%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET072-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 02:09:11 PM UTC 2026
% Result : Unsatisfiable 0.02s 0.61s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 14 unt; 7 def)
% Number of atoms : 111 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 96 ( 43 ~; 46 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/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(f105,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f106,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
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,z) = unordered_pair(y,z),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f201,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f202,plain,
x != y,
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(f212,plain,
( member(x,unordered_pair(y,z))
| ~ member(x,universal_class) ),
inference(paramodulation,[status(thm)],[f200,f106]) ).
fof(f214,definition,
( sQ0_spl
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( sQ0_spl
| ~ member(x,universal_class) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
( sQ1_spl
<=> member(x,unordered_pair(y,z)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ1_spl
| member(x,unordered_pair(y,z)) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f212,f214,f217]) ).
fof(f232,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[f113,f201]) ).
fof(f233,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f216]) ).
fof(f234,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f243,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f115,f201]) ).
fof(f253,plain,
( ~ sQ1_spl
| x = z
| x = y ),
inference(resolution,[status(thm)],[f218,f104]) ).
fof(f254,definition,
( sQ4_spl
<=> x = y ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ4_spl
| x = y ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ5_spl
<=> x = z ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ5_spl
| x = z ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ1_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f253,f254,f257,f217]) ).
fof(f261,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f202]) ).
fof(f262,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f266,plain,
( ~ sQ5_spl
| unordered_pair(z,z) = unordered_pair(y,z) ),
inference(backward_demodulation,[status(thm)],[f258,f200]) ).
fof(f267,plain,
( ~ sQ5_spl
| z != y ),
inference(backward_demodulation,[status(thm)],[f258,f202]) ).
fof(f270,plain,
( ~ sQ5_spl
| singleton(z) = unordered_pair(y,z) ),
inference(forward_demodulation,[status(thm)],[f110,f266]) ).
fof(f274,definition,
( sQ6_spl
<=> z = y ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ6_spl
| z = y ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f281,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f275,f267]) ).
fof(f282,plain,
( ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f285,plain,
( ~ sQ5_spl
| member(y,singleton(z))
| ~ member(y,universal_class) ),
inference(paramodulation,[status(thm)],[f270,f106]) ).
fof(f292,definition,
( sQ9_spl
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ9_spl
| ~ member(y,universal_class) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
( sQ10_spl
<=> member(y,singleton(z)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( ~ sQ10_spl
| member(y,singleton(z)) ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( ~ sQ5_spl
| sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f285,f292,f295,f257]) ).
fof(f299,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f294,f243]) ).
fof(f300,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( ~ sQ10_spl
| y = z ),
inference(resolution,[status(thm)],[f296,f210]) ).
fof(f303,plain,
( ~ sQ10_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f302,f274,f295]) ).
fof(f304,plain,
$false,
inference(sat_refutation,[status(thm)],[f220,f234,f260,f262,f282,f298,f300,f303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n016.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Mon Sep 21 04:55:09 UTC 2026
% 0.02/0.57 % CPUTime :
% 0.02/0.59 % Drodi V4.1.1
% 0.02/0.61 % Refutation found
% 0.02/0.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.64 % Elapsed time: 0.050877 seconds
% 0.14/0.64 % CPU time: 0.148725 seconds
% 0.14/0.64 % Total memory used: 82.108 MB
% 0.14/0.64 % Net memory used: 82.028 MB
%------------------------------------------------------------------------------