%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO666-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 03:42:56 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 71 ( 11 unt; 7 def)
% Number of atoms : 334 ( 0 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 526 ( 263 ~; 256 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 152 ( 152 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B_96,B_97,E,A_2,B_98,B_94,B_95] :
( ~ 'E'('0',f(B_95))
| ~ 'E'('0',f(B_98))
| ~ 'E'('0',f(suc(B_95)))
| ~ iLEQ(suc(A_2),suc(B_94))
| ~ 'E'('0',f(B_94))
| ~ 'E'('0',f(suc(B_98)))
| ~ iLEQ(suc(B_94),suc(B_95))
| ~ 'E'('0',f(B_96))
| ~ iLEQ(suc(B_95),suc(B_96))
| ~ 'E'('0',f(B_97))
| ~ 'E'('0',f(suc(B_94)))
| ~ 'E'('0',f(A_2))
| ~ 'E'('0',f(suc(B_97)))
| ~ iLEQ(suc(B_97),suc(B_98))
| ~ 'E'('0',f(suc(B_96)))
| ~ 'E'('0',f(suc(A_2)))
| ~ iLEQ(suc(B_96),suc(B_97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,A_2] :
( iLEQ(suc(A_2),suc(A_2))
| ~ 'E'('0',f(suc(A_2)))
| ~ 'E'('0',f(A_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [LE] : ~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [LE,B_93,E] :
( 'LE'(f(B_93),'0')
| 'E'('0',f(suc(B_93)))
| ~ 'LE'(f(suc(B_93)),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [LE,B_93,E] :
( 'LE'(f(B_93),'0')
| 'E'('0',f(B_93))
| ~ 'LE'(f(B_93),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [LE,A] : 'LE'(f(A),s(s('0'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [E,A_1] :
( iLEQ(suc(A_1),suc(A_1))
| ~ 'E'(s('0'),f(suc(A_1)))
| ~ 'E'(s('0'),f(A_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [LE,B_68,E] :
( 'LE'(f(B_68),s('0'))
| 'E'(s('0'),f(suc(B_68)))
| ~ 'LE'(f(suc(B_68)),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [LE,B_68,E] :
( 'LE'(f(B_68),s('0'))
| 'E'(s('0'),f(B_68))
| ~ 'LE'(f(B_68),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [E,B_69,B_71,B_72,A_1,B_70,B_73] :
( ~ 'E'(s('0'),f(suc(B_73)))
| ~ 'E'(s('0'),f(B_72))
| ~ 'E'(s('0'),f(B_70))
| ~ iLEQ(suc(A_1),suc(B_69))
| ~ 'E'(s('0'),f(suc(B_72)))
| ~ 'E'(s('0'),f(B_73))
| ~ 'E'(s('0'),f(suc(B_70)))
| ~ iLEQ(suc(B_72),suc(B_73))
| ~ 'E'(s('0'),f(suc(B_69)))
| ~ iLEQ(suc(B_69),suc(B_70))
| ~ 'E'(s('0'),f(suc(B_71)))
| ~ 'E'(s('0'),f(B_71))
| ~ iLEQ(suc(B_70),suc(B_71))
| ~ 'E'(s('0'),f(suc(A_1)))
| ~ 'E'(s('0'),f(A_1))
| ~ iLEQ(suc(B_71),suc(B_72))
| ~ 'E'(s('0'),f(B_69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [B_95] :
( ~ 'E'('0',f(B_95))
| ! [B_98] :
( ~ 'E'('0',f(B_98))
| ~ 'E'('0',f(suc(B_95)))
| ! [A_2,B_94] :
( ~ iLEQ(suc(A_2),suc(B_94))
| ~ 'E'('0',f(B_94))
| ~ 'E'('0',f(suc(B_98)))
| ~ iLEQ(suc(B_94),suc(B_95))
| ! [B_96] :
( ~ 'E'('0',f(B_96))
| ~ iLEQ(suc(B_95),suc(B_96))
| ! [B_97] :
( ~ 'E'('0',f(B_97))
| ~ 'E'('0',f(suc(B_94)))
| ~ 'E'('0',f(A_2))
| ~ 'E'('0',f(suc(B_97)))
| ~ iLEQ(suc(B_97),suc(B_98))
| ~ 'E'('0',f(suc(B_96)))
| ~ 'E'('0',f(suc(A_2)))
| ~ iLEQ(suc(B_96),suc(B_97)) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1,E,X2,X3,X4,X5] :
( ~ 'E'('0',f(X5))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X5)))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X4),suc(X5))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(X5),suc(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [A_2] :
( iLEQ(suc(A_2),suc(A_2))
| ~ 'E'('0',f(suc(A_2)))
