%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET636+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 : n001.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 02:10:19 PM UTC 2026
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 9 unt; 0 def)
% Number of atoms : 185 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 208 ( 87 ~; 80 |; 30 &)
% ( 9 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 131 ( 120 !; 11 ?)
% 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] :
( intersect(B,C)
<=> ? [D] :
( 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] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,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(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,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(f20,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)],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
( ! [B,C] :
( intersect(B,C)
| disjoint(B,C) )
& ! [B,C] :
( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f31,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)],[f30]) ).
fof(f34,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f38,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f39,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)],[f38]) ).
fof(f40,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)],[f39]) ).
fof(f41,plain,
( ! [B,C] :
( ( ~ member(sK1_skl(C,B),C)
& member(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f46,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f47,plain,
( ! [B] :
( ? [C] : member(C,B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
( ! [B] :
( member(sK2_skl(B),B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B))],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0] :
( member(sK2_skl(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f58,plain,
? [B,C] :
( disjoint(B,C)
<~> intersection(B,C) = empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f59,plain,
? [B,C] :
( ( intersection(B,C) != empty_set
| ~ disjoint(B,C) )
& ( intersection(B,C) = empty_set
| disjoint(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
( ( intersection(sK4_skl,sK5_skl) != empty_set
| ~ disjoint(sK4_skl,sK5_skl) )
& ( intersection(sK4_skl,sK5_skl) = empty_set
| disjoint(sK4_skl,sK5_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f59]) ).
fof(f61,plain,
( intersection(sK4_skl,sK5_skl) = empty_set
| disjoint(sK4_skl,sK5_skl) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
( intersection(sK4_skl,sK5_skl) != empty_set
| ~ disjoint(sK4_skl,sK5_skl) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f80,plain,
! [X0] :
( disjoint(sK4_skl,sK5_skl)
| ~ member(X0,sK5_skl)
| ~ member(X0,sK4_skl)
| member(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f61,f18]) ).
fof(f83,plain,
! [X0] :
( disjoint(sK4_skl,sK5_skl)
| ~ member(X0,sK5_skl)
| ~ member(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f25]) ).
fof(f84,plain,
! [X0] :
( ~ intersect(sK4_skl,sK5_skl)
| ~ member(X0,sK5_skl)
| ~ member(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f83,f28]) ).
fof(f87,plain,
! [X0,X1] :
( member(sK2_skl(intersection(X0,X1)),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[f50,f17]) ).
fof(f88,plain,
! [X0,X1] :
( member(sK2_skl(intersection(X0,X1)),X0)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[f50,f16]) ).
fof(f103,plain,
! [X0] :
( ~ member(X0,sK5_skl)
| ~ member(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f24]) ).
fof(f104,plain,
! [X0] :
( ~ intersect(X0,sK5_skl)
| ~ member(sK0_skl(sK5_skl,X0),sK4_skl) ),
inference(resolution,[status(thm)],[f103,f23]) ).
fof(f107,plain,
( ~ intersect(sK4_skl,sK5_skl)
| ~ intersect(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f104,f22]) ).
fof(f108,plain,
~ intersect(sK4_skl,sK5_skl),
inference(duplicate_literals_removal,[status(thm)],[f107]) ).
fof(f120,plain,
! [X0] :
( ~ member(sK2_skl(intersection(X0,sK5_skl)),sK4_skl)
| empty(intersection(X0,sK5_skl)) ),
inference(resolution,[status(thm)],[f87,f103]) ).
fof(f157,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f43,f25]) ).
fof(f158,plain,
! [X0,X1] :
( ~ empty(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f43,f49]) ).
fof(f165,plain,
( empty(intersection(sK4_skl,sK5_skl))
| empty(intersection(sK4_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f120,f88]) ).
fof(f169,plain,
empty(intersection(sK4_skl,sK5_skl)),
inference(duplicate_literals_removal,[status(thm)],[f165]) ).
fof(f171,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f157,f34]) ).
fof(f205,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f158,f171]) ).
fof(f208,plain,
intersection(sK4_skl,sK5_skl) = empty_set,
inference(resolution,[status(thm)],[f205,f169]) ).
fof(f298,plain,
( empty_set != empty_set
| ~ disjoint(sK4_skl,sK5_skl) ),
inference(backward_demodulation,[status(thm)],[f208,f62]) ).
fof(f314,plain,
~ disjoint(sK4_skl,sK5_skl),
inference(trivial_equality_resolution,[status(thm)],[f298]) ).
fof(f322,plain,
intersect(sK4_skl,sK5_skl),
inference(resolution,[status(thm)],[f314,f29]) ).
fof(f323,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f322,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 % Computer : n001.cluster.edu
% 0.19/0.48 % Model : x86_64 x86_64
% 0.19/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.48 % Memory : 8046.5625MB
% 0.19/0.48 % OS : Linux 6.8.0-71-generic
% 0.19/0.48 % CPULimit : 300
% 0.19/0.48 % WCLimit : 300
% 0.19/0.48 % DateTime : Mon Sep 21 05:36:28 UTC 2026
% 0.19/0.48 % CPUTime :
% 0.19/0.50 % Drodi V4.1.1
% 0.19/0.52 % Refutation found
% 0.19/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.59 % Elapsed time: 0.099903 seconds
% 0.24/0.59 % CPU time: 0.192709 seconds
% 0.24/0.59 % Total memory used: 32.940 MB
% 0.24/0.59 % Net memory used: 32.761 MB
%------------------------------------------------------------------------------