%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL003-1 : TPTP v9.3.1. Released v1.0.0.
% 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 01:06:34 PM UTC 2026
% Result : Unsatisfiable 201.97s 30.72s
% Output : CNFRefutation 201.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 120 ( 18 unt; 11 def)
% Number of atoms : 402 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 558 ( 276 ~; 271 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 12 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 450 ( 450 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(or(not(X),Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z,U,V] : is_a_theorem(or(not(or(not(or(not(X),Y)),or(Z,or(U,V)))),or(not(or(not(U),X)),or(Z,or(V,X))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(or(not(or(a,b)),or(b,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(or(not(X),Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(or(not(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))),or(not(or(not(X3),X0)),or(X2,or(X4,X0))))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(or(not(or(a,b)),or(b,a))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(or(not(or(not(X3),X0)),or(X2,or(X4,X0))))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(or(X2,or(X4,X0)))
| ~ is_a_theorem(or(not(X3),X0))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))) ),
inference(resolution,[status(thm)],[f8,f5]) ).
fof(f10,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( is_a_theorem(or(X5,or(X7,or(not(or(not(X0),X1)),or(X2,or(X3,X1))))))
| ~ is_a_theorem(or(not(or(not(or(not(or(not(X0),X1)),or(X2,or(X3,X1)))),X4)),or(X5,or(or(not(or(not(X1),X6)),or(X2,or(X0,X3))),X7)))) ),
inference(resolution,[status(thm)],[f9,f6]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ is_a_theorem(or(not(or(not(X2),X7)),or(X0,or(X5,X1))))
| is_a_theorem(or(X4,or(X6,or(X0,or(X1,X2)))))
| ~ is_a_theorem(or(not(or(not(or(X0,or(X1,X2))),X3)),or(X4,or(or(not(X5),X2),X6)))) ),
inference(resolution,[status(thm)],[f9,f8]) ).
fof(f13,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ is_a_theorem(or(not(or(not(X1),X7)),or(X0,or(X2,X5))))
| is_a_theorem(or(X4,or(X6,or(X0,or(X1,X2)))))
| ~ is_a_theorem(or(not(or(not(or(X0,or(X1,X2))),X3)),or(X4,or(or(not(X5),X2),X6)))) ),
inference(resolution,[status(thm)],[f11,f8]) ).
fof(f15,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ is_a_theorem(or(not(or(not(X1),X6)),or(X0,or(or(not(or(not(X2),X3)),or(X4,or(X5,X3))),or(not(or(not(X3),X7)),or(X4,or(X2,X5)))))))
| is_a_theorem(or(X0,or(X1,or(not(or(not(X2),X3)),or(X4,or(X5,X3)))))) ),
inference(resolution,[status(thm)],[f10,f8]) ).
fof(f20,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ is_a_theorem(or(not(or(not(X1),X7)),or(X0,or(or(X2,or(X3,X4)),or(not(X6),X4)))))
| ~ is_a_theorem(or(not(or(not(X3),X5)),or(X2,or(X4,X6))))
| is_a_theorem(or(X0,or(X1,or(X2,or(X3,X4))))) ),
inference(resolution,[status(thm)],[f13,f8]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ is_a_theorem(or(not(or(not(X4),X5)),or(X3,or(X1,X6))))
| is_a_theorem(or(not(or(not(X0),X1)),or(or(not(X1),X2),or(X3,or(X4,X1))))) ),
inference(resolution,[status(thm)],[f20,f6]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ is_a_theorem(or(not(or(not(X5),X6)),or(X3,or(X4,X1))))
| is_a_theorem(or(not(or(not(X0),X1)),or(or(not(X1),X2),or(X3,or(X4,X1))))) ),
inference(resolution,[status(thm)],[f33,f8]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ is_a_theorem(or(not(or(not(or(not(or(not(X3),X6)),or(X4,or(X2,X5)))),X7)),or(X0,or(X1,or(not(or(not(X2),X3)),or(X4,or(X5,X3)))))))
| is_a_theorem(or(X0,or(X1,or(not(or(not(X2),X3)),or(X4,or(X5,X3)))))) ),
inference(resolution,[status(thm)],[f15,f8]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ is_a_theorem(or(not(or(not(X1),X5)),or(X3,or(X6,X4))))
| is_a_theorem(or(not(or(not(X0),X1)),or(or(not(X1),X2),or(X3,or(X4,X1))))) ),
inference(resolution,[status(thm)],[f39,f8]) ).
