%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET926+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:10:59 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 37 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 18 ~; 12 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| set_difference(singleton(A),B) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
| set_difference(singleton(A),B) = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f12,plain,
! [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
( ! [A,B] :
( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ! [A,B] :
( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0,X1] :
( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [A,B] :
( ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
( ! [A,B] :
( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ! [A,B] :
( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f24,plain,
? [A,B] :
( set_difference(singleton(A),B) != singleton(A)
& set_difference(singleton(A),B) != empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
( set_difference(singleton(sK2_skl),sK3_skl) != singleton(sK2_skl)
& set_difference(singleton(sK2_skl),sK3_skl) != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f24]) ).
fof(f26,plain,
set_difference(singleton(sK2_skl),sK3_skl) != empty_set,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
set_difference(singleton(sK2_skl),sK3_skl) != singleton(sK2_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
~ in(sK2_skl,sK3_skl),
inference(resolution,[status(thm)],[f19,f26]) ).
fof(f30,plain,
in(sK2_skl,sK3_skl),
inference(resolution,[status(thm)],[f15,f27]) ).
fof(f37,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f30,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.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 05:42:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.052704 seconds
% 0.13/0.42 % CPU time: 0.146730 seconds
% 0.13/0.42 % Total memory used: 79.798 MB
% 0.13/0.42 % Net memory used: 79.304 MB
%------------------------------------------------------------------------------