%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET631+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 : n007.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 02:10:18 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 31 ~; 25 |; 15 &)
% ( 2 <=>; 3 =>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 54 !; 9 ?)
% 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] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,difference(C,D))
=> intersect(B,C) ),
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(f11,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ( member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
? [B,C,D] :
( ~ intersect(B,C)
& intersect(B,difference(C,D)) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
? [B,C] :
( ~ intersect(B,C)
& ? [D] : intersect(B,difference(C,D)) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
( ~ intersect(sK1_skl,sK2_skl)
& intersect(sK1_skl,difference(sK2_skl,sK3_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,
intersect(sK1_skl,difference(sK2_skl,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
~ intersect(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f27,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0_skl(X0,X1),X1) ),
inference(resolution,[status(thm)],[f14,f18]) ).
fof(f28,plain,
member(sK0_skl(sK1_skl,difference(sK2_skl,sK3_skl)),difference(sK2_skl,sK3_skl)),
inference(resolution,[status(thm)],[f27,f22]) ).
fof(f32,plain,
member(sK0_skl(sK1_skl,difference(sK2_skl,sK3_skl)),sK2_skl),
inference(resolution,[status(thm)],[f28,f8]) ).
fof(f34,plain,
! [X0] :
( ~ member(sK0_skl(sK1_skl,difference(sK2_skl,sK3_skl)),X0)
| intersect(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f32,f16]) ).
fof(f56,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f15,f18]) ).
fof(f60,plain,
member(sK0_skl(sK1_skl,difference(sK2_skl,sK3_skl)),sK1_skl),
inference(resolution,[status(thm)],[f56,f22]) ).
fof(f67,plain,
intersect(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f60,f34]) ).
fof(f69,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f67,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET631+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 : n007.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 05:28:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % 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
% 0.13/0.43 % Elapsed time: 0.048142 seconds
% 0.13/0.43 % CPU time: 0.108937 seconds
% 0.13/0.43 % Total memory used: 16.760 MB
% 0.13/0.43 % Net memory used: 16.261 MB
%------------------------------------------------------------------------------