%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET694+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 : n015.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 02:10:28 PM UTC 2026
% Result : Theorem 52.66s 7.26s
% Output : CNFRefutation 52.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 13 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 46 ~; 42 |; 12 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 76 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(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(f12,conjecture,
! [A,B] : subset(union(power_set(A),power_set(B)),power_set(union(A,B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] : subset(union(power_set(A),power_set(B)),power_set(union(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(f18,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X1,X0)
| member(sK0_skl(X0,X1),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(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(f28,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
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,union(X1,X2))
| ~ member(X0,X1) ),
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(f68,plain,
? [A,B] : ~ subset(union(power_set(A),power_set(B)),power_set(union(A,B))),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ subset(union(power_set(sK3_skl),power_set(sK4_skl)),power_set(union(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(union(power_set(sK3_skl),power_set(sK4_skl)),power_set(union(sK3_skl,sK4_skl))),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f88,plain,
! [X0,X1] :
( subset(X1,power_set(X0))
| ~ subset(sK0_skl(power_set(X0),X1),X0) ),
inference(resolution,[status(thm)],[f20,f29]) ).
fof(f89,plain,
! [X0,X1,X2] :
( subset(X2,union(X0,X1))
| ~ member(sK0_skl(union(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f20,f38]) ).
fof(f90,plain,
! [X0,X1,X2] :
( subset(X2,union(X0,X1))
| ~ member(sK0_skl(union(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f20,f39]) ).
fof(f102,plain,
~ subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),union(sK3_skl,sK4_skl)),
inference(resolution,[status(thm)],[f88,f70]) ).
fof(f108,plain,
~ member(sK0_skl(union(sK3_skl,sK4_skl),sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl)))),sK4_skl),
inference(resolution,[status(thm)],[f90,f102]) ).
fof(f112,plain,
~ member(sK0_skl(union(sK3_skl,sK4_skl),sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl)))),sK3_skl),
inference(resolution,[status(thm)],[f89,f102]) ).
fof(f121,plain,
! [X0] :
( ~ member(sK0_skl(union(sK3_skl,sK4_skl),sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl)))),X0)
| ~ subset(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f108,f18]) ).
fof(f122,plain,
! [X0] :
( ~ subset(X0,sK3_skl)
| ~ member(sK0_skl(union(sK3_skl,sK4_skl),sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl)))),X0) ),
inference(resolution,[status(thm)],[f112,f18]) ).
fof(f183,plain,
( ~ subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),sK3_skl)
| subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f19,f122]) ).
fof(f184,plain,
( ~ subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),sK4_skl)
| subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f19,f121]) ).
fof(f199,plain,
! [X0,X1,X2] :
( member(sK0_skl(X0,union(X1,X2)),X2)
| subset(union(X1,X2),X0)
| member(sK0_skl(X0,union(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f19,f37]) ).
fof(f201,plain,
~ subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f183,f102]) ).
fof(f202,plain,
~ subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f184,f102]) ).
fof(f367,plain,
( member(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),power_set(sK3_skl))
| member(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),power_set(sK4_skl)) ),
inference(resolution,[status(thm)],[f199,f70]) ).
fof(f578,plain,
( subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),sK4_skl)
| member(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),power_set(sK3_skl)) ),
inference(resolution,[status(thm)],[f367,f28]) ).
fof(f579,plain,
member(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),power_set(sK3_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f578,f202]) ).
fof(f618,plain,
subset(sK0_skl(power_set(union(sK3_skl,sK4_skl)),union(power_set(sK3_skl),power_set(sK4_skl))),sK3_skl),
inference(resolution,[status(thm)],[f579,f28]) ).
fof(f619,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f618,f201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET694+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.52 % Computer : n015.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 05:36:06 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.53 % Drodi V4.1.1
% 52.66/7.26 % Refutation found
% 52.66/7.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 52.66/7.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 52.66/7.30 % Elapsed time: 6.759994 seconds
% 52.66/7.30 % CPU time: 53.309781 seconds
% 52.66/7.30 % Total memory used: 426.930 MB
% 52.66/7.30 % Net memory used: 368.579 MB
%------------------------------------------------------------------------------