TSTP Solution File: NUM283-1.005 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM283-1.005 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:24:46 EDT 2023
% Result : Unsatisfiable 0.10s 0.36s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 43 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 39 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 25 ( 7 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 84 (; 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(X,n0,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(X,s(Y),s(Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(s(n0),X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [R,Y,Z,X] :
( ~ sum(R,Y,Z)
| ~ product(X,Y,R)
| product(s(X),Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
factorial(n0,s(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Z,Y] :
( ~ factorial(X,Z)
| ~ product(s(X),Z,Y)
| factorial(s(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [Result] : ~ factorial(s(s(s(s(s(n0))))),Result),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0] : sum(X0,n0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X0,s(X1),s(X2)) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f10,plain,
! [X0] : product(s(n0),X0,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f11,plain,
! [Y,Z,X] :
( ! [R] :
( ~ sum(R,Y,Z)
| ~ product(X,Y,R) )
| product(s(X),Y,Z) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(X3,X1,X0)
| product(s(X3),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f13,plain,
factorial(n0,s(n0)),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f14,plain,
! [X,Y] :
( ! [Z] :
( ~ factorial(X,Z)
| ~ product(s(X),Z,Y) )
| factorial(s(X),Y) ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ factorial(X0,X1)
| ~ product(s(X0),X1,X2)
| factorial(s(X0),X2) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0] : ~ factorial(s(s(s(s(s(n0))))),X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f17,plain,
! [X0] :
( ~ product(s(n0),s(n0),X0)
| factorial(s(n0),X0) ),
inference(resolution,[status(thm)],[f15,f13]) ).
fof(f18,plain,
! [X0] : sum(X0,s(n0),s(X0)),
inference(resolution,[status(thm)],[f9,f8]) ).
fof(f19,plain,
factorial(s(n0),s(n0)),
inference(resolution,[status(thm)],[f10,f17]) ).
fof(f20,plain,
! [X0] :
( ~ product(s(s(n0)),s(n0),X0)
| factorial(s(s(n0)),X0) ),
inference(resolution,[status(thm)],[f19,f15]) ).
fof(f21,plain,
! [X0] : sum(X0,s(s(n0)),s(s(X0))),
inference(resolution,[status(thm)],[f18,f9]) ).
fof(f22,plain,
! [X0] : sum(X0,s(s(s(n0))),s(s(s(X0)))),
inference(resolution,[status(thm)],[f21,f9]) ).
fof(f23,plain,
! [X0,X1] :
( ~ product(X0,s(s(n0)),X1)
| product(s(X0),s(s(n0)),s(s(X1))) ),
inference(resolution,[status(thm)],[f12,f21]) ).
fof(f24,plain,
! [X0,X1] :
( ~ product(X0,s(n0),X1)
| product(s(X0),s(n0),s(X1)) ),
inference(resolution,[status(thm)],[f12,f18]) ).
fof(f30,plain,
! [X0] :
( ~ product(s(n0),s(n0),X0)
| factorial(s(s(n0)),s(X0)) ),
inference(resolution,[status(thm)],[f24,f20]) ).
fof(f34,plain,
! [X0] : sum(X0,s(s(s(s(n0)))),s(s(s(s(X0))))),
inference(resolution,[status(thm)],[f22,f9]) ).
fof(f37,plain,
factorial(s(s(n0)),s(s(n0))),
inference(resolution,[status(thm)],[f30,f10]) ).
fof(f39,plain,
! [X0] :
( ~ product(s(s(s(n0))),s(s(n0)),X0)
| factorial(s(s(s(n0))),X0) ),
inference(resolution,[status(thm)],[f37,f15]) ).
fof(f41,plain,
! [X0] : sum(X0,s(s(s(s(s(n0))))),s(s(s(s(s(X0)))))),
inference(resolution,[status(thm)],[f34,f9]) ).
fof(f45,plain,
product(s(s(n0)),s(s(n0)),s(s(s(s(n0))))),
inference(resolution,[status(thm)],[f23,f10]) ).
fof(f46,plain,
product(s(s(s(n0))),s(s(n0)),s(s(s(s(s(s(n0))))))),
inference(resolution,[status(thm)],[f45,f23]) ).
fof(f48,plain,
! [X0] : sum(X0,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0))))))),
inference(resolution,[status(thm)],[f41,f9]) ).
fof(f93,plain,
factorial(s(s(s(n0))),s(s(s(s(s(s(n0))))))),
inference(resolution,[status(thm)],[f46,f39]) ).
fof(f100,plain,
! [X0] :
( ~ product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),X0)
| factorial(s(s(s(s(n0)))),X0) ),
inference(resolution,[status(thm)],[f93,f15]) ).
