%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU123+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:19:17 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 7 unt; 2 def)
% Number of atoms : 49 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 44 ( 18 ~; 14 |; 7 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 15 ( 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [A] :
( subset(A,empty_set)
=> A = empty_set ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f28,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f72,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f79,plain,
? [A] :
( A != empty_set
& subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f80,plain,
( sK6_skl != empty_set
& subset(sK6_skl,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f79]) ).
fof(f81,plain,
subset(sK6_skl,empty_set),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
sK6_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f103,plain,
( ~ subset(empty_set,sK6_skl)
| empty_set = sK6_skl ),
inference(resolution,[status(thm)],[f32,f81]) ).
fof(f105,definition,
( sQ0_spl
<=> empty_set = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ0_spl
| empty_set = sK6_skl ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
( sQ1_spl
<=> subset(empty_set,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( sQ1_spl
| ~ subset(empty_set,sK6_skl) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f103,f105,f108]) ).
fof(f112,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f82]) ).
fof(f113,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f112]) ).
fof(f114,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f72]) ).
fof(f115,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
$false,
inference(sat_refutation,[status(thm)],[f111,f113,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU123+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:57:13 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.050572 seconds
% 0.12/0.41 % CPU time: 0.140198 seconds
% 0.12/0.41 % Total memory used: 101.996 MB
% 0.12/0.41 % Net memory used: 101.845 MB
%------------------------------------------------------------------------------