TSTP Solution File: NUM283-1.005 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM283-1.005 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n016.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 : Thu Aug 31 11:29:07 EDT 2023
% Result : Unsatisfiable 4.09s 1.17s
% Output : CNFRefutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of clauses : 114 ( 18 unt; 0 nHn; 108 RR)
% Number of literals : 242 ( 0 equ; 133 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 121 ( 14 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 : 122 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
sum(X0,n0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_0) ).
cnf(c_50,plain,
( ~ sum(X0,X1,X2)
| sum(X0,s(X1),s(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add) ).
cnf(c_51,plain,
product(s(n0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times1) ).
cnf(c_52,plain,
( ~ sum(X0,X1,X2)
| ~ product(X3,X1,X0)
| product(s(X3),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
cnf(c_53,plain,
factorial(n0,s(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factorial_0) ).
cnf(c_54,plain,
( ~ product(s(X0),X1,X2)
| ~ factorial(X0,X1)
| factorial(s(X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factorial) ).
cnf(c_55,negated_conjecture,
~ factorial(s(s(s(s(s(n0))))),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_factorial) ).
cnf(c_85,plain,
( ~ product(s(n0),X0,X0)
| ~ sum(X0,X0,X1)
| product(s(s(n0)),X0,X1) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_90,plain,
( ~ product(s(n0),s(n0),X0)
| ~ factorial(n0,s(n0))
| factorial(s(n0),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_92,plain,
( ~ product(s(n0),s(n0),X0)
| factorial(s(n0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_53,c_90]) ).
cnf(c_95,plain,
( ~ sum(X0,n0,X0)
| sum(X0,s(n0),s(X0)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_101,plain,
( ~ product(s(n0),s(n0),s(n0))
| factorial(s(n0),s(n0)) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_102,plain,
( ~ sum(X0,s(n0),s(X0))
| sum(X0,s(s(n0)),s(s(X0))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_107,plain,
( ~ product(s(n0),X0,X0)
| ~ sum(X0,X0,X1)
| product(s(s(n0)),X0,X1) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_108,plain,
( ~ sum(X0,X0,X1)
| product(s(s(n0)),X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_107,c_51,c_85]) ).
cnf(c_113,plain,
( ~ sum(X0,n0,X0)
| sum(X0,s(n0),s(X0)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_114,plain,
sum(X0,s(n0),s(X0)),
inference(global_subsumption_just,[status(thm)],[c_113,c_49,c_95]) ).
cnf(c_116,plain,
( ~ product(s(s(n0)),X0,X1)
| ~ sum(X1,X0,X2)
| product(s(s(s(n0))),X0,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_123,plain,
product(s(n0),s(n0),s(n0)),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_124,plain,
( ~ sum(X0,s(s(n0)),s(s(X0)))
| sum(X0,s(s(s(n0))),s(s(s(X0)))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_133,plain,
( ~ product(s(s(n0)),s(n0),X0)
| ~ factorial(s(n0),s(n0))
| factorial(s(s(n0)),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_135,plain,
( ~ product(s(s(n0)),s(n0),X0)
| factorial(s(s(n0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_133,c_101,c_123,c_133]) ).
cnf(c_138,plain,
( ~ sum(X0,s(s(s(n0))),s(s(s(X0))))
| sum(X0,s(s(s(s(n0)))),s(s(s(s(X0))))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_145,plain,
( ~ product(s(s(s(n0))),X0,X1)
| ~ factorial(s(s(n0)),X0)
| factorial(s(s(s(n0))),X1) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_147,plain,
( ~ sum(X0,s(s(s(s(n0)))),s(s(s(s(X0)))))
| sum(X0,s(s(s(s(s(n0))))),s(s(s(s(s(X0)))))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_154,plain,
( ~ sum(s(n0),s(n0),X0)
| product(s(s(n0)),s(n0),X0) ),
inference(instantiation,[status(thm)],[c_108]) ).
