%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET366+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 : 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 02:09:51 PM UTC 2026
% Result : Theorem 0.15s 5.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 50 ( 21 ~; 17 |; 8 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A] : member(empty_set,power_set(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : member(empty_set,power_set(A)),
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(f26,plain,
! [X,A] :
( ( ~ subset(X,A)
| member(X,power_set(A)) )
& ( subset(X,A)
| ~ member(X,power_set(A)) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
( ! [X,A] :
( ~ subset(X,A)
| member(X,power_set(A)) )
& ! [X,A] :
( subset(X,A)
| ~ member(X,power_set(A)) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f68,plain,
? [A] : ~ member(empty_set,power_set(A)),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ member(empty_set,power_set(sK3_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f68]) ).
fof(f70,plain,
~ member(empty_set,power_set(sK3_skl)),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,plain,
! [X0,X1] :
( member(X1,power_set(X0))
| member(sK0_skl(X0,X1),X1) ),
inference(resolution,[status(thm)],[f19,f29]) ).
fof(f91,plain,
member(sK0_skl(sK3_skl,empty_set),empty_set),
inference(resolution,[status(thm)],[f76,f70]) ).
fof(f93,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f91,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET366+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.43 % Computer : n004.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Mon Sep 21 05:11:57 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.44 % Drodi V4.1.1
% 0.15/5.45 % Refutation found
% 0.15/5.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/5.52 % Elapsed time: 0.083592 seconds
% 0.20/5.52 % CPU time: 0.087695 seconds
% 0.20/5.52 % Total memory used: 2.544 MB
% 0.20/5.52 % Net memory used: 2.540 MB
%------------------------------------------------------------------------------