%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET027+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 : n006.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 02:08:58 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 7 unt; 2 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 35 ~; 27 |; 14 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ! [B,C] :
( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ! [B,C] :
( ( ~ member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f7]) ).
fof(f9,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f13,plain,
? [B,C,D] :
( ~ subset(B,D)
& subset(C,D)
& subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
? [B,D] :
( ~ subset(B,D)
& ? [C] :
( subset(C,D)
& subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
( ~ subset(sK1_skl,sK2_skl)
& subset(sK3_skl,sK2_skl)
& subset(sK1_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(B,sK1_skl),skolemize(D,sK2_skl),skolemize(C,sK3_skl)],[f14]) ).
fof(f16,plain,
subset(sK1_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
subset(sK3_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
~ subset(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
member(sK0_skl(sK2_skl,sK1_skl),sK1_skl),
inference(resolution,[status(thm)],[f10,f18]) ).
fof(f20,plain,
! [X0] :
( member(sK0_skl(sK2_skl,sK1_skl),X0)
| ~ subset(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f19,f9]) ).
fof(f22,plain,
! [X0,X1] :
( member(sK0_skl(sK2_skl,sK1_skl),X1)
| ~ subset(X0,X1)
| ~ subset(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f20,f9]) ).
fof(f23,definition,
( sQ0_spl
<=> subset(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f24,plain,
( ~ sQ0_spl
| subset(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f27,plain,
! [X0] :
( subset(sK1_skl,sK2_skl)
| ~ subset(X0,sK2_skl)
| ~ subset(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f22,f11]) ).
fof(f29,definition,
! [X0] :
( sQ1_spl
<=> ( ~ subset(X0,sK2_skl)
| ~ subset(sK1_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f30,plain,
! [X0] :
( ~ sQ1_spl
| ~ subset(X0,sK2_skl)
| ~ subset(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f27,f29,f23]) ).
fof(f33,plain,
( ~ sQ1_spl
| ~ subset(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f30,f16]) ).
fof(f36,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f17]) ).
fof(f37,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f18]) ).
fof(f39,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f40,plain,
$false,
inference(sat_refutation,[status(thm)],[f32,f37,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 04:44:12 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45 % Elapsed time: 0.051560 seconds
% 0.12/0.45 % CPU time: 0.133912 seconds
% 0.12/0.45 % Total memory used: 16.583 MB
% 0.12/0.45 % Net memory used: 16.037 MB
%------------------------------------------------------------------------------