cnf(c_156,plain,
( ~ sum(X0,s(s(s(s(s(n0))))),s(s(s(s(s(X0))))))
| sum(X0,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0))))))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_163,plain,
( ~ sum(s(n0),s(n0),s(s(n0)))
| product(s(s(n0)),s(n0),s(s(n0))) ),
inference(instantiation,[status(thm)],[c_154]) ).
cnf(c_164,plain,
( ~ sum(X0,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0)))))))
| sum(X0,s(s(s(s(s(s(s(n0))))))),s(s(s(s(s(s(s(X0)))))))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_171,plain,
( ~ product(s(s(n0)),s(n0),s(s(n0)))
| factorial(s(s(n0)),s(s(n0))) ),
inference(instantiation,[status(thm)],[c_135]) ).
cnf(c_173,plain,
( ~ sum(X0,s(s(s(s(s(s(s(n0))))))),s(s(s(s(s(s(s(X0))))))))
| sum(X0,s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(s(X0))))))))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_180,plain,
( ~ product(s(s(s(n0))),s(s(n0)),X0)
| ~ factorial(s(s(n0)),s(s(n0)))
| factorial(s(s(s(n0))),X0) ),
inference(instantiation,[status(thm)],[c_145]) ).
cnf(c_183,plain,
( ~ sum(X0,s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(s(X0)))))))))
| sum(X0,s(s(s(s(s(s(s(s(s(n0))))))))),s(s(s(s(s(s(s(s(s(X0)))))))))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_191,plain,
sum(s(n0),s(n0),s(s(n0))),
inference(instantiation,[status(thm)],[c_114]) ).
cnf(c_192,plain,
( ~ sum(X0,s(s(s(s(s(s(s(s(s(n0))))))))),s(s(s(s(s(s(s(s(s(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(instantiation,[status(thm)],[c_50]) ).
cnf(c_205,plain,
( ~ product(s(s(n0)),s(s(n0)),X0)
| ~ sum(X0,s(s(n0)),X1)
| product(s(s(s(n0))),s(s(n0)),X1) ),
inference(instantiation,[status(thm)],[c_116]) ).
cnf(c_207,plain,
( ~ sum(X0,s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(s(s(s(s(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(instantiation,[status(thm)],[c_50]) ).
cnf(c_214,plain,
( ~ sum(X0,s(s(n0)),s(s(X0)))
| ~ product(s(s(n0)),s(s(n0)),X0)
| product(s(s(s(n0))),s(s(n0)),s(s(X0))) ),
inference(instantiation,[status(thm)],[c_205]) ).
cnf(c_219,plain,
( ~ 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))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_232,plain,
( ~ 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)))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_241,plain,
( ~ 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))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_250,plain,
( ~ 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)))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_257,plain,
( ~ product(s(n0),X0,X0)
| ~ sum(X0,X0,X1)
| product(s(s(n0)),X0,X1) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_258,plain,
( ~ sum(X0,X0,X1)
| product(s(s(n0)),X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_257,c_51,c_85]) ).
cnf(c_266,plain,
( ~ product(s(s(n0)),X0,X1)
| ~ sum(X1,X0,X2)
| product(s(s(s(n0))),X0,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_270,plain,
( ~ sum(X0,s(n0),s(X0))
| sum(X0,s(s(n0)),s(s(X0))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_271,plain,
sum(X0,s(s(n0)),s(s(X0))),
inference(global_subsumption_just,[status(thm)],[c_270,c_49,c_95,c_102]) ).
cnf(c_273,plain,
( ~ product(s(s(s(n0))),X0,X1)
| ~ sum(X1,X0,X2)
| product(s(s(s(s(n0)))),X0,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_280,plain,
( ~ product(s(s(s(s(n0)))),X0,X1)
| ~ sum(X1,X0,X2)
| product(s(s(s(s(s(n0))))),X0,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_297,plain,
( ~ sum(X0,s(s(s(s(s(n0))))),s(s(s(s(s(X0))))))
| sum(X0,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0))))))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_298,plain,
sum(X0,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0))))))),
inference(global_subsumption_just,[status(thm)],[c_297,c_49,c_95,c_102,c_124,c_138,c_147,c_156]) ).
