%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET012+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 02:08:49 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 122 ( 52 ~; 45 |; 18 &)
% ( 4 <=>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 71 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,E] :
( subset(A,E)
=> equal_set(difference(E,difference(E,A)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,E] :
( subset(A,E)
=> equal_set(difference(E,difference(E,A)),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(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
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(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,E] :
( ~ equal_set(difference(E,difference(E,A)),A)
& subset(A,E) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
( ~ equal_set(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl)
& subset(sK3_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(E,sK4_skl)],[f68]) ).
fof(f70,plain,
subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
~ equal_set(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f75,plain,
! [X0] :
( member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f18,f70]) ).
fof(f76,plain,
( ~ subset(sK3_skl,difference(sK4_skl,difference(sK4_skl,sK3_skl)))
| ~ subset(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f25,f71]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(X2,difference(X0,X1)),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f44]) ).
fof(f80,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,difference(X0,X1)),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f43]) ).
fof(f87,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(f92,plain,
( ~ subset(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl)
| member(sK0_skl(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl),difference(sK4_skl,sK3_skl))
| ~ member(sK0_skl(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f87,f76]) ).
fof(f95,plain,
( ~ member(sK0_skl(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl),sK3_skl)
| ~ subset(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl)
| ~ member(sK0_skl(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f92,f44]) ).
fof(f97,plain,
( ~ member(sK0_skl(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl),sK3_skl)
| ~ subset(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f75]) ).
fof(f98,plain,
( subset(sK3_skl,difference(sK4_skl,difference(sK4_skl,sK3_skl)))
| ~ subset(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f97,f19]) ).
fof(f99,plain,
~ subset(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f98,f76]) ).
fof(f104,plain,
member(sK0_skl(sK3_skl,difference(sK4_skl,difference(sK4_skl,sK3_skl))),sK4_skl),
inference(resolution,[status(thm)],[f99,f80]) ).
fof(f105,plain,
~ member(sK0_skl(sK3_skl,difference(sK4_skl,difference(sK4_skl,sK3_skl))),difference(sK4_skl,sK3_skl)),
inference(resolution,[status(thm)],[f99,f79]) ).
fof(f106,plain,
( member(sK0_skl(sK3_skl,difference(sK4_skl,difference(sK4_skl,sK3_skl))),sK3_skl)
| ~ member(sK0_skl(sK3_skl,difference(sK4_skl,difference(sK4_skl,sK3_skl))),sK4_skl) ),
inference(resolution,[status(thm)],[f105,f45]) ).
fof(f107,plain,
member(sK0_skl(sK3_skl,difference(sK4_skl,difference(sK4_skl,sK3_skl))),sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f106,f104]) ).
fof(f108,plain,
subset(difference(sK4_skl,difference(sK4_skl,sK3_skl)),sK3_skl),
inference(resolution,[status(thm)],[f107,f20]) ).
fof(f109,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f108,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:41:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.066197 seconds
% 0.11/0.44 % CPU time: 0.232248 seconds
% 0.11/0.44 % Total memory used: 82.616 MB
% 0.11/0.44 % Net memory used: 82.107 MB
%------------------------------------------------------------------------------