))
| 'E'(s('0'),f(suc(B_53)))
| ~ 'LE'(f(suc(B_53)),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f53,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)],[f52]) ).
fof(f54,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))) ),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f64,plain,
! [E,X0] :
( ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f54]) ).
fof(f76,plain,
! [E,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(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(resolution,[status(thm)],[f32,f49]) ).
fof(f86,plain,
! [E,X0] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f76]) ).
fof(f97,plain,
! [LE,X0,E] :
( ~ 'E'(s(s('0')),f(X0))
| 'LE'(f(X0),s(s('0')))
| ~ 'LE'(f(suc(X0)),s(s(s('0')))) ),
inference(resolution,[status(thm)],[f37,f64]) ).
fof(f104,plain,
! [E,X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(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)],[f39,f20]) ).
fof(f119,plain,
! [E,X0] :
( ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f104]) ).
fof(f127,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| ~ 'LE'(f(suc(X0)),s('0'))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[status(thm)],[f119,f26]) ).
fof(f130,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,f22]) ).
fof(f132,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(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(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[status(thm)],[f45,f24]) ).
fof(f146,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f132]) ).
fof(f155,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| ~ 'LE'(f(suc(X0)),s(s('0')))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[status(thm)],[f146,f53]) ).
fof(f159,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)],[f47,f22]) ).
fof(f160,plain,
! [LE,X0,E] :
( ~ 'E'(s(s(s('0'))),f(X0))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(resolution,[status(thm)],[f159,f86]) ).
fof(f161,plain,
! [LE,X0] : 'LE'(f(X0),s(s(s('0')))),
inference(forward_subsumption_resolution,[status(thm)],[f160,f130]) ).
fof(f162,plain,
! [LE,X0,E] :
( ~ 'E'(s(s('0')),f(X0))
| 'LE'(f(X0),s(s('0'))) ),
inference(backward_subsumption_resolution,[status(thm)],[f97,f161]) ).
fof(f164,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f43,f161]) ).
fof(f166,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| ~ 'E'(s('0'),f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f155,f169]) ).
fof(f168,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f34,f169]) ).
fof(f169,plain,
! [LE,X0] : 'LE'(f(X0),s(s('0'))),
inference(forward_subsumption_resolution,[status(thm)],[f164,f162]) ).
fof(f172,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| ~ 'E'('0',f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f127,f176]) ).
fof(f174,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f176]) ).
fof(f176,plain,
! [LE,X0] : 'LE'(f(X0),s('0')),
inference(forward_subsumption_resolution,[status(thm)],[f168,f166]) ).
fof(f179,plain,
! [LE,X0] : 'LE'(f(X0),'0'),
inference(forward_subsumption_resolution,[status(thm)],[f174,f172]) ).
fof(f180,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f35,f179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO680-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 12:08:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.15/0.42 % Refutation found
% 0.15/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.048106 seconds
% 0.15/0.44 % CPU time: 0.242615 seconds
% 0.15/0.44 % Total memory used: 6.952 MB
% 0.15/0.44 % Net memory used: 6.291 MB
%------------------------------------------------------------------------------