%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET084-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 02:09:16 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 58 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 24 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 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(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(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(f16,axiom,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
singleton(x) = singleton(y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
x != y,
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(f109,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f111,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
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(f116,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f200,plain,
singleton(x) = singleton(y),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f201,plain,
member(y,universal_class),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f202,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f223,plain,
! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(x))) = ordered_pair(X0,y),
inference(paramodulation,[status(thm)],[f200,f111]) ).
fof(f227,plain,
! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
inference(paramodulation,[status(thm)],[f111,f109]) ).
fof(f229,plain,
! [X0] : ordered_pair(X0,x) = ordered_pair(X0,y),
inference(forward_demodulation,[status(thm)],[f111,f223]) ).
fof(f244,plain,
! [X0,X1,X2] :
( member(ordered_pair(X0,x),cross_product(X1,X2))
| ~ member(y,X2)
| ~ member(X0,X1) ),
inference(paramodulation,[status(thm)],[f229,f116]) ).
fof(f263,plain,
! [X0,X1,X2] :
( member(x,X2)
| ~ member(y,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f244,f115]) ).
fof(f305,plain,
! [X0,X1,X2] :
( ~ member(y,universal_class)
| member(x,unordered_pair(X2,y))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f263,f108]) ).
fof(f308,plain,
! [X0,X1,X2] :
( member(x,unordered_pair(X2,y))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f201]) ).
fof(f310,plain,
! [X0,X1,X2] :
( x = y
| x = X2
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f308,f104]) ).
fof(f312,plain,
! [X0,X1,X2] :
( x = X2
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f202]) ).
fof(f323,plain,
! [X0] : x = X0,
inference(resolution,[status(thm)],[f312,f227]) ).
fof(f338,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f202,f323]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET084-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n006.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % 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 04:50:43 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.061196 seconds
% 0.13/0.41 % CPU time: 0.179297 seconds
% 0.13/0.41 % Total memory used: 105.635 MB
% 0.13/0.41 % Net memory used: 105.451 MB
%------------------------------------------------------------------------------