cnf(c_301,plain,
( ~ product(s(s(s(n0))),s(s(n0)),X0)
| ~ factorial(s(s(n0)),s(s(n0)))
| factorial(s(s(s(n0))),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_302,plain,
( ~ product(s(s(s(n0))),s(s(n0)),X0)
| factorial(s(s(s(n0))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_301,c_163,c_171,c_180,c_191]) ).
cnf(c_309,plain,
( ~ product(s(s(n0)),s(s(n0)),X0)
| ~ sum(X0,s(s(n0)),X1)
| product(s(s(s(n0))),s(s(n0)),X1) ),
inference(instantiation,[status(thm)],[c_266]) ).
cnf(c_314,plain,
( ~ sum(X0,s(s(n0)),s(s(X0)))
| ~ product(s(s(n0)),s(s(n0)),X0)
| product(s(s(s(n0))),s(s(n0)),s(s(X0))) ),
inference(instantiation,[status(thm)],[c_309]) ).
cnf(c_315,plain,
( ~ product(s(s(n0)),s(s(n0)),X0)
| product(s(s(s(n0))),s(s(n0)),s(s(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_314,c_49,c_95,c_102,c_214]) ).
cnf(c_321,plain,
( ~ sum(s(s(n0)),s(s(n0)),X0)
| product(s(s(n0)),s(s(n0)),X0) ),
inference(instantiation,[status(thm)],[c_258]) ).
cnf(c_327,plain,
( ~ sum(s(s(n0)),s(s(n0)),s(s(s(s(n0)))))
| product(s(s(n0)),s(s(n0)),s(s(s(s(n0))))) ),
inference(instantiation,[status(thm)],[c_321]) ).
cnf(c_332,plain,
sum(s(s(n0)),s(s(n0)),s(s(s(s(n0))))),
inference(instantiation,[status(thm)],[c_271]) ).
cnf(c_340,plain,
( ~ product(s(s(n0)),s(s(n0)),s(s(s(s(n0)))))
| product(s(s(s(n0))),s(s(n0)),s(s(s(s(s(s(n0))))))) ),
inference(instantiation,[status(thm)],[c_315]) ).
cnf(c_348,plain,
( ~ product(s(s(s(n0))),s(s(n0)),s(s(s(s(s(s(n0)))))))
| factorial(s(s(s(n0))),s(s(s(s(s(s(n0))))))) ),
inference(instantiation,[status(thm)],[c_302]) ).
cnf(c_356,plain,
( ~ product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),X0)
| ~ factorial(s(s(s(n0))),s(s(s(s(s(s(n0)))))))
| factorial(s(s(s(s(n0)))),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_358,plain,
( ~ product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),X0)
| factorial(s(s(s(s(n0)))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_356,c_327,c_332,c_340,c_348,c_356]) ).
cnf(c_365,plain,
( ~ product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),X0)
| ~ sum(X0,s(s(s(s(s(s(n0)))))),X1)
| product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),X1) ),
inference(instantiation,[status(thm)],[c_273]) ).
cnf(c_367,plain,
( ~ 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))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_374,plain,
( ~ sum(X0,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0)))))))
| ~ product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),X0)
| product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0))))))) ),
inference(instantiation,[status(thm)],[c_365]) ).
cnf(c_376,plain,
( ~ product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),X0)
| product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0))))))) ),
inference(global_subsumption_just,[status(thm)],[c_374,c_49,c_95,c_102,c_124,c_138,c_147,c_156,c_374]) ).
cnf(c_379,plain,
( ~ 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)))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_386,plain,
( ~ product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0)))))))
| factorial(s(s(s(s(n0)))),s(s(s(s(s(s(X0))))))) ),
inference(instantiation,[status(thm)],[c_358]) ).
