%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL875-1 : TPTP v9.3.1. Bugfixed v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:09:01 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.60s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 145 ( 86 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 24 ( 24 usr; 23 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] : is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : is_a_theorem(implies(A,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U,V] : is_a_theorem(implies(implies(U,implies(U,V)),implies(U,V))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),w)),implies(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15),implies(implies(v16,implies(implies(implies(v17,v17),implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))))),v21)),v22))),v22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
~ is_a_theorem(implies(implies(implies(x,implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),w)),implies(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15),implies(implies(v16,implies(implies(implies(v17,v17),implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))))),v21)),v22))),v22)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f9,f8]) ).
fof(f18,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f10,f8]) ).
fof(f19,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f16,f8]) ).
fof(f21,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f18,f8]) ).
fof(f22,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(implies(x,implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),w)),implies(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15),implies(implies(v16,implies(implies(implies(v17,v17),implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))))),v21)),v22))),X0))
| ~ is_a_theorem(implies(X0,v22)) ),
inference(resolution,[status(thm)],[f19,f13]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f21,f16]) ).
fof(f31,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f21,f11]) ).
fof(f32,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,implies(X1,X2)),X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f31,f21]) ).
fof(f37,plain,
! [X0] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(implies(x,implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),w)),implies(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15),implies(implies(v16,implies(implies(implies(v17,v17),implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))))),v21)),v22))),implies(X0,v22))) ),
inference(resolution,[status(thm)],[f22,f31]) ).
fof(f140,plain,
( ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15))
| ~ is_a_theorem(implies(x,implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),w)))
| ~ is_a_theorem(implies(v16,implies(implies(implies(v17,v17),implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))))),v21))) ),
inference(resolution,[status(thm)],[f37,f32]) ).
fof(f146,plain,
( ~ is_a_theorem(implies(implies(implies(v17,v17),implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))))),implies(v16,v21)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15))
| ~ is_a_theorem(implies(x,implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),w))) ),
inference(resolution,[status(thm)],[f140,f18]) ).
fof(f149,plain,
( ~ is_a_theorem(implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(v17,v17),implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))))),implies(v16,v21)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(resolution,[status(thm)],[f146,f18]) ).
fof(f152,plain,
( ~ is_a_theorem(implies(implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21)))),implies(v16,v21)))
| ~ is_a_theorem(implies(v17,v17))
| ~ is_a_theorem(implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(resolution,[status(thm)],[f149,f28]) ).
fof(f160,plain,
( ~ is_a_theorem(implies(implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21)))),implies(v16,v21)))
| ~ is_a_theorem(implies(implies(implies(y,y),implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w))))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f11]) ).
fof(f162,plain,
( ~ is_a_theorem(implies(implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w)))),implies(x,w)))
| ~ is_a_theorem(implies(y,y))
| ~ is_a_theorem(implies(implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21)))),implies(v16,v21)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(resolution,[status(thm)],[f160,f28]) ).
fof(f170,plain,
( ~ is_a_theorem(implies(implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w)))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(v18,v18),implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21)))),implies(v16,v21)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f11]) ).
fof(f412,plain,
( ~ is_a_theorem(implies(implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))),implies(v16,v21)))
| ~ is_a_theorem(implies(v18,v18))
| ~ is_a_theorem(implies(implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w)))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(resolution,[status(thm)],[f170,f28]) ).
fof(f420,plain,
( ~ is_a_theorem(implies(implies(implies(v19,v19),implies(implies(v20,v20),implies(v16,v21))),implies(v16,v21)))
| ~ is_a_theorem(implies(implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w)))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f11]) ).
fof(f426,plain,
( ~ is_a_theorem(implies(v20,v20))
| ~ is_a_theorem(implies(v19,v19))
| ~ is_a_theorem(implies(implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w)))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(resolution,[status(thm)],[f420,f32]) ).
fof(f432,plain,
( ~ is_a_theorem(implies(v20,v20))
| ~ is_a_theorem(implies(implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w)))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f11]) ).
fof(f434,plain,
( ~ is_a_theorem(implies(implies(implies(z,z),implies(implies(u,u),implies(implies(v,v),implies(x,w)))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f11]) ).
fof(f435,plain,
( ~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w)))
| ~ is_a_theorem(implies(z,z))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(resolution,[status(thm)],[f434,f28]) ).
fof(f439,plain,
( ~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w)))
| ~ is_a_theorem(implies(implies(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))),implies(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14),v15)),v15)) ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f11]) ).
fof(f440,plain,
( ~ is_a_theorem(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14))
| ~ is_a_theorem(implies(implies(v6,v7),implies(implies(v7,v8),implies(v6,v8))))
| ~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w))) ),
inference(resolution,[status(thm)],[f439,f32]) ).
fof(f858,plain,
( ~ is_a_theorem(implies(implies(v7,v8),implies(implies(v6,v7),implies(v6,v8))))
| ~ is_a_theorem(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14))
| ~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w))) ),
inference(resolution,[status(thm)],[f440,f18]) ).
fof(f861,plain,
( ~ is_a_theorem(implies(implies(implies(implies(v9,implies(v9,v10)),implies(v9,v10)),implies(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))),v14)),v14))
| ~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w))) ),
inference(forward_subsumption_resolution,[status(thm)],[f858,f9]) ).
fof(f862,plain,
( ~ is_a_theorem(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))))
| ~ is_a_theorem(implies(implies(v9,implies(v9,v10)),implies(v9,v10)))
| ~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w))) ),
inference(resolution,[status(thm)],[f861,f32]) ).
fof(f866,plain,
( ~ is_a_theorem(implies(implies(v11,v12),implies(implies(v12,v13),implies(v11,v13))))
| ~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w))) ),
inference(forward_subsumption_resolution,[status(thm)],[f862,f12]) ).
fof(f869,plain,
( ~ is_a_theorem(implies(implies(v12,v13),implies(implies(v11,v12),implies(v11,v13))))
| ~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w))) ),
inference(resolution,[status(thm)],[f866,f18]) ).
fof(f872,plain,
~ is_a_theorem(implies(implies(implies(u,u),implies(implies(v,v),implies(x,w))),implies(x,w))),
inference(forward_subsumption_resolution,[status(thm)],[f869,f9]) ).
fof(f873,plain,
( ~ is_a_theorem(implies(v,v))
| ~ is_a_theorem(implies(u,u)) ),
inference(resolution,[status(thm)],[f872,f32]) ).
fof(f878,plain,
~ is_a_theorem(implies(v,v)),
inference(forward_subsumption_resolution,[status(thm)],[f873,f11]) ).
fof(f893,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f878,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL875-1 : TPTP v9.3.1. Bugfixed v5.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 01:08:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.60 % Refutation found
% 0.15/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.34/0.65 % Elapsed time: 0.259191 seconds
% 1.34/0.65 % CPU time: 1.708890 seconds
% 1.34/0.65 % Total memory used: 85.323 MB
% 1.34/0.65 % Net memory used: 82.336 MB
%------------------------------------------------------------------------------