%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT086+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 : 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 01:25:34 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 13 unt; 4 def)
% Number of atoms : 165 ( 23 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 195 ( 89 ~; 69 |; 29 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 70 ( 66 !; 4 ?)
% 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(f33,axiom,
less(v0,v200),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
less(v200,v400),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
less(v600,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] :
( ( ( in_lopen(Y,v0,v400)
& ~ in_lopen(X,v0,v600) )
| ( ~ in_lopen(Y,v0,v400)
& in_lopen(X,v0,v600) ) )
& in_lopen(Y,v0,v200)
& leq(v800,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ? [X,Y] :
( ( ( in_lopen(Y,v0,v400)
& ~ in_lopen(X,v0,v600) )
| ( ~ in_lopen(Y,v0,v400)
& in_lopen(X,v0,v600) ) )
& in_lopen(Y,v0,v200)
& leq(v800,X) ),
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(f55,plain,
! [X0,X1] :
( 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(f76,plain,
! [X0,X1,X2] :
( less(X1,X0)
| ~ in_lopen(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ in_lopen(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ leq(X0,X2)
| ~ less(X1,X0)
| in_lopen(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f132,plain,
less(v0,v200),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f136,plain,
less(v200,v400),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f141,plain,
less(v600,v800),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f151,plain,
v600 != v800,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f152,plain,
! [X,Y] :
( ( ( ~ in_lopen(Y,v0,v400)
| in_lopen(X,v0,v600) )
& ( in_lopen(Y,v0,v400)
| ~ in_lopen(X,v0,v600) ) )
| ~ in_lopen(Y,v0,v200)
| ~ leq(v800,X) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f154,plain,
! [X0,X1] :
( ~ in_lopen(X1,v0,v400)
| in_lopen(X0,v0,v600)
| ~ in_lopen(X1,v0,v200)
| ~ leq(v800,X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f162,definition,
! [X0] :
( sQ2_spl
<=> ( in_lopen(X0,v0,v600)
| ~ leq(v800,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f163,plain,
! [X0] :
( ~ sQ2_spl
| in_lopen(X0,v0,v600)
| ~ leq(v800,X0) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
! [X1] :
( sQ3_spl
<=> ( ~ in_lopen(X1,v0,v400)
| ~ in_lopen(X1,v0,v200) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f166,plain,
! [X0] :
( ~ sQ3_spl
| ~ in_lopen(X0,v0,v400)
| ~ in_lopen(X0,v0,v200) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f154,f162,f165]) ).
fof(f169,plain,
! [X0] : leq(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f55]) ).
fof(f186,plain,
leq(v200,v400),
inference(resolution,[status(thm)],[f136,f54]) ).
fof(f204,plain,
leq(v600,v800),
inference(resolution,[status(thm)],[f141,f54]) ).
fof(f351,plain,
( v800 = v600
| ~ leq(v800,v600) ),
inference(resolution,[status(thm)],[f204,f57]) ).
fof(f353,definition,
( sQ31_spl
<=> leq(v800,v600) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ31_spl
| ~ leq(v800,v600) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
( sQ32_spl
<=> v800 = v600 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( ~ sQ32_spl
| v800 = v600 ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,plain,
( sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f351,f353,f356]) ).
fof(f364,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f357,f151]) ).
fof(f365,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f382,plain,
! [X0] :
( leq(X0,v400)
| ~ leq(X0,v200) ),
inference(resolution,[status(thm)],[f68,f186]) ).
fof(f413,plain,
! [X0] :
( ~ sQ2_spl
| leq(X0,v600)
| ~ leq(v800,X0) ),
inference(resolution,[status(thm)],[f163,f77]) ).
fof(f415,plain,
( ~ sQ2_spl
| leq(v800,v600) ),
inference(resolution,[status(thm)],[f413,f169]) ).
fof(f416,plain,
( ~ sQ2_spl
| sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f355]) ).
fof(f417,plain,
( ~ sQ2_spl
| sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f419,plain,
! [X0] :
( ~ sQ3_spl
| ~ leq(X0,v400)
| ~ less(v0,X0)
| ~ in_lopen(X0,v0,v200) ),
inference(resolution,[status(thm)],[f166,f78]) ).
fof(f420,plain,
! [X0] :
( ~ sQ3_spl
| ~ leq(X0,v400)
| ~ in_lopen(X0,v0,v200) ),
inference(forward_subsumption_resolution,[status(thm)],[f419,f76]) ).
fof(f421,plain,
! [X0] :
( ~ sQ3_spl
| ~ leq(X0,v200)
| ~ less(v0,X0)
| ~ leq(X0,v400) ),
inference(resolution,[status(thm)],[f420,f78]) ).
fof(f508,plain,
! [X0] :
( ~ sQ3_spl
| ~ leq(X0,v200)
| ~ less(v0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f421,f382]) ).
fof(f511,plain,
( ~ sQ3_spl
| ~ less(v0,v200) ),
inference(resolution,[status(thm)],[f508,f169]) ).
fof(f512,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f132]) ).
fof(f513,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f514,plain,
$false,
inference(sat_refutation,[status(thm)],[f168,f359,f365,f417,f513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT086+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 : n003.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 01:27:00 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.065120 seconds
% 0.14/0.45 % CPU time: 0.222301 seconds
% 0.14/0.45 % Total memory used: 83.254 MB
% 0.14/0.45 % Net memory used: 83.042 MB
%------------------------------------------------------------------------------