%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET009+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 : n014.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 02:08:48 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 8 unt; 2 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 39 ~; 34 |; 14 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
( ! [B,C,D] :
( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ! [B,C,D] :
( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,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)],[f11]) ).
fof(f13,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)],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,plain,
? [B,C,D] :
( ~ subset(difference(D,C),difference(D,B))
& subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
? [B,C] :
( ? [D] : ~ subset(difference(D,C),difference(D,B))
& subset(B,C) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
( ~ subset(difference(sK3_skl,sK2_skl),difference(sK3_skl,sK1_skl))
& subset(sK1_skl,sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl)],[f20]) ).
fof(f22,plain,
subset(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
~ subset(difference(sK3_skl,sK2_skl),difference(sK3_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,plain,
member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),difference(sK3_skl,sK2_skl)),
inference(resolution,[status(thm)],[f16,f23]) ).
fof(f25,plain,
~ member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),sK2_skl),
inference(resolution,[status(thm)],[f24,f9]) ).
fof(f26,plain,
member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),sK3_skl),
inference(resolution,[status(thm)],[f24,f8]) ).
fof(f29,plain,
! [X0] :
( member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),X0)
| member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),difference(sK3_skl,X0)) ),
inference(resolution,[status(thm)],[f26,f10]) ).
fof(f54,plain,
( member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),sK1_skl)
| subset(difference(sK3_skl,sK2_skl),difference(sK3_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f17,f29]) ).
fof(f55,definition,
( sQ3_spl
<=> subset(difference(sK3_skl,sK2_skl),difference(sK3_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ3_spl
| subset(difference(sK3_skl,sK2_skl),difference(sK3_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,definition,
( sQ4_spl
<=> member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ4_spl
| member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),sK1_skl) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f54,f55,f58]) ).
fof(f62,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f23]) ).
fof(f63,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f72,plain,
! [X0] :
( ~ sQ4_spl
| member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),X0)
| ~ subset(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f59,f15]) ).
fof(f81,plain,
( ~ sQ4_spl
| member(sK0_skl(difference(sK3_skl,sK1_skl),difference(sK3_skl,sK2_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f72,f22]) ).
fof(f84,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f25]) ).
fof(f85,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f84]) ).
fof(f86,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f63,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:41:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.047424 seconds
% 0.14/0.43 % CPU time: 0.083889 seconds
% 0.14/0.43 % Total memory used: 2.379 MB
% 0.14/0.43 % Net memory used: 2.351 MB
%------------------------------------------------------------------------------