%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET063+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:09:08 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% 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(f1,axiom,
! [B] : subset(empty_set,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B] :
( subset(B,empty_set)
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f29,plain,
? [B] :
( B != empty_set
& subset(B,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
( sK2_skl != empty_set
& subset(sK2_skl,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B,sK2_skl)],[f29]) ).
fof(f31,plain,
subset(sK2_skl,empty_set),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
sK2_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f36,plain,
( ~ subset(empty_set,sK2_skl)
| empty_set = sK2_skl ),
inference(resolution,[status(thm)],[f22,f31]) ).
fof(f38,definition,
( sQ0_spl
<=> empty_set = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ0_spl
| empty_set = sK2_skl ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ1_spl
<=> subset(empty_set,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ1_spl
| ~ subset(empty_set,sK2_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f38,f41]) ).
fof(f45,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f32]) ).
fof(f46,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f45]) ).
fof(f47,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f9]) ).
fof(f48,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f47]) ).
fof(f49,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f46,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET063+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:51:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.036010 seconds
% 0.10/0.42 % CPU time: 0.069107 seconds
% 0.10/0.42 % Total memory used: 4.990 MB
% 0.10/0.42 % Net memory used: 4.967 MB
%------------------------------------------------------------------------------