%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:10:36 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 2 unt; 3 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 85 ( 39 ~; 32 |; 8 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 29 ( 20 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [Y] :
! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(Z,X)
& element(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ~ ? [Y] :
! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(Z,X)
& element(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [Y] :
! [X] :
( element(X,Y)
<=> ! [Z] :
( ~ element(Z,X)
| ~ element(X,Z) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [Y] :
! [X] :
( ( ? [Z] :
( element(Z,X)
& element(X,Z) )
| element(X,Y) )
& ( ! [Z] :
( ~ element(Z,X)
| ~ element(X,Z) )
| ~ element(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
? [Y] :
( ! [X] :
( ? [Z] :
( element(Z,X)
& element(X,Z) )
| element(X,Y) )
& ! [X] :
( ! [Z] :
( ~ element(Z,X)
| ~ element(X,Z) )
| ~ element(X,Y) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ! [X] :
( ( element(sK1_skl(X),X)
& element(X,sK1_skl(X)) )
| element(X,sK0_skl) )
& ! [X] :
( ! [Z] :
( ~ element(Z,X)
| ~ element(X,Z) )
| ~ element(X,sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(Z,sK1_skl(X))],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| ~ element(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] :
( element(X0,sK1_skl(X0))
| element(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0] :
( element(sK1_skl(X0),X0)
| element(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0] :
( element(sK0_skl,sK0_skl)
| ~ element(X0,sK1_skl(sK0_skl))
| ~ element(sK1_skl(sK0_skl),X0) ),
inference(resolution,[status(thm)],[f7,f9]) ).
fof(f11,definition,
! [X0] :
( sQ0_spl
<=> ( ~ element(X0,sK1_skl(sK0_skl))
| ~ element(sK1_skl(sK0_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f12,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,sK1_skl(sK0_skl))
| ~ element(sK1_skl(sK0_skl),X0) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,definition,
( sQ1_spl
<=> element(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f15,plain,
( ~ sQ1_spl
| element(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f14]) ).
fof(f17,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f11,f14]) ).
fof(f18,plain,
( ~ sQ0_spl
| element(sK0_skl,sK0_skl)
| ~ element(sK0_skl,sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f12,f9]) ).
fof(f20,definition,
( sQ2_spl
<=> element(sK0_skl,sK1_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( sQ2_spl
| ~ element(sK0_skl,sK1_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f20]) ).
fof(f23,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f18,f20,f14,f11]) ).
fof(f31,plain,
! [X0] :
( ~ sQ1_spl
| ~ element(X0,sK0_skl)
| ~ element(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f15,f7]) ).
fof(f33,plain,
( ~ sQ1_spl
| ~ element(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f31,f15]) ).
fof(f35,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f15]) ).
fof(f36,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f35]) ).
fof(f37,plain,
( sQ2_spl
| element(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f22,f8]) ).
fof(f38,plain,
( sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f37,f14,f20]) ).
fof(f39,plain,
$false,
inference(sat_refutation,[status(thm)],[f17,f23,f36,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:38:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.41 % Elapsed time: 0.041204 seconds
% 0.09/0.41 % CPU time: 0.106872 seconds
% 0.09/0.41 % Total memory used: 12.871 MB
% 0.09/0.41 % Net memory used: 12.417 MB
%------------------------------------------------------------------------------