%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU153+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:19:25 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 78 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 97 ( 39 ~; 32 |; 24 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 46 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f59,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f91,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f92,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f91]) ).
fof(f94,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f177,plain,
? [A,B] :
( in(A,B)
& disjoint(singleton(A),B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f178,plain,
( in(sK8_skl,sK9_skl)
& disjoint(singleton(sK8_skl),sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f177]) ).
fof(f179,plain,
disjoint(singleton(sK8_skl),sK9_skl),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f180,plain,
in(sK8_skl,sK9_skl),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f240,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f241,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ! [A,B] :
( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f240]) ).
fof(f242,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ! [A,B] :
( ( in(sK13_skl(B,A),B)
& in(sK13_skl(B,A),A) )
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(C,sK13_skl(B,A))],[f241]) ).
fof(f245,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
fof(f290,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f326,plain,
! [X0] :
( ~ disjoint(X0,sK9_skl)
| ~ in(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f245,f180]) ).
fof(f330,plain,
~ in(sK8_skl,singleton(sK8_skl)),
inference(resolution,[status(thm)],[f326,f179]) ).
fof(f332,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f330,f290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU153+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:54:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.067704 seconds
% 0.13/0.43 % CPU time: 0.171050 seconds
% 0.13/0.43 % Total memory used: 105.467 MB
% 0.13/0.43 % Net memory used: 105.398 MB
%------------------------------------------------------------------------------