%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET156+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:09:31 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 10 unt; 0 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 201 ( 83 ~; 78 |; 31 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 125 ( 120 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,E] :
( ( subset(B,E)
& subset(A,E) )
=> equal_set(difference(E,intersection(A,B)),union(difference(E,A),difference(E,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,E] :
( ( subset(B,E)
& subset(A,E) )
=> equal_set(difference(E,intersection(A,B)),union(difference(E,A),difference(E,B))) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f30,plain,
! [X,A,B] :
( ( ~ member(X,B)
| ~ member(X,A)
| member(X,intersection(A,B)) )
& ( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
( ! [X,A,B] :
( ~ member(X,B)
| ~ member(X,A)
| member(X,intersection(A,B)) )
& ! [X,A,B] :
( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ! [X,A,B] :
( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( ! [B,A,E] :
( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ! [B,A,E] :
( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f68,plain,
? [A,B,E] :
( ~ equal_set(difference(E,intersection(A,B)),union(difference(E,A),difference(E,B)))
& subset(B,E)
& subset(A,E) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
( ~ equal_set(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)))
& subset(sK4_skl,sK5_skl)
& subset(sK3_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(E,sK5_skl)],[f68]) ).
fof(f72,plain,
~ equal_set(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f88,plain,
( ~ subset(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl)))
| ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f72,f25]) ).
fof(f90,plain,
! [X0,X1,X2] :
( subset(union(X1,X2),X0)
| member(sK0_skl(X0,union(X1,X2)),X2)
| member(sK0_skl(X0,union(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f37,f19]) ).
fof(f91,plain,
! [X0,X1,X2] :
( subset(X2,union(X0,X1))
| ~ member(sK0_skl(union(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f38,f20]) ).
fof(f93,plain,
! [X0,X1,X2] :
( subset(X2,union(X0,X1))
| ~ member(sK0_skl(union(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f39,f20]) ).
fof(f95,plain,
! [X0,X1,X2] :
( subset(difference(X1,X2),X0)
| member(sK0_skl(X0,difference(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f43,f19]) ).
fof(f96,plain,
! [X0,X1,X2] :
( subset(difference(X1,X2),X0)
| ~ member(sK0_skl(X0,difference(X1,X2)),X2) ),
inference(resolution,[status(thm)],[f44,f19]) ).
fof(f102,plain,
! [X0,X1,X2] :
( subset(X2,difference(X0,X1))
| member(sK0_skl(difference(X0,X1),X2),X1)
| ~ member(sK0_skl(difference(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f45,f20]) ).
fof(f110,plain,
( ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)))
| member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),difference(sK5_skl,sK4_skl))
| member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),difference(sK5_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f90,f88]) ).
fof(f120,plain,
( ~ member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK4_skl)
| ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)))
| member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),difference(sK5_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f110,f44]) ).
fof(f121,plain,
( member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK5_skl)
| ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)))
| member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),difference(sK5_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f110,f43]) ).
fof(f122,plain,
( member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK5_skl)
| ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f121,f43]) ).
fof(f123,plain,
( ~ member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK3_skl)
| ~ member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK4_skl)
| ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f120,f44]) ).
fof(f137,plain,
( ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)))
| member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),intersection(sK3_skl,sK4_skl))
| ~ member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK5_skl) ),
inference(resolution,[status(thm)],[f102,f88]) ).
fof(f139,plain,
( ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)))
| member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),intersection(sK3_skl,sK4_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f122]) ).
fof(f140,plain,
( member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK4_skl)
| ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f139,f33]) ).
fof(f141,plain,
( member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK3_skl)
| ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f139,f32]) ).
fof(f143,plain,
( ~ member(sK0_skl(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),sK3_skl)
| ~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))) ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f140]) ).
fof(f144,plain,
~ subset(difference(sK5_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f143,f141]) ).
fof(f149,plain,
~ member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),intersection(sK3_skl,sK4_skl)),
inference(resolution,[status(thm)],[f144,f96]) ).
fof(f150,plain,
member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK5_skl),
inference(resolution,[status(thm)],[f144,f95]) ).
fof(f151,plain,
~ member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),difference(sK5_skl,sK4_skl)),
inference(resolution,[status(thm)],[f144,f93]) ).
fof(f152,plain,
~ member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),difference(sK5_skl,sK3_skl)),
inference(resolution,[status(thm)],[f144,f91]) ).
fof(f153,plain,
( ~ member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK4_skl)
| ~ member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f149,f34]) ).
fof(f158,plain,
( member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK4_skl)
| ~ member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK5_skl) ),
inference(resolution,[status(thm)],[f151,f45]) ).
fof(f159,plain,
~ member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK3_skl),
inference(backward_subsumption_resolution,[status(thm)],[f153,f160]) ).
fof(f160,plain,
member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f158,f150]) ).
fof(f161,plain,
( member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK3_skl)
| ~ member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK5_skl) ),
inference(resolution,[status(thm)],[f152,f45]) ).
fof(f163,plain,
member(sK0_skl(union(difference(sK5_skl,sK3_skl),difference(sK5_skl,sK4_skl)),difference(sK5_skl,intersection(sK3_skl,sK4_skl))),sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f161,f150]) ).
fof(f164,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f159,f163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET156+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:56:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.44 % Refutation found
% 0.09/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.47 % Elapsed time: 0.092719 seconds
% 0.17/0.47 % CPU time: 0.406812 seconds
% 0.17/0.47 % Total memory used: 84.836 MB
% 0.17/0.47 % Net memory used: 84.233 MB
%------------------------------------------------------------------------------