%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET880+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 02:10:53 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 63 ( 40 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 71 ( 27 ~; 26 |; 13 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,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)],[f2]) ).
fof(f12,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)],[f11]) ).
fof(f13,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))],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f19,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(f20,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)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( in(X0,X1)
| set_difference(singleton(X0),X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f27,plain,
? [A,B] :
( A != B
& set_difference(singleton(A),singleton(B)) = empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
( sK3_skl != sK4_skl
& set_difference(singleton(sK3_skl),singleton(sK4_skl)) = empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f27]) ).
fof(f29,plain,
set_difference(singleton(sK3_skl),singleton(sK4_skl)) = empty_set,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
sK3_skl != sK4_skl,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f14]) ).
fof(f34,plain,
in(sK3_skl,singleton(sK4_skl)),
inference(resolution,[status(thm)],[f21,f29]) ).
fof(f45,plain,
sK3_skl = sK4_skl,
inference(resolution,[status(thm)],[f34,f31]) ).
fof(f46,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f45,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET880+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:47:59 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.059467 seconds
% 0.13/0.42 % CPU time: 0.148149 seconds
% 0.13/0.42 % Total memory used: 101.260 MB
% 0.13/0.42 % Net memory used: 100.815 MB
%------------------------------------------------------------------------------