fof(f184,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(or(not(or(not(X0),or(not(X1),or(X2,X1)))),or(X3,or(not(or(not(X4),X1)),or(not(X1),or(X2,X1)))))),
inference(resolution,[status(thm)],[f43,f6]) ).
fof(f207,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(or(X0,or(not(or(not(X1),or(not(X2),X3))),or(not(or(not(X2),X3)),or(X4,or(not(X2),X3)))))),
inference(resolution,[status(thm)],[f184,f43]) ).
fof(f212,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(or(not(or(not(X0),X1)),or(or(not(X1),X2),or(X3,or(or(not(X4),or(X5,X4)),X1))))),
inference(resolution,[status(thm)],[f184,f53]) ).
fof(f217,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(or(X3,or(not(or(not(X4),X1)),or(not(X1),or(X2,X1)))))
| ~ is_a_theorem(or(not(X0),or(not(X1),or(X2,X1)))) ),
inference(resolution,[status(thm)],[f184,f5]) ).
fof(f240,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(or(not(or(not(X0),X1)),or(or(not(X1),X2),or(or(not(X3),X4),or(X5,X1))))),
inference(resolution,[status(thm)],[f212,f33]) ).
fof(f251,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(or(or(not(or(X0,or(X1,X2))),X3),or(X4,or(not(or(not(X1),X5)),or(X0,or(X2,X5)))))),
inference(resolution,[status(thm)],[f240,f15]) ).
fof(f282,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(or(not(or(not(X1),or(not(X2),X3))),or(not(or(not(X2),X3)),or(X4,or(not(X2),X3)))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f207,f5]) ).
fof(f283,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f284,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,definition,
! [X1,X2,X3,X4] :
( sQ1_spl
<=> is_a_theorem(or(not(or(not(X1),or(not(X2),X3))),or(not(or(not(X2),X3)),or(X4,or(not(X2),X3))))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f287,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(or(not(or(not(X0),or(not(X1),X2))),or(not(or(not(X1),X2)),or(X3,or(not(X1),X2))))) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f282,f283,f286]) ).
fof(f290,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f251,f284]) ).
fof(f311,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f341,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ is_a_theorem(or(not(or(not(X1),X7)),or(X0,or(or(X2,or(X3,X4)),or(not(X6),X4)))))
| ~ is_a_theorem(or(not(or(not(X4),X5)),or(X2,or(X6,X3))))
| is_a_theorem(or(X0,or(X1,or(X2,or(X3,X4))))) ),
inference(resolution,[status(thm)],[f11,f8]) ).
fof(f349,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(or(not(or(not(X4),X1)),or(not(X1),or(X2,X1))))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(or(not(X0),or(not(X1),or(X2,X1)))) ),
inference(resolution,[status(thm)],[f217,f5]) ).
fof(f350,definition,
! [X0,X1,X2,X4] :
( sQ3_spl
<=> ( is_a_theorem(or(not(or(not(X4),X1)),or(not(X1),or(X2,X1))))
| ~ is_a_theorem(or(not(X0),or(not(X1),or(X2,X1)))) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f351,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| is_a_theorem(or(not(or(not(X3),X1)),or(not(X1),or(X2,X1))))
| ~ is_a_theorem(or(not(X0),or(not(X1),or(X2,X1)))) ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f349,f350,f283]) ).
fof(f356,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| is_a_theorem(or(not(X1),or(X2,X1)))
| ~ is_a_theorem(or(not(X3),X1))
| ~ is_a_theorem(or(not(X0),or(not(X1),or(X2,X1)))) ),
inference(resolution,[status(thm)],[f351,f5]) ).
fof(f361,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ3_spl
| ~ is_a_theorem(or(not(or(not(X1),X3)),or(not(X1),or(X4,X2))))
| is_a_theorem(or(not(X1),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f356,f8]) ).
fof(f384,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ3_spl
| ~ is_a_theorem(or(not(or(not(X2),X3)),or(not(X1),or(X1,X4))))
| is_a_theorem(or(not(X1),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f361,f8]) ).
