%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET046-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:09:03 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 2 unt; 5 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 93 ( 45 ~; 43 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X,Y] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [X] :
( element(X,a)
| element(X,f(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [X] :
( element(X,a)
| element(f(X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| ~ element(X0,a) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0] :
( element(X0,a)
| element(X0,f(X0)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
! [X0] :
( element(X0,a)
| element(f(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1] :
( element(X0,f(X0))
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(resolution,[status(thm)],[f4,f5]) ).
fof(f9,definition,
! [X0] :
( sQ0_spl
<=> ( ~ element(X0,f(a))
| ~ element(f(a),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f10,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,f(a))
| ~ element(f(a),X0) ),
inference(component_clause,[status(thm)],[f9]) ).
fof(f12,definition,
( sQ1_spl
<=> element(a,a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f14,plain,
( sQ1_spl
| ~ element(a,a) ),
inference(component_clause,[status(thm)],[f12]) ).
fof(f17,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,a)
| ~ element(a,X0)
| ~ element(f(a),a) ),
inference(resolution,[status(thm)],[f10,f8]) ).
fof(f21,definition,
( sQ3_spl
<=> element(f(a),a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( ~ sQ3_spl
| element(f(a),a) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f23,plain,
( sQ3_spl
| ~ element(f(a),a) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f25,definition,
! [X0] :
( sQ4_spl
<=> ( ~ element(X0,a)
| ~ element(a,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f26,plain,
! [X0] :
( ~ sQ4_spl
| ~ element(X0,a)
| ~ element(a,X0) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( ~ sQ0_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f17,f21,f25,f9]) ).
fof(f30,plain,
( ~ sQ4_spl
| element(a,f(a))
| ~ element(a,a) ),
inference(resolution,[status(thm)],[f26,f5]) ).
fof(f32,definition,
( sQ5_spl
<=> element(a,f(a)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( ~ sQ5_spl
| element(a,f(a)) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( ~ sQ4_spl
| sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f30,f12,f32,f25]) ).
fof(f36,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ element(f(a),a) ),
inference(resolution,[status(thm)],[f33,f10]) ).
fof(f37,plain,
( sQ3_spl
| element(a,a) ),
inference(resolution,[status(thm)],[f23,f6]) ).
fof(f39,plain,
! [X0] :
( sQ3_spl
| ~ element(X0,a)
| ~ element(a,X0) ),
inference(resolution,[status(thm)],[f37,f4]) ).
fof(f40,plain,
( sQ3_spl
| ~ element(a,a) ),
inference(resolution,[status(thm)],[f39,f37]) ).
fof(f43,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f37]) ).
fof(f44,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0] :
( ~ sQ3_spl
| ~ element(X0,f(a))
| ~ element(f(a),X0) ),
inference(resolution,[status(thm)],[f22,f4]) ).
fof(f47,plain,
( ~ sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f9,f21]) ).
fof(f48,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f36,f21,f32,f9]) ).
fof(f53,plain,
( sQ1_spl
| element(a,f(a)) ),
inference(resolution,[status(thm)],[f14,f5]) ).
fof(f54,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f53,f32,f12]) ).
fof(f55,plain,
$false,
inference(sat_refutation,[status(thm)],[f28,f35,f44,f47,f48,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET046-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 04:52:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.036032 seconds
% 0.13/0.40 % CPU time: 0.048102 seconds
% 0.13/0.40 % Total memory used: 3.122 MB
% 0.13/0.40 % Net memory used: 3.077 MB
%------------------------------------------------------------------------------