%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:19:28 PM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 5 unt; 3 def)
% Number of atoms : 95 ( 37 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 36 ~; 44 |; 8 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f15,plain,
? [A,B] :
( subset(A,singleton(B))
<~> ( A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f16,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)],[f15]) ).
fof(f17,plain,
( ( ( sK2_skl != singleton(sK3_skl)
& sK2_skl != empty_set )
| ~ subset(sK2_skl,singleton(sK3_skl)) )
& ( sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| subset(sK2_skl,singleton(sK3_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f16]) ).
fof(f18,plain,
( sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| subset(sK2_skl,singleton(sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
( sK2_skl != empty_set
| ~ subset(sK2_skl,singleton(sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
( sK2_skl != singleton(sK3_skl)
| ~ subset(sK2_skl,singleton(sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,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)],[f7]) ).
fof(f22,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)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( X0 != empty_set
| subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,definition,
( sQ0_spl
<=> subset(sK2_skl,singleton(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( ~ sQ0_spl
| subset(sK2_skl,singleton(sK3_skl)) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f28,plain,
( sQ0_spl
| ~ subset(sK2_skl,singleton(sK3_skl)) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,definition,
( sQ1_spl
<=> sK2_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( ~ sQ1_spl
| sK2_skl = empty_set ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,definition,
( sQ2_spl
<=> sK2_skl = singleton(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( ~ sQ2_spl
| sK2_skl = singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f26,f29,f32]) ).
fof(f36,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f26,f29]) ).
fof(f37,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f26,f32]) ).
fof(f38,plain,
! [X0] : subset(empty_set,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f24]) ).
fof(f42,plain,
( sQ0_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f28,f43]) ).
fof(f43,plain,
! [X0] :
( ~ sQ1_spl
| subset(sK2_skl,singleton(X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f38]) ).
fof(f45,plain,
( sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f42]) ).
fof(f46,plain,
( ~ sQ0_spl
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set ),
inference(resolution,[status(thm)],[f23,f27]) ).
fof(f49,plain,
( ~ sQ0_spl
| sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f46,f29,f32,f26]) ).
fof(f57,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ subset(sK2_skl,sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f33,f28]) ).
fof(f60,plain,
( sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f9]) ).
fof(f61,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
$false,
inference(sat_refutation,[status(thm)],[f35,f36,f37,f45,f49,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:53:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.035438 seconds
% 0.10/0.41 % CPU time: 0.061121 seconds
% 0.10/0.41 % Total memory used: 4.992 MB
% 0.10/0.41 % Net memory used: 4.975 MB
%------------------------------------------------------------------------------