fof(f456,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ is_a_theorem(or(not(X3),or(not(X1),or(X1,X1))))
| is_a_theorem(or(not(X1),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f384,f351]) ).
fof(f547,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| is_a_theorem(or(not(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))),or(X5,or(not(or(not(X3),X0)),or(X2,or(X4,X0)))))) ),
inference(resolution,[status(thm)],[f15,f287]) ).
fof(f587,definition,
! [X3,X4,X5] :
( sQ6_spl
<=> ~ is_a_theorem(or(not(X3),or(not(X4),X5))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f588,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ is_a_theorem(or(not(X0),or(not(X1),X2))) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f619,plain,
( ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f588]) ).
fof(f623,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f619]) ).
fof(f821,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ is_a_theorem(or(not(or(not(X4),X5)),or(X3,or(X1,X0))))
| is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,or(X4,X1))))) ),
inference(resolution,[status(thm)],[f20,f287]) ).
fof(f840,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| is_a_theorem(or(X5,or(X2,or(X0,X3))))
| ~ is_a_theorem(or(not(X4),X3))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))) ),
inference(resolution,[status(thm)],[f821,f5]) ).
fof(f864,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| is_a_theorem(or(X2,or(X0,X3)))
| ~ is_a_theorem(X5)
| ~ is_a_theorem(or(not(X4),X3))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))) ),
inference(resolution,[status(thm)],[f840,f5]) ).
fof(f865,definition,
! [X0,X1,X2,X3,X4] :
( sQ18_spl
<=> ( is_a_theorem(or(X2,or(X0,X3)))
| ~ is_a_theorem(or(not(X4),X3))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f866,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ18_spl
| is_a_theorem(or(X2,or(X0,X3)))
| ~ is_a_theorem(or(not(X4),X3))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X4)))) ),
inference(component_clause,[status(thm)],[f865]) ).
fof(f868,plain,
( ~ sQ1_spl
| sQ0_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f864,f865,f283,f286]) ).
fof(f1049,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| is_a_theorem(or(X0,or(not(or(not(X1),or(not(X2),X2))),or(not(or(not(X3),X2)),or(X4,or(not(X2),X2)))))) ),
inference(resolution,[status(thm)],[f43,f547]) ).
fof(f1102,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| is_a_theorem(or(not(or(not(X1),or(not(X2),X2))),or(not(or(not(X3),X2)),or(X4,or(not(X2),X2)))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1049,f5]) ).
fof(f1103,definition,
! [X1,X2,X3,X4] :
( sQ20_spl
<=> is_a_theorem(or(not(or(not(X1),or(not(X2),X2))),or(not(or(not(X3),X2)),or(X4,or(not(X2),X2))))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1104,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| is_a_theorem(or(not(or(not(X0),or(not(X1),X1))),or(not(or(not(X2),X1)),or(X3,or(not(X1),X1))))) ),
inference(component_clause,[status(thm)],[f1103]) ).
fof(f1106,plain,
( ~ sQ1_spl
| sQ20_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1102,f283,f1103,f286]) ).
fof(f1117,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| ~ is_a_theorem(or(not(or(not(X4),X5)),or(X3,or(X1,X1))))
| is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,or(X4,X1))))) ),
inference(resolution,[status(thm)],[f1104,f20]) ).
fof(f1118,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| ~ is_a_theorem(or(not(or(not(X1),X5)),or(X3,or(X1,X4))))
| is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,or(X4,X1))))) ),
inference(resolution,[status(thm)],[f1104,f341]) ).
fof(f1207,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| is_a_theorem(or(X5,or(X2,or(X0,X3))))
| ~ is_a_theorem(or(not(X4),X3))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X3)))) ),
inference(resolution,[status(thm)],[f1117,f5]) ).
fof(f1242,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| is_a_theorem(or(X2,or(X0,X3)))
| ~ is_a_theorem(X5)
| ~ is_a_theorem(or(not(X4),X3))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X3)))) ),
inference(resolution,[status(thm)],[f1207,f5]) ).
fof(f1243,definition,
! [X0,X1,X2,X3,X4] :
( sQ23_spl
<=> ( is_a_theorem(or(X2,or(X0,X3)))
| ~ is_a_theorem(or(not(X4),X3))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X3)))) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1244,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ23_spl
| is_a_theorem(or(X2,or(X0,X3)))
| ~ is_a_theorem(or(not(X4),X3))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X3,X3)))) ),
inference(component_clause,[status(thm)],[f1243]) ).
