%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET017-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 02:08:53 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 14 unt; 6 def)
% Number of atoms : 102 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 85 ( 37 ~; 42 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f104,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f107,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f108,plain,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f112,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f200,plain,
unordered_pair(x,y) = unordered_pair(x,z),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f201,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f202,plain,
y != z,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f209,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f110,f104]) ).
fof(f210,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f209]) ).
fof(f223,plain,
( member(y,unordered_pair(x,z))
| ~ member(y,universal_class) ),
inference(paramodulation,[status(thm)],[f200,f108]) ).
fof(f225,definition,
( sQ2_spl
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ2_spl
| ~ member(y,universal_class) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,definition,
( sQ3_spl
<=> member(y,unordered_pair(x,z)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( ~ sQ3_spl
| member(y,unordered_pair(x,z)) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f223,f225,f228]) ).
fof(f232,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f113,f201]) ).
fof(f233,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f227]) ).
fof(f234,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f243,plain,
member(z,universal_class),
inference(resolution,[status(thm)],[f115,f201]) ).
fof(f253,plain,
( ~ sQ3_spl
| y = z
| y = x ),
inference(resolution,[status(thm)],[f229,f104]) ).
fof(f254,definition,
( sQ4_spl
<=> y = x ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ4_spl
| y = x ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ5_spl
<=> y = z ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ5_spl
| y = z ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ3_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f253,f254,f257,f228]) ).
fof(f267,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f202]) ).
fof(f268,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f277,plain,
( ~ sQ4_spl
| unordered_pair(y,y) = unordered_pair(x,z) ),
inference(forward_demodulation,[status(thm)],[f255,f200]) ).
fof(f278,plain,
( ~ sQ4_spl
| singleton(y) = unordered_pair(x,z) ),
inference(forward_demodulation,[status(thm)],[f110,f277]) ).
fof(f280,plain,
( ~ sQ4_spl
| singleton(y) = unordered_pair(y,z) ),
inference(forward_demodulation,[status(thm)],[f255,f278]) ).
fof(f281,plain,
( ~ sQ4_spl
| member(z,singleton(y))
| ~ member(z,universal_class) ),
inference(paramodulation,[status(thm)],[f280,f108]) ).
fof(f285,definition,
( sQ7_spl
<=> member(z,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ7_spl
| ~ member(z,universal_class) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,definition,
( sQ8_spl
<=> member(z,singleton(y)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( ~ sQ8_spl
| member(z,singleton(y)) ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( ~ sQ4_spl
| sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f281,f285,f288,f254]) ).
fof(f296,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f243]) ).
fof(f297,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( ~ sQ8_spl
| z = y ),
inference(resolution,[status(thm)],[f289,f210]) ).
fof(f300,plain,
( ~ sQ8_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f299,f257,f288]) ).
fof(f301,plain,
$false,
inference(sat_refutation,[status(thm)],[f231,f234,f260,f268,f291,f297,f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET017-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:45:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.060296 seconds
% 0.14/0.45 % CPU time: 0.169170 seconds
% 0.14/0.45 % Total memory used: 105.001 MB
% 0.14/0.45 % Net memory used: 104.919 MB
%------------------------------------------------------------------------------