%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU152+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 : n008.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 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 5 unt; 0 def)
% Number of atoms : 31 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 13 ~; 7 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f174,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f175,plain,
( set_union2(singleton(sK8_skl),sK9_skl) != sK9_skl
& in(sK8_skl,sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f174]) ).
fof(f176,plain,
in(sK8_skl,sK9_skl),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f177,plain,
set_union2(singleton(sK8_skl),sK9_skl) != sK9_skl,
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f178,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f179,plain,
( ! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) )
& ! [A,B] :
( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(miniscoping,[status(thm)],[f178]) ).
fof(f181,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f205,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f206,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f482,plain,
~ subset(singleton(sK8_skl),sK9_skl),
inference(resolution,[status(thm)],[f206,f177]) ).
fof(f488,plain,
~ in(sK8_skl,sK9_skl),
inference(resolution,[status(thm)],[f482,f181]) ).
fof(f489,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f488,f176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.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 05:53:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.067500 seconds
% 0.11/0.44 % CPU time: 0.180605 seconds
% 0.11/0.44 % Total memory used: 105.900 MB
% 0.11/0.44 % Net memory used: 105.767 MB
%------------------------------------------------------------------------------