fof(f1246,plain,
( ~ sQ20_spl
| sQ0_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1242,f1243,f283,f1103]) ).
fof(f1399,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| is_a_theorem(or(X5,or(X2,or(X3,X0))))
| ~ is_a_theorem(or(not(X4),X0))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X0,X3)))) ),
inference(resolution,[status(thm)],[f1118,f5]) ).
fof(f1438,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ20_spl
| is_a_theorem(or(X2,or(X3,X0)))
| ~ is_a_theorem(X5)
| ~ is_a_theorem(or(not(X4),X0))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X0,X3)))) ),
inference(resolution,[status(thm)],[f1399,f5]) ).
fof(f1439,definition,
! [X0,X1,X2,X3,X4] :
( sQ26_spl
<=> ( is_a_theorem(or(X2,or(X3,X0)))
| ~ is_a_theorem(or(not(X4),X0))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X0,X3)))) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1440,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ26_spl
| is_a_theorem(or(X2,or(X3,X0)))
| ~ is_a_theorem(or(not(X4),X0))
| ~ is_a_theorem(or(not(or(not(X0),X1)),or(X2,or(X0,X3)))) ),
inference(component_clause,[status(thm)],[f1439]) ).
fof(f1442,plain,
( ~ sQ20_spl
| sQ0_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1438,f1439,f283,f1103]) ).
fof(f1451,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ26_spl
| ~ is_a_theorem(or(not(X3),or(not(X2),or(X1,X2))))
| is_a_theorem(or(not(X2),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f1440,f351]) ).
fof(f1544,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ3_spl
| ~ sQ26_spl
| ~ is_a_theorem(or(not(or(not(X2),X3)),or(not(X2),or(X4,X1))))
| is_a_theorem(or(not(X2),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f1451,f8]) ).
fof(f2557,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ3_spl
| ~ sQ26_spl
| ~ is_a_theorem(or(not(or(not(X1),X3)),or(not(X2),or(X2,X4))))
| is_a_theorem(or(not(X2),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f1544,f8]) ).
fof(f6172,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| ~ sQ26_spl
| ~ is_a_theorem(or(not(X3),or(not(X2),or(X2,X2))))
| is_a_theorem(or(not(X2),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f2557,f351]) ).
fof(f6225,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ3_spl
| ~ sQ26_spl
| ~ is_a_theorem(or(not(or(not(X2),X3)),or(not(X2),or(X4,X2))))
| is_a_theorem(or(not(X2),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f6172,f8]) ).
fof(f6797,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ3_spl
| ~ sQ26_spl
| ~ is_a_theorem(or(not(X3),or(not(X2),or(X4,X2))))
| is_a_theorem(or(not(X2),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f6225,f351]) ).
fof(f7121,definition,
! [X5,X6] :
( sQ461_spl
<=> ~ is_a_theorem(or(not(X5),X6)) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f7122,plain,
! [X0,X1] :
( ~ sQ461_spl
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(component_clause,[status(thm)],[f7121]) ).
fof(f7176,plain,
( ~ sQ461_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f7122]) ).
fof(f7206,plain,
~ sQ461_spl,
inference(contradiction_clause,[status(thm)],[f7176]) ).
fof(f7717,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ is_a_theorem(or(not(or(not(X1),X5)),or(X3,or(X6,X4))))
| is_a_theorem(or(not(or(not(X0),X1)),or(or(not(X1),X2),or(X3,or(X4,X1))))) ),
inference(resolution,[status(thm)],[f341,f6]) ).
fof(f8678,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(not(or(not(X2),X0)),or(X3,X1)))
| ~ is_a_theorem(or(not(or(not(X0),X0)),X1)) ),
inference(resolution,[status(thm)],[f1104,f866]) ).
fof(f8693,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ23_spl
| ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(X3,or(X4,X1)))
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(or(not(or(not(X0),X0)),or(X1,X1))) ),
inference(resolution,[status(thm)],[f8678,f1244]) ).
fof(f9062,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ23_spl
| ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(X4,X1))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(or(not(or(not(X0),X0)),or(X1,X1))) ),
inference(resolution,[status(thm)],[f8693,f5]) ).
