%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET008+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 : n004.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 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 127 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 136 ( 56 ~; 49 |; 24 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 105 !; 6 ?)
% 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,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [B,C] : intersection(difference(B,C),C) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [B,C] : intersection(difference(B,C),C) = empty_set,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,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(f13,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)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,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)],[f2]) ).
fof(f18,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)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f24,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)],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f28,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f30,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)],[f29]) ).
fof(f31,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)],[f30]) ).
fof(f32,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))],[f31]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f37,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( ! [B] :
( ? [C] : member(C,B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [B] :
( member(sK1_skl(B),B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B))],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0] :
( member(sK1_skl(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f49,plain,
? [B,C] : intersection(difference(B,C),C) != empty_set,
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f50,plain,
intersection(difference(sK3_skl,sK4_skl),sK4_skl) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f49]) ).
fof(f51,plain,
intersection(difference(sK3_skl,sK4_skl),sK4_skl) != empty_set,
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f58,plain,
intersection(sK4_skl,difference(sK3_skl,sK4_skl)) != empty_set,
inference(paramodulation,[status(thm)],[f28,f51]) ).
fof(f74,plain,
! [X0,X1] :
( member(sK1_skl(intersection(X0,X1)),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[f41,f15]) ).
fof(f75,plain,
! [X0,X1] :
( member(sK1_skl(intersection(X0,X1)),X0)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[f41,f14]) ).
fof(f83,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f34,f22]) ).
fof(f84,plain,
! [X0,X1] :
( ~ empty(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f34,f40]) ).
fof(f85,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f83,f27]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ member(sK1_skl(intersection(X0,difference(X1,X2))),X2)
| empty(intersection(X0,difference(X1,X2))) ),
inference(resolution,[status(thm)],[f74,f20]) ).
fof(f129,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f84,f85]) ).
fof(f773,plain,
! [X0,X1] :
( empty(intersection(X0,difference(X1,X0)))
| empty(intersection(X0,difference(X1,X0))) ),
inference(resolution,[status(thm)],[f111,f75]) ).
fof(f782,plain,
! [X0,X1] : empty(intersection(X0,difference(X1,X0))),
inference(duplicate_literals_removal,[status(thm)],[f773]) ).
fof(f813,plain,
! [X0,X1] : intersection(X0,difference(X1,X0)) = empty_set,
inference(resolution,[status(thm)],[f782,f129]) ).
fof(f1006,plain,
empty_set != empty_set,
inference(backward_demodulation,[status(thm)],[f813,f58]) ).
fof(f1049,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1006]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:41:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.15/0.46 % Refutation found
% 0.15/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.50 % Elapsed time: 0.121001 seconds
% 0.15/0.50 % CPU time: 0.465442 seconds
% 0.15/0.50 % Total memory used: 54.535 MB
% 0.15/0.50 % Net memory used: 53.940 MB
%------------------------------------------------------------------------------