%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 01:07:38 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 52 ( 22 ~; 14 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 56 ( 53 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q] :
( a_truth(Q)
| ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ~ ( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [P,Q] :
( a_truth(Q)
| ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [A] : ~ a_truth(implies(A,A))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [Q] :
( a_truth(Q)
| ! [P] :
( ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f4,plain,
( ~ a_truth(implies(sK0_skl,sK0_skl))
& ! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))
& ! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))
& ! [P,Q] : a_truth(implies(P,implies(Q,P)))
& ! [Q] :
( a_truth(Q)
| ! [P] :
( ~ a_truth(P)
| ~ a_truth(implies(P,Q)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( a_truth(X1)
| ~ a_truth(X0)
| ~ a_truth(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1] : a_truth(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f7,plain,
! [X0,X1,X2] : a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f9,plain,
~ a_truth(implies(sK0_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2] :
( a_truth(implies(implies(X0,X1),implies(X0,X2)))
| ~ a_truth(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f7,f5]) ).
fof(f24,plain,
! [X0,X1,X2] :
( a_truth(implies(X0,X2))
| ~ a_truth(implies(X0,X1))
| ~ a_truth(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f12,f5]) ).
fof(f39,plain,
! [X0,X1,X2] :
( a_truth(implies(X0,X2))
| ~ a_truth(implies(X0,implies(implies(X1,X0),X2))) ),
inference(resolution,[status(thm)],[f24,f6]) ).
fof(f46,plain,
! [X0] : a_truth(implies(X0,X0)),
inference(resolution,[status(thm)],[f39,f6]) ).
fof(f48,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f9,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.43 % Computer : n003.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8046.5625MB
% 0.14/0.43 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Mon Sep 21 00:30:45 UTC 2026
% 0.14/0.44 % CPUTime :
% 0.14/0.45 % Drodi V4.1.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.55 % Elapsed time: 0.104273 seconds
% 0.22/0.55 % CPU time: 0.095290 seconds
% 0.22/0.55 % Total memory used: 1.810 MB
% 0.22/0.55 % Net memory used: 1.801 MB
%------------------------------------------------------------------------------