| ~ 'E'('0',f(A_2)) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f14,plain,
! [E,X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [LE] : ~ 'LE'(f(z),'0'),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [B_93] :
( 'LE'(f(B_93),'0')
| 'E'('0',f(suc(B_93)))
| ~ 'LE'(f(suc(B_93)),s('0')) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f17,plain,
! [LE,X0,E] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| ~ 'LE'(f(suc(X0)),s('0')) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [B_93] :
( 'LE'(f(B_93),'0')
| 'E'('0',f(B_93))
| ~ 'LE'(f(B_93),s('0')) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f19,plain,
! [LE,X0,E] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| ~ 'LE'(f(X0),s('0')) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [A] : 'LE'(f(A),s(s('0'))),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f21,plain,
! [LE,X0] : 'LE'(f(X0),s(s('0'))),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [A_1] :
( iLEQ(suc(A_1),suc(A_1))
| ~ 'E'(s('0'),f(suc(A_1)))
| ~ 'E'(s('0'),f(A_1)) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f23,plain,
! [E,X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [B_68] :
( 'LE'(f(B_68),s('0'))
| 'E'(s('0'),f(suc(B_68)))
| ~ 'LE'(f(suc(B_68)),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [B_68] :
( 'LE'(f(B_68),s('0'))
| 'E'(s('0'),f(B_68))
| ~ 'LE'(f(B_68),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f27,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)],[f26]) ).
fof(f28,plain,
! [B_73] :
( ~ 'E'(s('0'),f(suc(B_73)))
| ! [B_72] :
( ~ 'E'(s('0'),f(B_72))
| ! [B_70] :
( ~ 'E'(s('0'),f(B_70))
| ! [B_69,A_1] :
( ~ iLEQ(suc(A_1),suc(B_69))
| ~ 'E'(s('0'),f(suc(B_72)))
| ~ 'E'(s('0'),f(B_73))
| ~ 'E'(s('0'),f(suc(B_70)))
| ~ iLEQ(suc(B_72),suc(B_73))
| ~ 'E'(s('0'),f(suc(B_69)))
| ~ iLEQ(suc(B_69),suc(B_70))
| ! [B_71] :
( ~ 'E'(s('0'),f(suc(B_71)))
| ~ 'E'(s('0'),f(B_71))
| ~ iLEQ(suc(B_70),suc(B_71))
| ~ 'E'(s('0'),f(suc(A_1)))
| ~ 'E'(s('0'),f(A_1))
| ~ iLEQ(suc(B_71),suc(B_72))
| ~ 'E'(s('0'),f(B_69)) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f29,plain,
! [E,X0,X1,X2,X3,X4,X5] :
( ~ 'E'(s('0'),f(suc(X5)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X3),suc(X0))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X4))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1))
| ~ iLEQ(suc(X4),suc(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X3))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s('0'),f(X0)) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f21]) ).
fof(f31,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f21]) ).
fof(f32,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(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[status(thm)],[f29,f23]) ).
fof(f37,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f32]) ).
fof(f38,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f23]) ).
fof(f43,plain,
! [E,X0,LE] :
( 'LE'(f(X0),s('0'))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[status(thm)],[f38,f30]) ).
fof(f45,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[f17,f47]) ).
fof(f46,plain,
! [E,X0,LE] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f19,f47]) ).
fof(f47,plain,
! [LE,X0] : 'LE'(f(X0),s('0')),
inference(forward_subsumption_resolution,[status(thm)],[f43,f31]) ).