cnf(c_389,plain,
( ~ 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))))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_396,plain,
( ~ product(s(s(s(s(s(n0))))),s(s(s(s(s(s(X0)))))),X1)
| ~ factorial(s(s(s(s(n0)))),s(s(s(s(s(s(X0)))))))
| factorial(s(s(s(s(s(n0))))),X1) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_398,plain,
( ~ 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)))))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_406,plain,
( ~ product(s(s(n0)),s(s(s(s(s(s(n0)))))),X0)
| ~ sum(X0,s(s(s(s(s(s(n0)))))),X1)
| product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),X1) ),
inference(instantiation,[status(thm)],[c_266]) ).
cnf(c_408,plain,
( ~ 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))))))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_415,plain,
( ~ sum(X0,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0)))))))
| ~ product(s(s(n0)),s(s(s(s(s(s(n0)))))),X0)
| product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0))))))) ),
inference(instantiation,[status(thm)],[c_406]) ).
cnf(c_417,plain,
( ~ product(s(s(n0)),s(s(s(s(s(s(n0)))))),X0)
| product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0))))))) ),
inference(global_subsumption_just,[status(thm)],[c_415,c_49,c_95,c_102,c_124,c_138,c_147,c_156,c_415]) ).
cnf(c_420,plain,
( ~ 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)))))))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_427,plain,
( ~ product(s(s(s(n0))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(X0)))))))
| product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))) ),
inference(instantiation,[status(thm)],[c_376]) ).
cnf(c_430,plain,
( ~ 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))))))))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_438,plain,
( ~ product(s(s(s(s(n0)))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))
| factorial(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(s(s(s(X0))))))))))))) ),
inference(instantiation,[status(thm)],[c_386]) ).
cnf(c_441,plain,
( ~ 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)))))))))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_448,plain,
( ~ product(s(s(s(s(s(n0))))),s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))),X1)
| ~ factorial(s(s(s(s(n0)))),s(s(s(s(s(s(s(s(s(s(s(s(X0)))))))))))))
| factorial(s(s(s(s(s(n0))))),X1) ),
inference(instantiation,[status(thm)],[c_396]) ).
cnf(c_451,plain,
( ~ 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))))))))))))))))))))))))
| 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(instantiation,[status(thm)],[c_50]) ).
cnf(c_453,plain,
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(global_subsumption_just,[status(thm)],[c_451,c_49,c_95,c_102,c_124,c_138,c_147,c_156,c_164,c_173,c_183,c_192,c_207,c_219,c_232,c_241,c_250,c_367,c_379,c_389,c_398,c_408,c_420,c_430,c_441,c_451]) ).
cnf(c_460,plain,
( ~ sum(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(n0)))))),X0)
| product(s(s(n0)),s(s(s(s(s(s(n0)))))),X0) ),
inference(instantiation,[status(thm)],[c_258]) ).
cnf(c_469,plain,
( ~ sum(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))
| product(s(s(n0)),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))) ),
inference(instantiation,[status(thm)],[c_460]) ).
cnf(c_477,plain,
sum(s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(n0))))))))))))),
inference(instantiation,[status(thm)],[c_298]) ).
cnf(c_489,plain,
( ~ product(s(s(n0)),s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(s(s(s(s(s(s(n0)))))))))))))
| product(s(s(s(n0))),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(n0))))))))))))))))))) ),
inference(instantiation,[status(thm)],[c_417]) ).
cnf(c_501,plain,
( ~ product(s(s(s(n0))),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(n0)))))))))))))))))))
| product(s(s(s(s(n0)))),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(n0))))))))))))))))))))))))) ),
inference(instantiation,[status(thm)],[c_427]) ).
cnf(c_514,plain,
( ~ product(s(s(s(s(n0)))),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(n0)))))))))))))))))))))))))
| factorial(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))))))))))))))))))))))))) ),
inference(instantiation,[status(thm)],[c_438]) ).
cnf(c_526,plain,
( ~ 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)
| ~ factorial(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)))))))))))))))))))))))))
| factorial(s(s(s(s(s(n0))))),X0) ),
inference(instantiation,[status(thm)],[c_448]) ).