fof(f101,plain,
! [X0,X1] :
( ~ product(X0,s(s(s(s(s(s(n0)))))),X1)
| product(s(X0),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X1))))))) ),
inference(resolution,[status(thm)],[f48,f12]) ).
fof(f102,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(n0))))))),s(s(s(s(s(s(s(X0)))))))),
inference(resolution,[status(thm)],[f48,f9]) ).
fof(f106,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(s(X0))))))))),
inference(resolution,[status(thm)],[f102,f9]) ).
fof(f111,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(n0))))))))),s(s(s(s(s(s(s(s(s(X0)))))))))),
inference(resolution,[status(thm)],[f106,f9]) ).
fof(f129,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(s(s(s(s(X0))))))))))),
inference(resolution,[status(thm)],[f111,f9]) ).
fof(f133,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(n0))))))))))),s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))),
inference(resolution,[status(thm)],[f129,f9]) ).
fof(f137,plain,
! [X0] :
( ~ product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),X0)
| factorial(s(s(s(s(n0)))),s(s(s(s(s(s(X0))))))) ),
inference(resolution,[status(thm)],[f101,f100]) ).
fof(f151,plain,
! [X0,X1] :
( ~ product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),X0)
| ~ product(s(s(s(s(s(n0))))),s(s(s(s(s(s(X0)))))),X1)
| factorial(s(s(s(s(s(n0))))),X1) ),
inference(resolution,[status(thm)],[f137,f15]) ).
fof(f152,plain,
! [X0,X1] :
( ~ product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),X0)
| ~ product(s(s(s(s(s(n0))))),s(s(s(s(s(s(X0)))))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f16]) ).
fof(f153,plain,
! [X0,X1] :
( ~ product(s(s(s(s(s(n0))))),s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))),X1)
| ~ product(s(s(n0)),s(s(s(s(s(s(n0)))))),X0) ),
inference(resolution,[status(thm)],[f152,f101]) ).
fof(f154,plain,
! [X0,X1] :
( ~ product(s(s(s(s(s(n0))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))))))),X1)
| ~ product(s(n0),s(s(s(s(s(s(n0)))))),X0) ),
inference(resolution,[status(thm)],[f153,f101]) ).
fof(f155,plain,
! [X0] : ~ product(s(s(s(s(s(n0))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),X0),
inference(resolution,[status(thm)],[f154,f10]) ).
fof(f158,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))),
inference(resolution,[status(thm)],[f133,f9]) ).
fof(f163,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))),
inference(resolution,[status(thm)],[f158,f9]) ).
fof(f180,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))))),
inference(resolution,[status(thm)],[f163,f9]) ).
fof(f198,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))))),
inference(resolution,[status(thm)],[f180,f9]) ).
fof(f229,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))))))),
inference(resolution,[status(thm)],[f198,f9]) ).
fof(f233,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))))))),
inference(resolution,[status(thm)],[f229,f9]) ).
fof(f238,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))))))))),
inference(resolution,[status(thm)],[f233,f9]) ).
fof(f243,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))))))))),
inference(resolution,[status(thm)],[f238,f9]) ).
fof(f287,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))))))))))),
inference(resolution,[status(thm)],[f243,f9]) ).
fof(f291,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))))))))))),
inference(resolution,[status(thm)],[f287,f9]) ).
fof(f296,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))))))))))))),
inference(resolution,[status(thm)],[f291,f9]) ).
fof(f313,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))))))))))))),
inference(resolution,[status(thm)],[f296,f9]) ).
fof(f318,plain,
! [X0] : sum(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))))))))))))))),
inference(resolution,[status(thm)],[f313,f9]) ).
fof(f322,plain,
! [X0,X1] :
( ~ product(X0,s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),X1)
| product(s(X0),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1))))))))))))))))))))))))) ),
inference(resolution,[status(thm)],[f318,f12]) ).
fof(f493,plain,
! [X0] : ~ product(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),X0),
inference(resolution,[status(thm)],[f322,f155]) ).
fof(f507,plain,
! [X0] : ~ product(s(s(s(n0))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),X0),
inference(resolution,[status(thm)],[f493,f322]) ).
fof(f508,plain,
! [X0] : ~ product(s(s(n0)),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),X0),
inference(resolution,[status(thm)],[f507,f322]) ).
fof(f509,plain,
! [X0] : ~ product(s(n0),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))))))))))))),X0),
inference(resolution,[status(thm)],[f508,f322]) ).
fof(f510,plain,
$false,
inference(resolution,[status(thm)],[f509,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : NUM283-1.005 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n027.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 10:14:47 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 0.10/0.36 % Refutation found
% 0.10/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.59 % Elapsed time: 0.055953 seconds
% 0.21/0.59 % CPU time: 0.131625 seconds
% 0.21/0.59 % Memory used: 14.512 MB
%------------------------------------------------------------------------------