%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 01:07:53 PM UTC 2026
% Result : Theorem 0.15s 5.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 42 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 15 ~; 12 |; 4 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ equivalence_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f99,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| equivalence_1 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f100,plain,
( ( ~ is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl)))
| equivalence_1 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl]),skolemize(X,sK26_skl),skolemize(Y,sK27_skl)],[f99]) ).
fof(f102,plain,
( ~ is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl)))
| equivalence_1 ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f115,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P))
| kn2 )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f116,plain,
( ( ~ is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl))
| kn2 )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f163,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f164,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f167,plain,
op_equiv,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f170,plain,
kn2,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f176,plain,
~ equivalence_1,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f182,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f117,f170]) ).
fof(f205,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f164,f167]) ).
fof(f209,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(paramodulation,[status(thm)],[f205,f182]) ).
fof(f230,plain,
~ is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f102,f176]) ).
fof(f231,plain,
$false,
inference(resolution,[status(thm)],[f230,f209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n001.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 00:42:20 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.38 % Drodi V4.1.1
% 0.15/5.41 % Refutation found
% 0.15/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.45 % Elapsed time: 0.058684 seconds
% 0.15/5.45 % CPU time: 0.152076 seconds
% 0.15/5.45 % Total memory used: 83.139 MB
% 0.15/5.45 % Net memory used: 83.089 MB
%------------------------------------------------------------------------------