%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET702+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 02:10:29 PM UTC 2026
% Result : Theorem 63.01s 8.52s
% Output : CNFRefutation 63.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 101 ( 39 ~; 38 |; 17 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] : subset(intersection(product(A),product(B)),product(intersection(A,B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] : subset(intersection(product(A),product(B)),product(intersection(A,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(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(f33,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f61,plain,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(X,Y)
| ~ member(Y,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f62,plain,
! [X,A] :
( ( ? [Y] :
( ~ member(X,Y)
& member(Y,A) )
| member(X,product(A)) )
& ( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
( ! [X,A] :
( ? [Y] :
( ~ member(X,Y)
& member(Y,A) )
| member(X,product(A)) )
& ! [X,A] :
( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [X,A] :
( ( ~ member(X,sK2_skl(A,X))
& member(sK2_skl(A,X),A) )
| member(X,product(A)) )
& ! [X,A] :
( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(A,X))],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X2,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( member(sK2_skl(X1,X0),X1)
| member(X0,product(X1)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0,X1] :
( ~ member(X0,sK2_skl(X1,X0))
| member(X0,product(X1)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
? [A,B] : ~ subset(intersection(product(A),product(B)),product(intersection(A,B))),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ subset(intersection(product(sK3_skl),product(sK4_skl)),product(intersection(sK3_skl,sK4_skl))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f68]) ).
fof(f70,plain,
~ subset(intersection(product(sK3_skl),product(sK4_skl)),product(intersection(sK3_skl,sK4_skl))),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f77,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,intersection(X0,X1)),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f86,plain,
member(sK0_skl(product(intersection(sK3_skl,sK4_skl)),intersection(product(sK3_skl),product(sK4_skl))),product(sK4_skl)),
inference(resolution,[status(thm)],[f77,f70]) ).
fof(f93,plain,
! [X0] :
( member(sK0_skl(product(intersection(sK3_skl,sK4_skl)),intersection(product(sK3_skl),product(sK4_skl))),X0)
| ~ member(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f86,f65]) ).
fof(f302,plain,
! [X0,X1] :
( subset(X1,product(X0))
| member(sK2_skl(X0,sK0_skl(product(X0),X1)),X0) ),
inference(resolution,[status(thm)],[f66,f20]) ).
fof(f305,plain,
! [X0,X1] :
( subset(X1,product(X0))
| ~ member(sK0_skl(product(X0),X1),sK2_skl(X0,sK0_skl(product(X0),X1))) ),
inference(resolution,[status(thm)],[f67,f20]) ).
fof(f703,plain,
member(sK2_skl(intersection(sK3_skl,sK4_skl),sK0_skl(product(intersection(sK3_skl,sK4_skl)),intersection(product(sK3_skl),product(sK4_skl)))),intersection(sK3_skl,sK4_skl)),
inference(resolution,[status(thm)],[f302,f70]) ).
fof(f717,plain,
( ~ member(sK2_skl(intersection(sK3_skl,sK4_skl),sK0_skl(product(intersection(sK3_skl,sK4_skl)),intersection(product(sK3_skl),product(sK4_skl)))),sK4_skl)
| subset(intersection(product(sK3_skl),product(sK4_skl)),product(intersection(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f305,f93]) ).
fof(f729,plain,
~ member(sK2_skl(intersection(sK3_skl,sK4_skl),sK0_skl(product(intersection(sK3_skl,sK4_skl)),intersection(product(sK3_skl),product(sK4_skl)))),sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f717,f70]) ).
fof(f753,plain,
member(sK2_skl(intersection(sK3_skl,sK4_skl),sK0_skl(product(intersection(sK3_skl,sK4_skl)),intersection(product(sK3_skl),product(sK4_skl)))),sK4_skl),
inference(resolution,[status(thm)],[f703,f33]) ).
fof(f755,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f753,f729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET702+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n010.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 05:33:55 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 63.01/8.52 % Refutation found
% 63.01/8.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 63.01/8.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.53/8.58 % Elapsed time: 8.118760 seconds
% 18.53/8.58 % CPU time: 63.701121 seconds
% 18.53/8.58 % Total memory used: 338.821 MB
% 18.53/8.58 % Net memory used: 294.048 MB
%------------------------------------------------------------------------------