%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT073+1 : TPTP v9.3.1. Released v9.3.0.
% 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 01:25:33 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 11 unt; 2 def)
% Number of atoms : 96 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 98 ( 43 ~; 38 |; 12 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 51 ( 49 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y,Z] :
( ( less(Y,Z)
& less(X,Y) )
=> less(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(X,B)
& leq(A,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
less(n0,n5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
less(n5,n10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
? [X] :
( in_closed(X,n5,n10)
& in_closed(X,n0,n10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ? [X] :
( in_closed(X,n5,n10)
& in_closed(X,n0,n10) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f43,plain,
! [X,Y,Z] :
( less(X,Z)
| ~ less(Y,Z)
| ~ less(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f44,plain,
! [X,Z] :
( less(X,Z)
| ! [Y] :
( ~ less(Y,Z)
| ~ less(X,Y) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,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(f48,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)],[f47]) ).
fof(f50,plain,
! [X0,X1] :
( ~ less(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( X0 != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f65,plain,
! [X,A,B] :
( ( ~ leq(X,B)
| ~ leq(A,X)
| in_closed(X,A,B) )
& ( ( leq(X,B)
& leq(A,X) )
| ~ in_closed(X,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f66,plain,
( ! [X,A,B] :
( ~ leq(X,B)
| ~ leq(A,X)
| in_closed(X,A,B) )
& ! [X,A,B] :
( ( leq(X,B)
& leq(A,X) )
| ~ in_closed(X,A,B) ) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ leq(X0,X2)
| ~ leq(X1,X0)
| in_closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f168,plain,
less(n0,n5),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f169,plain,
less(n5,n10),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f171,plain,
! [X] :
( ~ in_closed(X,n5,n10)
| ~ in_closed(X,n0,n10) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f172,plain,
! [X0] :
( ~ in_closed(X0,n5,n10)
| ~ in_closed(X0,n0,n10) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [X0] : leq(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f182,plain,
leq(n5,n10),
inference(resolution,[status(thm)],[f50,f169]) ).
fof(f185,plain,
! [X0] :
( less(X0,n10)
| ~ less(X0,n5) ),
inference(resolution,[status(thm)],[f45,f169]) ).
fof(f187,plain,
less(n0,n10),
inference(resolution,[status(thm)],[f185,f168]) ).
fof(f189,plain,
leq(n0,n10),
inference(resolution,[status(thm)],[f187,f50]) ).
fof(f343,plain,
! [X0] :
( ~ in_closed(X0,n5,n10)
| ~ leq(X0,n10)
| ~ leq(n0,X0) ),
inference(resolution,[status(thm)],[f69,f172]) ).
fof(f347,plain,
! [X0] :
( ~ in_closed(X0,n5,n10)
| ~ leq(n0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f68]) ).
fof(f354,plain,
! [X0] :
( ~ leq(X0,n10)
| ~ leq(n5,X0)
| ~ leq(n0,X0) ),
inference(resolution,[status(thm)],[f347,f69]) ).
fof(f355,plain,
( ~ leq(n10,n10)
| ~ leq(n5,n10) ),
inference(resolution,[status(thm)],[f354,f189]) ).
fof(f359,definition,
( sQ15_spl
<=> leq(n5,n10) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( sQ15_spl
| ~ leq(n5,n10) ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,definition,
( sQ16_spl
<=> leq(n10,n10) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ16_spl
| ~ leq(n10,n10) ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,plain,
( ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f355,f359,f362]) ).
fof(f374,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f361,f182]) ).
fof(f375,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f376,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f173]) ).
fof(f377,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f378,plain,
$false,
inference(sat_refutation,[status(thm)],[f365,f375,f377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT073+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 01:24:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.058181 seconds
% 0.11/0.43 % CPU time: 0.147434 seconds
% 0.11/0.43 % Total memory used: 51.729 MB
% 0.11/0.43 % Net memory used: 51.628 MB
%------------------------------------------------------------------------------