fof(f9063,definition,
! [X0,X1,X2,X5] :
( sQ575_spl
<=> ( is_a_theorem(or(X5,X1))
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(or(not(or(not(X0),X0)),or(X1,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f9064,plain,
! [X0,X1,X2,X3] :
( ~ sQ575_spl
| is_a_theorem(or(X3,X1))
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(or(not(or(not(X0),X0)),or(X1,X1))) ),
inference(component_clause,[status(thm)],[f9063]) ).
fof(f9071,plain,
( ~ sQ23_spl
| ~ sQ18_spl
| ~ sQ20_spl
| sQ0_spl
| sQ575_spl ),
inference(split_clause,[status(thm)],[f9062,f9063,f283,f1103,f865,f1243]) ).
fof(f9103,plain,
! [X0,X1,X2,X3] :
( ~ sQ575_spl
| is_a_theorem(X1)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(or(not(or(not(X0),X0)),or(X1,X1))) ),
inference(resolution,[status(thm)],[f9064,f5]) ).
fof(f9104,definition,
! [X0,X1,X2] :
( sQ577_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(or(not(or(not(X0),X0)),or(X1,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ577_spl])],[split_symbol_definition]) ).
fof(f9105,plain,
! [X0,X1,X2] :
( ~ sQ577_spl
| is_a_theorem(X1)
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(or(not(or(not(X0),X0)),or(X1,X1))) ),
inference(component_clause,[status(thm)],[f9104]) ).
fof(f9113,plain,
( ~ sQ575_spl
| sQ0_spl
| sQ577_spl ),
inference(split_clause,[status(thm)],[f9103,f9104,f283,f9063]) ).
fof(f9127,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ577_spl
| ~ is_a_theorem(or(not(or(not(X2),X2)),X1))
| is_a_theorem(X1)
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f9105,f8678]) ).
fof(f9989,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(or(not(or(not(X0),or(not(X1),X2))),or(not(or(not(X3),X1)),or(or(X4,X1),or(not(X1),X2))))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f10006,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(or(not(or(not(or(X0,X1)),X2)),or(not(or(not(X3),X1)),or(or(not(X1),X4),X2)))),
inference(resolution,[status(thm)],[f9989,f8]) ).
fof(f10198,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(or(not(or(not(X0),or(not(X1),or(X2,X1)))),or(X3,or(not(or(not(X4),X1)),or(not(X1),or(X2,X1)))))),
inference(resolution,[status(thm)],[f10006,f10]) ).
fof(f10914,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ is_a_theorem(or(not(or(not(X1),X6)),or(X0,or(or(X2,or(or(not(X3),or(X4,X3)),X5)),or(not(not(or(not(X7),X3))),X5)))))
| is_a_theorem(or(X0,or(X1,or(X2,or(or(not(X3),or(X4,X3)),X5))))) ),
inference(resolution,[status(thm)],[f10198,f341]) ).
fof(f10917,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(or(not(or(not(not(or(not(X0),X1))),X2)),or(X3,or(or(not(X1),or(X4,X1)),X2)))),
inference(resolution,[status(thm)],[f10198,f8]) ).
fof(f13316,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ26_spl
| is_a_theorem(or(not(X2),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f6797,f10917]) ).
fof(f29825,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(or(X0,or(not(or(not(X1),X2)),or(not(X2),or(or(not(X3),or(X4,X3)),X2))))),
inference(resolution,[status(thm)],[f10914,f10917]) ).
fof(f30209,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ577_spl
| is_a_theorem(or(not(or(not(X1),X2)),or(not(X2),or(or(not(X3),or(X4,X3)),X2))))
| ~ is_a_theorem(or(not(X0),or(not(or(not(X1),X2)),or(not(X2),or(or(not(X3),or(X4,X3)),X2))))) ),
inference(resolution,[status(thm)],[f29825,f9127]) ).
fof(f30377,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ577_spl
| is_a_theorem(or(not(or(not(X0),X1)),or(not(X1),or(or(not(X2),or(X3,X2)),X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f30209,f29825]) ).
fof(f30400,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ577_spl
| is_a_theorem(or(not(or(not(X0),X1)),or(or(not(X1),X2),or(not(X3),or(X3,X1))))) ),
inference(resolution,[status(thm)],[f30377,f7717]) ).
