%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT081+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 01:25:34 PM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 95 ( 20 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 104 ( 41 ~; 27 |; 32 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 50 ( 44 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
=> X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,A,B] :
( in_lopen(X,A,B)
<=> ( leq(X,B)
& less(A,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
less(v400,v800),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
( v600 != v800
& v400 != v800
& v400 != v600
& v200 != v800
& v200 != v600
& v200 != v400
& v0 != v800
& v0 != v600
& v0 != v400
& v0 != v200 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
~ ? [X,Y] :
( leq(v200,Y)
& in_lopen(Y,v0,v600)
& leq(v800,X)
& in_lopen(X,v0,v400) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ~ ? [X,Y] :
( leq(v200,Y)
& in_lopen(Y,v0,v600)
& leq(v800,X)
& in_lopen(X,v0,v400) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f51,plain,
! [X,Y] :
( ( ( X != Y
& ~ less(X,Y) )
| leq(X,Y) )
& ( X = Y
| less(X,Y)
| ~ leq(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f52,plain,
( ! [X,Y] :
( ( X != Y
& ~ less(X,Y) )
| leq(X,Y) )
& ! [X,Y] :
( X = Y
| less(X,Y)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0,X1] :
( ~ less(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
! [X,Y] :
( X = Y
| ~ leq(Y,X)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f66,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f67,plain,
! [X,Z] :
( leq(X,Z)
| ! [Y] :
( ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f74,plain,
! [X,A,B] :
( ( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) )
& ( ( leq(X,B)
& less(A,X) )
| ~ in_lopen(X,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f75,plain,
( ! [X,A,B] :
( ~ leq(X,B)
| ~ less(A,X)
| in_lopen(X,A,B) )
& ! [X,A,B] :
( ( leq(X,B)
& less(A,X) )
| ~ in_lopen(X,A,B) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f77,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ in_lopen(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f140,plain,
less(v400,v800),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f150,plain,
v400 != v800,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f152,plain,
? [Y] :
( leq(v200,Y)
& in_lopen(Y,v0,v600)
& ? [X] :
( leq(v800,X)
& in_lopen(X,v0,v400) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f153,plain,
( leq(v200,sK3_skl)
& in_lopen(sK3_skl,v0,v600)
& leq(v800,sK4_skl)
& in_lopen(sK4_skl,v0,v400) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(Y,sK3_skl),skolemize(X,sK4_skl)],[f152]) ).
fof(f154,plain,
in_lopen(sK4_skl,v0,v400),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
leq(v800,sK4_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f173,plain,
leq(v400,v800),
inference(resolution,[status(thm)],[f140,f54]) ).
fof(f240,plain,
( v400 = v800
| ~ leq(v800,v400) ),
inference(resolution,[status(thm)],[f173,f57]) ).
fof(f242,plain,
~ leq(v800,v400),
inference(forward_subsumption_resolution,[status(thm)],[f240,f150]) ).
fof(f292,plain,
leq(sK4_skl,v400),
inference(resolution,[status(thm)],[f77,f154]) ).
fof(f310,plain,
! [X0] :
( leq(v800,X0)
| ~ leq(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f68,f155]) ).
fof(f554,plain,
leq(v800,v400),
inference(resolution,[status(thm)],[f310,f292]) ).
fof(f556,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f554,f242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT081+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 01:25:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.46 % Elapsed time: 0.073501 seconds
% 0.09/0.46 % CPU time: 0.252005 seconds
% 0.09/0.46 % Total memory used: 83.899 MB
% 0.09/0.46 % Net memory used: 83.717 MB
%------------------------------------------------------------------------------