%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:07:57 PM UTC 2026
% Result : Theorem 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 17 unt; 10 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 175 ( 67 ~; 72 |; 19 &)
% ( 15 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 16 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(Y)
& is_a_theorem(X) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,conjecture,
adjunction,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,negated_conjecture,
~ adjunction,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
( modus_ponens
<=> ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f92,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
( ( ? [Y] :
( ~ is_a_theorem(Y)
& ? [X] :
( is_a_theorem(implies(X,Y))
& is_a_theorem(X) ) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
( ( ( ~ is_a_theorem(sK0_skl)
& is_a_theorem(implies(sK1_skl,sK0_skl))
& is_a_theorem(sK1_skl) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f129,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f130,plain,
( ( ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f214,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f215,plain,
modus_tollens,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f221,plain,
and_3,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f243,plain,
( adjunction
<=> ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f244,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(Y)
& is_a_theorem(X) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(NNF_transformation,[status(thm)],[f243]) ).
fof(f245,plain,
( ( ( ~ is_a_theorem(and(sK58_skl,sK59_skl))
& is_a_theorem(sK59_skl)
& is_a_theorem(sK58_skl) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58_skl,sK59_skl]),skolemize(X,sK58_skl),skolemize(Y,sK59_skl)],[f244]) ).
fof(f247,plain,
( is_a_theorem(sK58_skl)
| adjunction ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f248,plain,
( is_a_theorem(sK59_skl)
| adjunction ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f249,plain,
( ~ is_a_theorem(and(sK58_skl,sK59_skl))
| adjunction ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f344,plain,
axiom_4,
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f352,plain,
~ adjunction,
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f353,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
! [X0,X1] :
( sQ1_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f357,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f95,f353,f356]) ).
fof(f387,definition,
( sQ9_spl
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ9_spl
| ~ modus_tollens ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f453,definition,
( sQ27_spl
<=> and_3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ27_spl
| ~ and_3 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,definition,
! [X0,X1] :
( sQ28_spl
<=> is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f457,plain,
! [X0,X1] :
( ~ sQ28_spl
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f131,f453,f456]) ).
fof(f711,definition,
( sQ97_spl
<=> adjunction ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f712,plain,
( ~ sQ97_spl
| adjunction ),
inference(component_clause,[status(thm)],[f711]) ).
fof(f718,definition,
( sQ99_spl
<=> is_a_theorem(sK58_skl) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( sQ99_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f247,f711,f718]) ).
fof(f722,definition,
( sQ100_spl
<=> is_a_theorem(sK59_skl) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f725,plain,
( sQ100_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f248,f711,f722]) ).
fof(f726,definition,
( sQ101_spl
<=> is_a_theorem(and(sK58_skl,sK59_skl)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f728,plain,
( sQ101_spl
| ~ is_a_theorem(and(sK58_skl,sK59_skl)) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,plain,
( ~ sQ101_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f249,f711,f726]) ).
fof(f767,definition,
( sQ112_spl
<=> axiom_4 ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f769,plain,
( sQ112_spl
| ~ axiom_4 ),
inference(component_clause,[status(thm)],[f767]) ).
fof(f982,plain,
( ~ sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f712,f352]) ).
fof(f983,plain,
~ sQ97_spl,
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f996,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f214]) ).
fof(f997,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f996]) ).
fof(f1085,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ sQ1_spl
| is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f357,f457]) ).
fof(f1211,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ sQ1_spl
| ~ is_a_theorem(X1)
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f357,f1085]) ).
fof(f1368,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f221]) ).
fof(f1369,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1368]) ).
fof(f1402,plain,
( sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f769,f344]) ).
fof(f1403,plain,
sQ112_spl,
inference(contradiction_clause,[status(thm)],[f1402]) ).
fof(f1415,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f215]) ).
fof(f1416,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1415]) ).
fof(f1557,plain,
( sQ101_spl
| ~ sQ28_spl
| ~ sQ1_spl
| ~ is_a_theorem(sK58_skl)
| ~ is_a_theorem(sK59_skl) ),
inference(resolution,[status(thm)],[f1211,f728]) ).
fof(f1571,plain,
( sQ101_spl
| ~ sQ28_spl
| ~ sQ1_spl
| ~ sQ99_spl
| ~ sQ100_spl ),
inference(split_clause,[status(thm)],[f1557,f722,f718,f356,f456,f726]) ).
fof(f1579,plain,
$false,
inference(sat_refutation,[status(thm)],[f359,f459,f721,f725,f729,f983,f997,f1369,f1403,f1416,f1571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:37:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45 % Elapsed time: 0.086764 seconds
% 0.12/0.45 % CPU time: 0.364662 seconds
% 0.12/0.45 % Total memory used: 94.193 MB
% 0.12/0.45 % Net memory used: 93.817 MB
%------------------------------------------------------------------------------