%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 17 unt; 5 def)
% Number of atoms : 97 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 35 ~; 40 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 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(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(f108,axiom,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f125,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f126,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f128,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f134,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f136,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f243,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f252,plain,
unordered_pair(x,y) = unordered_pair(x,z),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f253,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f254,plain,
y != z,
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f259,plain,
unordered_pair(x,z) = unordered_pair(y,x),
inference(paramodulation,[status(thm)],[f252,f243]) ).
fof(f270,plain,
unordered_pair(z,x) = unordered_pair(y,x),
inference(paramodulation,[status(thm)],[f243,f259]) ).
fof(f271,plain,
unordered_pair(z,x) = unordered_pair(y,x),
inference(paramodulation,[status(thm)],[f243,f259]) ).
fof(f293,definition,
( sQ2_spl
<=> member(z,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( sQ2_spl
| ~ member(z,universal_class) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f302,plain,
( member(y,unordered_pair(z,x))
| ~ member(y,universal_class) ),
inference(paramodulation,[status(thm)],[f270,f128]) ).
fof(f309,definition,
( sQ5_spl
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ5_spl
| ~ member(y,universal_class) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,definition,
( sQ6_spl
<=> member(y,unordered_pair(z,x)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( ~ sQ6_spl
| member(y,unordered_pair(z,x)) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f302,f309,f312]) ).
fof(f316,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f135,f253]) ).
fof(f317,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f311]) ).
fof(f318,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f317]) ).
fof(f319,plain,
member(z,universal_class),
inference(resolution,[status(thm)],[f137,f253]) ).
fof(f320,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f319,f295]) ).
fof(f321,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f330,plain,
( ~ sQ6_spl
| y = x
| y = z ),
inference(resolution,[status(thm)],[f313,f126]) ).
fof(f331,definition,
( sQ7_spl
<=> y = z ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ7_spl
| y = z ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,definition,
( sQ8_spl
<=> y = x ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ8_spl
| y = x ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( ~ sQ6_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f330,f331,f334,f312]) ).
fof(f338,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f254]) ).
fof(f339,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f338]) ).
fof(f361,plain,
( ~ sQ8_spl
| unordered_pair(z,y) = unordered_pair(y,x) ),
inference(forward_demodulation,[status(thm)],[f335,f271]) ).
fof(f362,plain,
( ~ sQ8_spl
| unordered_pair(z,y) = unordered_pair(y,y) ),
inference(forward_demodulation,[status(thm)],[f335,f361]) ).
fof(f365,plain,
! [X0] :
( ~ sQ8_spl
| X0 = y
| X0 = y
| ~ member(X0,unordered_pair(z,y)) ),
inference(paramodulation,[status(thm)],[f362,f126]) ).
fof(f372,plain,
! [X0] :
( ~ sQ8_spl
| X0 = y
| ~ member(X0,unordered_pair(z,y)) ),
inference(duplicate_literals_removal,[status(thm)],[f365]) ).
fof(f382,plain,
( ~ sQ8_spl
| ~ member(z,universal_class)
| z = y ),
inference(resolution,[status(thm)],[f372,f128]) ).
fof(f385,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f382,f331,f293,f334]) ).
fof(f386,plain,
$false,
inference(sat_refutation,[status(thm)],[f315,f318,f321,f337,f339,f385]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:42:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.047885 seconds
% 0.12/0.40 % CPU time: 0.062326 seconds
% 0.12/0.40 % Total memory used: 3.365 MB
% 0.12/0.40 % Net memory used: 3.362 MB
%------------------------------------------------------------------------------