%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT082+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:25:34 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 9 unt; 5 def)
% Number of atoms : 157 ( 39 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 171 ( 67 ~; 46 |; 50 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 45 ( 36 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y] :
( leq(X,Y)
<=> ( X = Y
| less(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
=> X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,A,B] :
( in_closed(X,A,B)
<=> ( leq(X,B)
& leq(A,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
less(v600,v601),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
( v600 != v601
& v500 != v601
& v500 != v600
& v300 != v601
& v300 != v600
& v300 != v500
& v32 != v601
& v32 != v600
& v32 != v500
& v32 != v300
& v16 != v601
& v16 != v600
& v16 != v500
& v16 != v300
& v16 != v32
& v0 != v601
& v0 != v600
& v0 != v500
& v0 != v300
& v0 != v32
& v0 != v16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,conjecture,
~ ? [X,Y,Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& in_open(Y,v0,v500)
& less(v300,Y)
& in_closed(X,v601,v601)
& in_closed(X,v600,v600) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
~ ~ ? [X,Y,Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& in_open(Y,v0,v500)
& less(v300,Y)
& in_closed(X,v601,v601)
& in_closed(X,v600,v600) ),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f64,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(f65,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)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| less(X0,X1)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ~ less(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [X,Y] :
( X = Y
| ~ leq(Y,X)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f70,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f82,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(f83,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)],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( leq(X1,X0)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f167,plain,
less(v600,v601),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f188,plain,
v600 != v601,
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f189,plain,
? [Z] :
( in_lopen(Z,v0,v32)
& leq(v16,Z)
& ? [Y] :
( in_open(Y,v0,v500)
& less(v300,Y)
& ? [X] :
( in_closed(X,v601,v601)
& in_closed(X,v600,v600) ) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f190,plain,
( in_lopen(sK3_skl,v0,v32)
& leq(v16,sK3_skl)
& in_open(sK4_skl,v0,v500)
& less(v300,sK4_skl)
& in_closed(sK5_skl,v601,v601)
& in_closed(sK5_skl,v600,v600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(Z,sK3_skl),skolemize(Y,sK4_skl),skolemize(X,sK5_skl)],[f189]) ).
fof(f191,plain,
in_closed(sK5_skl,v600,v600),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
in_closed(sK5_skl,v601,v601),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f241,plain,
leq(v601,sK5_skl),
inference(resolution,[status(thm)],[f84,f192]) ).
fof(f242,plain,
leq(v600,sK5_skl),
inference(resolution,[status(thm)],[f84,f191]) ).
fof(f246,plain,
( sK5_skl = v601
| ~ leq(sK5_skl,v601) ),
inference(resolution,[status(thm)],[f241,f70]) ).
fof(f248,definition,
( sQ3_spl
<=> leq(sK5_skl,v601) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ3_spl
| ~ leq(sK5_skl,v601) ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
( sQ4_spl
<=> sK5_skl = v601 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ4_spl
| sK5_skl = v601 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f246,f248,f251]) ).
fof(f268,plain,
( ~ sQ4_spl
| v600 != sK5_skl ),
inference(forward_demodulation,[status(thm)],[f252,f188]) ).
fof(f269,plain,
leq(sK5_skl,v600),
inference(resolution,[status(thm)],[f85,f191]) ).
fof(f290,plain,
( v600 = sK5_skl
| less(v600,sK5_skl) ),
inference(resolution,[status(thm)],[f242,f66]) ).
fof(f294,definition,
( sQ7_spl
<=> sK5_skl = v600 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( ~ sQ7_spl
| sK5_skl = v600 ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f298,definition,
( sQ8_spl
<=> less(v600,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( ~ sQ8_spl
| less(v600,sK5_skl) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f290,f298,f294]) ).
fof(f302,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f268]) ).
fof(f303,plain,
( ~ sQ7_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f302]) ).
fof(f329,plain,
( v600 = sK5_skl
| ~ leq(v600,sK5_skl) ),
inference(resolution,[status(thm)],[f269,f70]) ).
fof(f331,definition,
( sQ9_spl
<=> leq(v600,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( sQ9_spl
| ~ leq(v600,sK5_skl) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f329,f331,f294]) ).
fof(f363,plain,
( ~ sQ7_spl
| less(sK5_skl,v601) ),
inference(forward_demodulation,[status(thm)],[f295,f167]) ).
fof(f389,plain,
( sQ3_spl
| ~ less(sK5_skl,v601) ),
inference(resolution,[status(thm)],[f250,f67]) ).
fof(f390,plain,
( sQ3_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f363]) ).
fof(f391,plain,
( sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f440,plain,
( sQ9_spl
| ~ less(v600,sK5_skl) ),
inference(resolution,[status(thm)],[f333,f67]) ).
fof(f441,plain,
( sQ9_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f299]) ).
fof(f442,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f443,plain,
$false,
inference(sat_refutation,[status(thm)],[f254,f301,f303,f334,f391,f442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT082+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 01:30:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.057182 seconds
% 0.14/0.43 % CPU time: 0.188573 seconds
% 0.14/0.43 % Total memory used: 83.626 MB
% 0.14/0.43 % Net memory used: 83.510 MB
%------------------------------------------------------------------------------