%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU148+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 02:19:23 PM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 8 unt; 2 def)
% Number of atoms : 95 ( 51 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 103 ( 41 ~; 40 |; 15 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 43 !; 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] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,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(f14,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)],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f21,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
( ! [A,B] :
( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ! [A,B] :
( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f33,plain,
? [A,B] :
( A != B
& subset(singleton(A),singleton(B)) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
( sK3_skl != sK4_skl
& subset(singleton(sK3_skl),singleton(sK4_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f33]) ).
fof(f35,plain,
subset(singleton(sK3_skl),singleton(sK4_skl)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
sK3_skl != sK4_skl,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f16]) ).
fof(f38,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f17]) ).
fof(f44,plain,
( singleton(sK3_skl) = singleton(sK4_skl)
| singleton(sK3_skl) = empty_set ),
inference(resolution,[status(thm)],[f24,f35]) ).
fof(f53,definition,
( sQ2_spl
<=> singleton(sK3_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ2_spl
| singleton(sK3_skl) = empty_set ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ3_spl
<=> singleton(sK3_skl) = singleton(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ3_spl
| singleton(sK3_skl) = singleton(sK4_skl) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f44,f53,f56]) ).
fof(f60,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f21]) ).
fof(f61,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f67,plain,
( ~ sQ3_spl
| in(sK4_skl,singleton(sK3_skl)) ),
inference(paramodulation,[status(thm)],[f57,f38]) ).
fof(f70,plain,
( ~ sQ3_spl
| sK4_skl = sK3_skl ),
inference(resolution,[status(thm)],[f67,f37]) ).
fof(f72,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f36]) ).
fof(f73,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f72]) ).
fof(f74,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f61,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU148+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:52:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.41 % Elapsed time: 0.031014 seconds
% 0.11/0.41 % CPU time: 0.062829 seconds
% 0.11/0.41 % Total memory used: 5.010 MB
% 0.11/0.41 % Net memory used: 4.999 MB
%------------------------------------------------------------------------------