%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET592+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 : n003.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 02:10:10 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 7 unt; 2 def)
% Number of atoms : 63 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 20 ~; 15 |; 14 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 19 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( ( subset(B,D)
& subset(B,C) )
=> subset(B,intersection(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [B,C,D] :
( ( intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [B] :
( B = empty_set
| ~ subset(B,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [B,C,D] :
( subset(B,intersection(C,D))
| ~ subset(B,D)
| ~ subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f49,plain,
? [B,C,D] :
( B != empty_set
& intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f50,plain,
? [B] :
( B != empty_set
& ? [C,D] :
( intersection(C,D) = empty_set
& subset(B,D)
& subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
( sK3_skl != empty_set
& intersection(sK4_skl,sK5_skl) = empty_set
& subset(sK3_skl,sK5_skl)
& subset(sK3_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f50]) ).
fof(f52,plain,
subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
subset(sK3_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
intersection(sK4_skl,sK5_skl) = empty_set,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
sK3_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f89,plain,
! [X0] :
( subset(X0,empty_set)
| ~ subset(X0,sK5_skl)
| ~ subset(X0,sK4_skl) ),
inference(paramodulation,[status(thm)],[f54,f16]) ).
fof(f151,plain,
( subset(sK3_skl,empty_set)
| ~ subset(sK3_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f89,f52]) ).
fof(f153,definition,
( sQ6_spl
<=> subset(sK3_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ6_spl
| ~ subset(sK3_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
( sQ7_spl
<=> subset(sK3_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ7_spl
| subset(sK3_skl,empty_set) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f151,f153,f156]) ).
fof(f167,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f53]) ).
fof(f168,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
( ~ sQ7_spl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f157,f14]) ).
fof(f172,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f55]) ).
fof(f173,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
$false,
inference(sat_refutation,[status(thm)],[f159,f168,f173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET592+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 % Computer : n003.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Mon Sep 21 05:29:32 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.42 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.49 % Elapsed time: 0.087378 seconds
% 0.18/0.49 % CPU time: 0.099207 seconds
% 0.18/0.49 % Total memory used: 3.236 MB
% 0.18/0.49 % Net memory used: 3.233 MB
%------------------------------------------------------------------------------