%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET473-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 02:09:59 PM UTC 2026
% Result : Unsatisfiable 34.92s 5.22s
% Output : CNFRefutation 34.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 20 unt; 0 def)
% Number of atoms : 100 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 84 ( 41 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 102 ( 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
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(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
y = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
domain_of(restrict(x,y,y)) != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f116,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f134,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f137,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f142,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f143,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f147,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f152,plain,
! [X0,X1,X2] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f153,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f189,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f246,plain,
y = null_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
domain_of(restrict(x,y,y)) != y,
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f254,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != y ),
inference(forward_demodulation,[status(thm)],[f246,f153]) ).
fof(f426,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = y ),
inference(forward_demodulation,[status(thm)],[f246,f189]) ).
fof(f427,plain,
! [X0,X1] :
( ordered_pair(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))) = regular(cross_product(X0,X1))
| cross_product(X0,X1) = y ),
inference(resolution,[status(thm)],[f426,f138]) ).
fof(f431,plain,
! [X0] :
( restrict(X0,singleton(regular(domain_of(X0))),universal_class) != y
| domain_of(X0) = y ),
inference(resolution,[status(thm)],[f426,f254]) ).
fof(f432,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = y ),
inference(resolution,[status(thm)],[f426,f116]) ).
fof(f434,plain,
! [X0] :
( complement(X0) = y
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f147,f426]) ).
fof(f442,plain,
! [X0,X1] :
( intersection(X0,X1) = y
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f143,f426]) ).
fof(f464,plain,
! [X0] :
( member(regular(X0),universal_class)
| X0 = y ),
inference(resolution,[status(thm)],[f432,f119]) ).
fof(f474,plain,
! [X0,X1,X2,X3] :
( cross_product(X0,X1) = y
| member(second(regular(cross_product(X0,X1))),X3)
| ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3)) ),
inference(paramodulation,[status(thm)],[f427,f135]) ).
fof(f486,plain,
( complement(universal_class) = y
| complement(universal_class) = y ),
inference(resolution,[status(thm)],[f434,f464]) ).
fof(f487,plain,
complement(universal_class) = y,
inference(duplicate_literals_removal,[status(thm)],[f486]) ).
fof(f489,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,y) ),
inference(paramodulation,[status(thm)],[f487,f147]) ).
fof(f602,plain,
! [X0] :
( ~ member(regular(intersection(y,X0)),universal_class)
| intersection(y,X0) = y ),
inference(resolution,[status(thm)],[f442,f489]) ).
fof(f614,plain,
! [X0,X1,X2] :
( intersection(cross_product(X1,X2),X0) = y
| member(regular(restrict(X0,X1,X2)),cross_product(X1,X2)) ),
inference(paramodulation,[status(thm)],[f152,f442]) ).
fof(f616,plain,
! [X0] : intersection(y,X0) = y,
inference(forward_subsumption_resolution,[status(thm)],[f602,f464]) ).
fof(f622,plain,
! [X0,X1,X2] :
( restrict(X0,X1,X2) = y
| member(regular(restrict(X0,X1,X2)),cross_product(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f152,f614]) ).
fof(f632,plain,
! [X0,X1] : restrict(y,X0,X1) = y,
inference(paramodulation,[status(thm)],[f151,f616]) ).
fof(f638,plain,
domain_of(y) = y,
inference(resolution,[status(thm)],[f632,f431]) ).
fof(f661,plain,
! [X0] :
( ~ member(X0,y)
| restrict(y,singleton(X0),universal_class) != y ),
inference(paramodulation,[status(thm)],[f638,f254]) ).
fof(f670,plain,
! [X0] :
( ~ member(X0,y)
| y != y ),
inference(forward_demodulation,[status(thm)],[f632,f661]) ).
fof(f671,plain,
! [X0] : ~ member(X0,y),
inference(trivial_equality_resolution,[status(thm)],[f670]) ).
fof(f1843,plain,
! [X0,X1] :
( cross_product(X0,X1) = y
| cross_product(X0,X1) = y
| member(second(regular(cross_product(X0,X1))),X1) ),
inference(resolution,[status(thm)],[f474,f426]) ).
fof(f1845,plain,
! [X0,X1] :
( cross_product(X0,X1) = y
| member(second(regular(cross_product(X0,X1))),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1843]) ).
fof(f20026,plain,
! [X0] : cross_product(X0,y) = y,
inference(resolution,[status(thm)],[f1845,f671]) ).
fof(f20098,plain,
! [X0,X1] :
( restrict(X0,X1,y) = y
| member(regular(restrict(X0,X1,y)),y) ),
inference(paramodulation,[status(thm)],[f20026,f622]) ).
fof(f20200,plain,
! [X0,X1] : restrict(X0,X1,y) = y,
inference(forward_subsumption_resolution,[status(thm)],[f20098,f671]) ).
fof(f20226,plain,
domain_of(y) != y,
inference(backward_demodulation,[status(thm)],[f20200,f247]) ).
fof(f20295,plain,
y != y,
inference(forward_demodulation,[status(thm)],[f638,f20226]) ).
fof(f20296,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f20295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET473-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.65 % Computer : n014.cluster.edu
% 0.18/0.65 % Model : x86_64 x86_64
% 0.18/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.65 % Memory : 8046.5625MB
% 0.18/0.65 % OS : Linux 6.8.0-71-generic
% 0.05/0.65 % CPULimit : 300
% 0.05/0.65 % WCLimit : 300
% 0.05/0.65 % DateTime : Mon Sep 21 05:19:35 UTC 2026
% 0.05/0.65 % CPUTime :
% 0.05/0.68 % Drodi V4.1.1
% 34.92/5.22 % Refutation found
% 34.92/5.22 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 34.92/5.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 34.76/5.30 % Elapsed time: 4.622643 seconds
% 34.76/5.30 % CPU time: 36.204432 seconds
% 34.76/5.30 % Total memory used: 373.829 MB
% 34.76/5.30 % Net memory used: 339.700 MB
%------------------------------------------------------------------------------