fof(f30405,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ577_spl
| is_a_theorem(or(not(or(not(or(not(X0),or(X1,X0))),X2)),or(not(X3),or(X3,X2)))) ),
inference(resolution,[status(thm)],[f30377,f8]) ).
fof(f33236,plain,
! [X0,X1] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(not(X1),or(X1,X1)))
| ~ is_a_theorem(or(not(X0),or(not(X1),or(X1,X1)))) ),
inference(resolution,[status(thm)],[f30400,f9105]) ).
fof(f33458,plain,
! [X0,X1] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(not(or(not(X0),X1)),or(or(not(X0),X1),or(not(X0),X1)))) ),
inference(resolution,[status(thm)],[f33236,f6]) ).
fof(f33508,plain,
! [X0,X1,X2] :
( ~ sQ575_spl
| ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(X2,or(not(X1),X1)))
| ~ is_a_theorem(or(not(X0),or(not(X1),X1))) ),
inference(resolution,[status(thm)],[f33458,f9064]) ).
fof(f33509,plain,
! [X0,X1] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(not(X1),X1))
| ~ is_a_theorem(or(not(X0),or(not(X1),X1))) ),
inference(resolution,[status(thm)],[f33458,f9105]) ).
fof(f38439,plain,
! [X0] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(not(X0),or(X0,X0))) ),
inference(resolution,[status(thm)],[f30405,f33236]) ).
fof(f38441,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ577_spl
| is_a_theorem(or(not(X1),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f30405,f456]) ).
fof(f38754,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ26_spl
| ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| is_a_theorem(or(not(X0),or(X0,or(X1,X1)))) ),
inference(resolution,[status(thm)],[f38439,f13316]) ).
fof(f39264,plain,
! [X0] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| is_a_theorem(or(not(or(X0,X0)),or(X0,X0))) ),
inference(resolution,[status(thm)],[f38754,f33509]) ).
fof(f40710,plain,
! [X0,X1] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| is_a_theorem(or(not(or(X0,X0)),or(X1,or(X0,X0)))) ),
inference(resolution,[status(thm)],[f38441,f39264]) ).
fof(f40777,plain,
! [X0,X1] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| is_a_theorem(or(not(or(not(not(X0)),X0)),or(X1,or(not(X0),X0)))) ),
inference(resolution,[status(thm)],[f40710,f8]) ).
fof(f55751,plain,
! [X0] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| is_a_theorem(or(not(or(not(X0),X0)),or(not(X0),X0))) ),
inference(resolution,[status(thm)],[f40777,f33509]) ).
fof(f56574,plain,
! [X0,X1] :
( ~ sQ575_spl
| ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| is_a_theorem(or(X0,or(not(X1),X1))) ),
inference(resolution,[status(thm)],[f55751,f33508]) ).
fof(f56575,plain,
! [X0] :
( ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| is_a_theorem(or(not(X0),X0)) ),
inference(resolution,[status(thm)],[f55751,f33509]) ).
fof(f57413,plain,
! [X0,X1,X2] :
( ~ sQ575_spl
| ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| is_a_theorem(or(not(or(X0,X2)),or(X2,X1)))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[f9,f56574]) ).
fof(f66123,plain,
( ~ sQ575_spl
| ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| ~ is_a_theorem(or(not(a),a)) ),
inference(resolution,[status(thm)],[f57413,f7]) ).
fof(f66128,plain,
( ~ sQ575_spl
| ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f66123,f56575]) ).
fof(f66129,plain,
( ~ sQ575_spl
| ~ sQ577_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f66128]) ).
fof(f66130,plain,
$false,
inference(sat_refutation,[status(thm)],[f289,f311,f353,f623,f868,f1106,f1246,f1442,f7206,f9071,f9113,f66129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % 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 : Sun Sep 20 23:59:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 201.97/30.72 % Refutation found
% 201.97/30.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 201.97/30.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.85/31.46 % Elapsed time: 31.096444 seconds
% 12.85/31.46 % CPU time: 240.797325 seconds
% 12.85/31.46 % Total memory used: 1.041 GB
% 12.85/31.46 % Net memory used: 946.360 MB
%------------------------------------------------------------------------------