%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.09s 0.60s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 53 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 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(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
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(f115,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f126,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f127,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f129,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f135,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f255,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f256,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f257,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f261,plain,
! [X0] :
( X0 = z
| X0 = y
| ~ member(X0,unordered_pair(x,z)) ),
inference(paramodulation,[status(thm)],[f255,f127]) ).
fof(f272,plain,
( member(y,unordered_pair(x,z))
| ~ member(y,universal_class) ),
inference(paramodulation,[status(thm)],[f255,f129]) ).
fof(f279,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[f136,f256]) ).
fof(f280,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f138,f256]) ).
fof(f290,plain,
( ~ member(x,universal_class)
| x = z
| x = y ),
inference(resolution,[status(thm)],[f261,f129]) ).
fof(f291,plain,
( ~ member(x,universal_class)
| x = z ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f257]) ).
fof(f292,plain,
member(y,unordered_pair(x,z)),
inference(forward_subsumption_resolution,[status(thm)],[f272,f280]) ).
fof(f294,plain,
( y = z
| y = x ),
inference(resolution,[status(thm)],[f292,f127]) ).
fof(f295,plain,
y = z,
inference(forward_subsumption_resolution,[status(thm)],[f294,f257]) ).
fof(f302,plain,
( ~ member(x,universal_class)
| x = y ),
inference(forward_demodulation,[status(thm)],[f295,f291]) ).
fof(f304,plain,
~ member(x,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[f302,f257]) ).
fof(f305,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f279,f304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n007.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 04:48:21 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.59 % Drodi V4.1.1
% 0.09/0.60 % Refutation found
% 0.09/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.63 % Elapsed time: 0.049342 seconds
% 0.09/0.63 % CPU time: 0.125786 seconds
% 0.09/0.63 % Total memory used: 62.895 MB
% 0.09/0.63 % Net memory used: 62.844 MB
%------------------------------------------------------------------------------