%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 01:07:55 PM UTC 2026
% Result : Theorem 0.10s 0.34s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 11 unt; 9 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 178 ( 70 ~; 73 |; 19 &)
% ( 14 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 13 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 44 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f88,conjecture,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,negated_conjecture,
~ adjunction,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,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(f91,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)],[f90]) ).
fof(f92,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)],[f91]) ).
fof(f93,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)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f128,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(f129,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)],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f213,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f220,plain,
and_3,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f242,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(f243,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)],[f242]) ).
fof(f244,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)],[f243]) ).
fof(f246,plain,
( is_a_theorem(sK58_skl)
| adjunction ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f247,plain,
( is_a_theorem(sK59_skl)
| adjunction ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f248,plain,
( ~ is_a_theorem(and(sK58_skl,sK59_skl))
| adjunction ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f350,plain,
~ adjunction,
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f351,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,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(f355,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f94,f351,f354]) ).
fof(f451,definition,
( sQ27_spl
<=> and_3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( sQ27_spl
| ~ and_3 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,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(f455,plain,
! [X0,X1] :
( ~ sQ28_spl
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f130,f451,f454]) ).
fof(f709,definition,
( sQ97_spl
<=> adjunction ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( ~ sQ97_spl
| adjunction ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f712,definition,
! [X0,X1] :
( sQ98_spl
<=> ( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f713,plain,
! [X0,X1] :
( ~ sQ98_spl
| is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f716,definition,
( sQ99_spl
<=> is_a_theorem(sK58_skl) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f719,plain,
( sQ99_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f246,f709,f716]) ).
fof(f720,definition,
( sQ100_spl
<=> is_a_theorem(sK59_skl) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f723,plain,
( sQ100_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f247,f709,f720]) ).
fof(f724,definition,
( sQ101_spl
<=> is_a_theorem(and(sK58_skl,sK59_skl)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f726,plain,
( sQ101_spl
| ~ is_a_theorem(and(sK58_skl,sK59_skl)) ),
inference(component_clause,[status(thm)],[f724]) ).
fof(f727,plain,
( ~ sQ101_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f248,f709,f724]) ).
fof(f980,plain,
( ~ sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f710,f350]) ).
fof(f981,plain,
~ sQ97_spl,
inference(contradiction_clause,[status(thm)],[f980]) ).
fof(f994,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f213]) ).
fof(f995,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f994]) ).
fof(f1080,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ sQ1_spl
| is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f355,f455]) ).
fof(f1199,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)],[f355,f1080]) ).
fof(f1212,plain,
( sQ101_spl
| ~ sQ98_spl
| ~ is_a_theorem(sK59_skl)
| ~ is_a_theorem(sK58_skl) ),
inference(resolution,[status(thm)],[f713,f726]) ).
fof(f1223,plain,
( sQ101_spl
| ~ sQ98_spl
| ~ sQ100_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f1212,f716,f720,f712,f724]) ).
fof(f1355,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f453,f220]) ).
fof(f1356,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1355]) ).
fof(f1357,plain,
( ~ sQ28_spl
| ~ sQ1_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1199,f712,f354,f454]) ).
fof(f1358,plain,
$false,
inference(sat_refutation,[status(thm)],[f357,f457,f719,f723,f727,f981,f995,f1223,f1356,f1357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 21 00:36:52 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.31 % Drodi V4.1.1
% 0.10/0.34 % Refutation found
% 0.10/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.36 % Elapsed time: 0.058197 seconds
% 0.10/0.36 % CPU time: 0.170892 seconds
% 0.10/0.36 % Total memory used: 90.805 MB
% 0.10/0.36 % Net memory used: 90.610 MB
%------------------------------------------------------------------------------