fof(f48,plain,
! [E] : 'E'('0',f(suc(z))),
inference(resolution,[status(thm)],[f45,f15]) ).
fof(f49,plain,
! [E] : 'E'('0',f(z)),
inference(resolution,[status(thm)],[f46,f15]) ).
fof(f50,plain,
! [E] :
( iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(z)) ),
inference(resolution,[status(thm)],[f48,f14]) ).
fof(f52,plain,
! [X0,X1,E,X2,X3,X4] :
( ~ 'E'('0',f(z))
| ~ 'E'('0',f(X3))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(suc(X3)))
| ~ iLEQ(suc(X4),suc(z))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(resolution,[status(thm)],[f48,f12]) ).
fof(f57,definition,
! [E] :
( sQ0_spl
<=> 'E'('0',f(z)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
! [E] :
( sQ0_spl
| ~ 'E'('0',f(z)) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ1_spl
<=> iLEQ(suc(z),suc(z)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ1_spl
| iLEQ(suc(z),suc(z)) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f57,f60]) ).
fof(f67,definition,
! [E,X2] :
( sQ3_spl
<=> ( ~ iLEQ(suc(X2),suc(z))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f68,plain,
! [E,X0] :
( ~ sQ3_spl
| ~ iLEQ(suc(X0),suc(z))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f71,definition,
! [X0,X1,E,X3] :
( sQ4_spl
<=> ( ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f72,plain,
! [X0,X1,E,X2] :
( ~ sQ4_spl
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X0))
| ~ iLEQ(suc(z),suc(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1)) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,definition,
! [E,X2,X4] :
( sQ5_spl
<=> ( ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'('0',f(X4))
| ~ iLEQ(suc(X4),suc(z))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f75,plain,
! [E,X0,X1] :
( ~ sQ5_spl
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(X1))
| ~ iLEQ(suc(X1),suc(z))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( ~ sQ0_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f52,f71,f74,f57]) ).
fof(f88,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f49]) ).
fof(f89,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0,E,X1] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(z))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(z)))
| ~ iLEQ(suc(z),suc(X0)) ),
inference(resolution,[status(thm)],[f61,f72]) ).
fof(f91,plain,
! [E] :
( ~ sQ3_spl
| ~ sQ1_spl
| ~ 'E'('0',f(z))
| ~ 'E'('0',f(suc(z))) ),
inference(resolution,[status(thm)],[f61,f68]) ).
fof(f92,definition,
! [X0,X1,E] :
( sQ8_spl
<=> ( ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(z),suc(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f93,plain,
! [X0,X1,E] :
( ~ sQ8_spl
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(z),suc(X0)) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
! [E] :
( sQ9_spl
<=> 'E'('0',f(suc(z))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f97,plain,
! [E] :
( sQ9_spl
| ~ 'E'('0',f(suc(z))) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f90,f92,f95,f57,f60,f71]) ).
fof(f99,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f91,f95,f57,f60,f67]) ).
fof(f100,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f48]) ).
fof(f101,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f100]) ).
fof(f102,plain,
! [E,X0] :
( ~ sQ5_spl
| ~ iLEQ(suc(X0),suc(z))
| ~ 'E'('0',f(z))
| ~ iLEQ(suc(z),suc(z))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(resolution,[status(thm)],[f75,f48]) ).
fof(f103,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f102,f67,f60,f57,f74]) ).
fof(f113,plain,
! [E] :
( ~ sQ8_spl
| ~ 'E'('0',f(z))
| ~ 'E'('0',f(z))
| ~ iLEQ(suc(z),suc(z))
| ~ iLEQ(suc(z),suc(z)) ),
inference(resolution,[status(thm)],[f93,f48]) ).
fof(f116,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f113,f60,f57,f92]) ).
fof(f125,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f77,f89,f98,f99,f101,f103,f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO666-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 12:08:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.025620 seconds
% 0.09/0.40 % CPU time: 0.084658 seconds
% 0.09/0.40 % Total memory used: 2.655 MB
% 0.09/0.40 % Net memory used: 2.414 MB
%------------------------------------------------------------------------------