%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET196+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 : n008.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 02:09:37 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 22 ~; 21 |; 11 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 49 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(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(f6,conjecture,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [B,C] : subset(intersection(B,C),B),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
( ! [B,C,D] :
( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ! [B,C,D] :
( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f13,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f14,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)],[f13]) ).
fof(f15,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)],[f14]) ).
fof(f16,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))],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f29,plain,
? [B,C] : ~ subset(intersection(B,C),B),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
~ subset(intersection(sK2_skl,sK3_skl),sK2_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f29]) ).
fof(f31,plain,
~ subset(intersection(sK2_skl,sK3_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f46,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,intersection(X0,X1)),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f18,f10]) ).
fof(f55,plain,
! [X0,X1] :
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f19,f46]) ).
fof(f59,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f55]) ).
fof(f63,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f31,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET196+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 : n008.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
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:00:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.063427 seconds
% 0.09/0.45 % CPU time: 0.133669 seconds
% 0.09/0.45 % Total memory used: 31.698 MB
% 0.09/0.45 % Net memory used: 31.612 MB
%------------------------------------------------------------------------------