%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET635+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 : n018.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 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 25 unt; 0 def)
% Number of atoms : 54 ( 35 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 42 ( 21 ~; 12 |; 7 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 56 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f19,plain,
! [B,C] :
( ( ~ subset(B,C)
| difference(B,C) = empty_set )
& ( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
( ! [B,C] :
( ~ subset(B,C)
| difference(B,C) = empty_set )
& ! [B,C] :
( subset(B,C)
| difference(B,C) != empty_set ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f22,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f43,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f64,plain,
? [B,C,D] : intersection(B,difference(C,D)) != difference(intersection(B,C),intersection(B,D)),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f65,plain,
intersection(sK3_skl,difference(sK4_skl,sK5_skl)) != difference(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_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)],[f64]) ).
fof(f66,plain,
intersection(sK3_skl,difference(sK4_skl,sK5_skl)) != difference(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f38]) ).
fof(f69,plain,
intersection(sK3_skl,difference(sK4_skl,sK5_skl)) != difference(intersection(sK3_skl,sK4_skl),intersection(sK5_skl,sK3_skl)),
inference(backward_demodulation,[status(thm)],[f43,f66]) ).
fof(f74,plain,
intersection(sK3_skl,difference(sK4_skl,sK5_skl)) != difference(intersection(sK4_skl,sK3_skl),intersection(sK5_skl,sK3_skl)),
inference(forward_demodulation,[status(thm)],[f43,f69]) ).
fof(f78,plain,
intersection(sK3_skl,difference(sK4_skl,sK5_skl)) != intersection(sK4_skl,difference(sK3_skl,intersection(sK5_skl,sK3_skl))),
inference(backward_demodulation,[status(thm)],[f25,f74]) ).
fof(f79,plain,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X1,X0),X2),
inference(paramodulation,[status(thm)],[f43,f25]) ).
fof(f82,plain,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = intersection(X1,difference(X0,X2)),
inference(forward_demodulation,[status(thm)],[f25,f79]) ).
fof(f93,plain,
! [X0] : difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[f22,f67]) ).
fof(f142,plain,
! [X0,X1] : difference(X0,intersection(X1,X0)) = union(difference(X0,X1),empty_set),
inference(paramodulation,[status(thm)],[f93,f24]) ).
fof(f145,plain,
! [X0,X1] : difference(X0,intersection(X1,X0)) = difference(X0,X1),
inference(forward_demodulation,[status(thm)],[f23,f142]) ).
fof(f222,plain,
intersection(sK4_skl,difference(sK3_skl,sK5_skl)) != intersection(sK4_skl,difference(sK3_skl,intersection(sK5_skl,sK3_skl))),
inference(backward_demodulation,[status(thm)],[f82,f78]) ).
fof(f588,plain,
intersection(sK4_skl,difference(sK3_skl,sK5_skl)) != intersection(sK4_skl,difference(sK3_skl,sK5_skl)),
inference(backward_demodulation,[status(thm)],[f145,f222]) ).
fof(f620,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:32:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.072850 seconds
% 0.14/0.45 % CPU time: 0.311292 seconds
% 0.14/0.45 % Total memory used: 105.128 MB
% 0.14/0.45 % Net memory used: 104.511 MB
%------------------------------------------------------------------------------