%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 01:38:31 PM UTC 2026
% Result : Unsatisfiable 1.14s 0.59s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 12 unt; 5 def)
% Number of atoms : 102 ( 37 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 79 ( 26 ~; 48 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( X = Y
| little_set(f1(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,non_ordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : little_set(non_ordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : singleton_set(X) = non_ordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [Z] : ~ member(Z,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f169,axiom,
! [Z] :
( member(empty_set,f44(Z))
| ~ little_set(Z)
| member(Z,natural_numbers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f171,axiom,
! [Z] :
( ~ member(Z,f44(Z))
| member(Z,natural_numbers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f220,negated_conjecture,
~ member(empty_set,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f223,plain,
! [X0,X1] :
( X0 = X1
| little_set(f1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f224,plain,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f226,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,non_ordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f227,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,non_ordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f232,plain,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f233,plain,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f295,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f434,plain,
! [X0] :
( member(empty_set,f44(X0))
| ~ little_set(X0)
| member(X0,natural_numbers) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f436,plain,
! [X0] :
( ~ member(X0,f44(X0))
| member(X0,natural_numbers) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f487,plain,
~ member(empty_set,natural_numbers),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f507,plain,
! [X0] :
( X0 = empty_set
| member(f1(X0,empty_set),X0) ),
inference(resolution,[status(thm)],[f224,f295]) ).
fof(f517,plain,
! [X0,X1] :
( f1(non_ordered_pair(X0,X1),empty_set) = X1
| f1(non_ordered_pair(X0,X1),empty_set) = X0
| non_ordered_pair(X0,X1) = empty_set ),
inference(resolution,[status(thm)],[f507,f227]) ).
fof(f519,definition,
( sQ0_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ0_spl
| empty_set != empty_set ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f528,definition,
( sQ2_spl
<=> little_set(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f593,plain,
! [X0] :
( f1(non_ordered_pair(X0,X0),empty_set) = X0
| f1(non_ordered_pair(X0,X0),empty_set) = X0
| singleton_set(X0) = empty_set ),
inference(paramodulation,[status(thm)],[f233,f517]) ).
fof(f595,plain,
! [X0] : little_set(singleton_set(X0)),
inference(paramodulation,[status(thm)],[f233,f232]) ).
fof(f599,definition,
( sQ12_spl
<=> f1(singleton_set(empty_set),empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( ~ sQ12_spl
| f1(singleton_set(empty_set),empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f606,plain,
! [X0] :
( f1(non_ordered_pair(X0,X0),empty_set) = X0
| f1(singleton_set(X0),empty_set) = X0
| singleton_set(X0) = empty_set ),
inference(forward_demodulation,[status(thm)],[f233,f593]) ).
fof(f607,plain,
! [X0] :
( f1(singleton_set(X0),empty_set) = X0
| f1(singleton_set(X0),empty_set) = X0
| singleton_set(X0) = empty_set ),
inference(forward_demodulation,[status(thm)],[f233,f606]) ).
fof(f608,plain,
! [X0] :
( f1(singleton_set(X0),empty_set) = X0
| singleton_set(X0) = empty_set ),
inference(duplicate_literals_removal,[status(thm)],[f607]) ).
fof(f748,plain,
( ~ sQ12_spl
| singleton_set(empty_set) = empty_set
| little_set(empty_set) ),
inference(paramodulation,[status(thm)],[f600,f223]) ).
fof(f752,definition,
( sQ24_spl
<=> singleton_set(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f753,plain,
( ~ sQ24_spl
| singleton_set(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f752]) ).
fof(f754,plain,
( sQ24_spl
| singleton_set(empty_set) != empty_set ),
inference(component_clause,[status(thm)],[f752]) ).
fof(f761,plain,
( ~ sQ12_spl
| sQ24_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f748,f528,f752,f599]) ).
fof(f766,plain,
( ~ sQ24_spl
| little_set(empty_set) ),
inference(paramodulation,[status(thm)],[f753,f595]) ).
fof(f771,plain,
( sQ24_spl
| f1(singleton_set(empty_set),empty_set) = empty_set
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f608,f754]) ).
fof(f775,plain,
( sQ24_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f771,f519,f599,f752]) ).
fof(f778,plain,
( ~ sQ24_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f766,f528,f752]) ).
fof(f4238,plain,
( ~ little_set(empty_set)
| member(empty_set,natural_numbers)
| member(empty_set,natural_numbers) ),
inference(resolution,[status(thm)],[f436,f434]) ).
fof(f4244,definition,
( sQ134_spl
<=> member(empty_set,natural_numbers) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f4245,plain,
( ~ sQ134_spl
| member(empty_set,natural_numbers) ),
inference(component_clause,[status(thm)],[f4244]) ).
fof(f4247,plain,
( ~ sQ2_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f4238,f4244,f528]) ).
fof(f4248,plain,
( ~ sQ134_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4245,f487]) ).
fof(f4249,plain,
~ sQ134_spl,
inference(contradiction_clause,[status(thm)],[f4248]) ).
fof(f4250,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f521]) ).
fof(f4251,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f4250]) ).
fof(f4252,plain,
$false,
inference(sat_refutation,[status(thm)],[f761,f775,f778,f4247,f4249,f4251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 01:57:58 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 1.14/0.59 % Refutation found
% 1.14/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.14/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.14/0.63 % Elapsed time: 0.249896 seconds
% 1.14/0.63 % CPU time: 1.690064 seconds
% 1.14/0.63 % Total memory used: 143.249 MB
% 1.14/0.63 % Net memory used: 141.199 MB
%------------------------------------------------------------------------------