%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT071+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 : n004.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 01:25:32 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 11 unt; 8 def)
% Number of atoms : 182 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 186 ( 79 ~; 81 |; 14 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 53 ( 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ less(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f5,axiom,
! [X,Y] :
( ( leq(Y,X)
& leq(X,Y) )
=> 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(f38,hypothesis,
less(n5,n10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,conjecture,
~ ? [X] :
( in_closed(X,n10,n15)
& in_closed(X,n0,n5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
~ ~ ? [X] :
( in_closed(X,n10,n15)
& in_closed(X,n0,n5) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f43,plain,
! [X0] : ~ less(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f44,plain,
! [X,Y,Z] :
( less(X,Z)
| ~ less(Y,Z)
| ~ less(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f45,plain,
! [X,Z] :
( less(X,Z)
| ! [Y] :
( ~ less(Y,Z)
| ~ less(X,Y) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,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(f49,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)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( X0 = X1
| less(X0,X1)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ less(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X,Y] :
( X = Y
| ~ leq(Y,X)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f66,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(f67,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)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( leq(X1,X0)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ in_closed(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f170,plain,
less(n5,n10),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f173,plain,
( in_closed(sK3_skl,n10,n15)
& in_closed(sK3_skl,n0,n5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(X,sK3_skl)],[f42]) ).
fof(f174,plain,
in_closed(sK3_skl,n0,n5),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f175,plain,
in_closed(sK3_skl,n10,n15),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f186,plain,
leq(n5,n10),
inference(resolution,[status(thm)],[f51,f170]) ).
fof(f191,plain,
leq(n10,sK3_skl),
inference(resolution,[status(thm)],[f68,f175]) ).
fof(f195,plain,
leq(sK3_skl,n5),
inference(resolution,[status(thm)],[f69,f174]) ).
fof(f200,plain,
( sK3_skl = n5
| less(sK3_skl,n5) ),
inference(resolution,[status(thm)],[f50,f195]) ).
fof(f205,plain,
( n10 = sK3_skl
| less(n10,sK3_skl) ),
inference(resolution,[status(thm)],[f50,f191]) ).
fof(f208,definition,
( sQ0_spl
<=> less(sK3_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ0_spl
| less(sK3_skl,n5) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ1_spl
<=> sK3_skl = n5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ1_spl
| sK3_skl = n5 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f200,f208,f211]) ).
fof(f239,definition,
( sQ9_spl
<=> n5 = n10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ9_spl
| n5 = n10 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f243,definition,
( sQ10_spl
<=> less(n10,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ10_spl
| less(n10,sK3_skl) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,definition,
( sQ11_spl
<=> n10 = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ11_spl
| n10 = sK3_skl ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f205,f243,f246]) ).
fof(f261,plain,
( n10 = n5
| ~ leq(n10,n5) ),
inference(resolution,[status(thm)],[f54,f186]) ).
fof(f262,plain,
( sK3_skl = n10
| ~ leq(sK3_skl,n10) ),
inference(resolution,[status(thm)],[f54,f191]) ).
fof(f281,definition,
( sQ18_spl
<=> leq(n10,n5) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ18_spl
| ~ leq(n10,n5) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( sQ9_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f261,f281,f239]) ).
fof(f285,definition,
( sQ19_spl
<=> leq(sK3_skl,n10) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ19_spl
| ~ leq(sK3_skl,n10) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( sQ11_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f262,f285,f246]) ).
fof(f310,plain,
( ~ sQ1_spl
| leq(sK3_skl,n10) ),
inference(forward_demodulation,[status(thm)],[f212,f186]) ).
fof(f313,plain,
( ~ sQ1_spl
| less(sK3_skl,n10) ),
inference(forward_demodulation,[status(thm)],[f212,f170]) ).
fof(f323,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| less(n5,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f240,f244]) ).
fof(f344,plain,
! [X0] :
( ~ sQ0_spl
| less(X0,n5)
| ~ less(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f209,f46]) ).
fof(f351,plain,
( ~ sQ1_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f287]) ).
fof(f352,plain,
( ~ sQ1_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f358,plain,
( ~ sQ11_spl
| leq(n5,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f247,f186]) ).
fof(f359,plain,
( ~ sQ11_spl
| sK3_skl = n5
| ~ leq(sK3_skl,n5) ),
inference(resolution,[status(thm)],[f358,f54]) ).
fof(f361,definition,
( sQ21_spl
<=> leq(sK3_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ21_spl
| ~ leq(sK3_skl,n5) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( ~ sQ11_spl
| sQ1_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f359,f361,f211,f246]) ).
fof(f369,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| less(sK3_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f247,f313]) ).
fof(f370,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f43]) ).
fof(f371,plain,
( ~ sQ1_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f383,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f363,f195]) ).
fof(f384,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f463,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| less(n10,n5) ),
inference(resolution,[status(thm)],[f344,f244]) ).
fof(f466,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| leq(n10,n5) ),
inference(resolution,[status(thm)],[f463,f51]) ).
fof(f467,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f466,f283]) ).
fof(f468,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f484,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| less(n5,n5) ),
inference(resolution,[status(thm)],[f323,f344]) ).
fof(f487,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f43]) ).
fof(f488,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f489,plain,
$false,
inference(sat_refutation,[status(thm)],[f214,f249,f284,f288,f352,f364,f371,f384,f468,f488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT071+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.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 01:24:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % 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
% 0.14/0.42 % Elapsed time: 0.051511 seconds
% 0.14/0.42 % CPU time: 0.152106 seconds
% 0.14/0.42 % Total memory used: 57.268 MB
% 0.14/0.42 % Net memory used: 57.134 MB
%------------------------------------------------------------------------------