cnf(c_528,plain,
~ 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(global_subsumption_just,[status(thm)],[c_526,c_55,c_469,c_477,c_489,c_501,c_514,c_526]) ).
cnf(c_539,plain,
( ~ 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)
| ~ 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)))))))))))))))))))))))),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(s(s(s(s(s(s(n0)))))))))))))))))))))))),X1) ),
inference(instantiation,[status(thm)],[c_280]) ).
cnf(c_548,plain,
( ~ 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)))))))))))))))))))))))))
| ~ 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)
| 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)))))))))))))))))))))))),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(instantiation,[status(thm)],[c_539]) ).
cnf(c_550,plain,
( ~ 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)
| 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)))))))))))))))))))))))),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(global_subsumption_just,[status(thm)],[c_548,c_49,c_95,c_102,c_124,c_138,c_147,c_156,c_164,c_173,c_183,c_192,c_207,c_219,c_232,c_241,c_250,c_367,c_379,c_389,c_398,c_408,c_420,c_430,c_441,c_451,c_548]) ).
cnf(c_560,plain,
~ 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)))))))))))))))))))))))),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(instantiation,[status(thm)],[c_528]) ).
cnf(c_571,plain,
( ~ 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)
| ~ 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)))))))))))))))))))))))),X1)
| 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)))))))))))))))))))))))),X1) ),
inference(instantiation,[status(thm)],[c_273]) ).
cnf(c_580,plain,
( ~ 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)))))))))))))))))))))))))
| ~ 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)
| 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)))))))))))))))))))))))),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(instantiation,[status(thm)],[c_571]) ).
cnf(c_582,plain,
( ~ 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)
| 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)))))))))))))))))))))))),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(global_subsumption_just,[status(thm)],[c_580,c_49,c_95,c_102,c_124,c_138,c_147,c_156,c_164,c_173,c_183,c_192,c_207,c_219,c_232,c_241,c_250,c_367,c_379,c_389,c_398,c_408,c_420,c_430,c_441,c_451,c_580]) ).
cnf(c_592,plain,
( ~ 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)))))))))))))))))))))))),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)))))))))))))))))))))))))
| 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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(instantiation,[status(thm)],[c_550]) ).
cnf(c_603,plain,
~ 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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(instantiation,[status(thm)],[c_560]) ).
cnf(c_615,plain,
( ~ 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)
| ~ 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)))))))))))))))))))))))),X1)
| 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)))))))))))))))))))))))),X1) ),
inference(instantiation,[status(thm)],[c_266]) ).
cnf(c_624,plain,
( ~ 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)))))))))))))))))))))))))
| ~ 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)
| 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)))))))))))))))))))))))),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(instantiation,[status(thm)],[c_615]) ).
cnf(c_626,plain,
( ~ 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)
| 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)))))))))))))))))))))))),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(global_subsumption_just,[status(thm)],[c_624,c_49,c_95,c_102,c_124,c_138,c_147,c_156,c_164,c_173,c_183,c_192,c_207,c_219,c_232,c_241,c_250,c_367,c_379,c_389,c_398,c_408,c_420,c_430,c_441,c_451,c_624]) ).
cnf(c_636,plain,
( ~ 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)))))))))))))))))))))))),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)))))))))))))))))))))))))
| 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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(instantiation,[status(thm)],[c_582]) ).
cnf(c_647,plain,
( ~ 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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)))))))))))))))))))))))))))))))))))))))))))))))))
| 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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(instantiation,[status(thm)],[c_592]) ).
cnf(c_659,plain,
( ~ sum(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(n0)))))))))))))))))))))))),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(instantiation,[status(thm)],[c_258]) ).
cnf(c_668,plain,
( ~ sum(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(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(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)))))))))))))))))))))))))))))))))))))))))))))))))
| 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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))))))))))))))))))))))))))))))))))))))))))))))))) ),
inference(instantiation,[status(thm)],[c_659]) ).
cnf(c_676,plain,
( ~ 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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)))))))))))))))))))))))))))))))))))))))))))))))))
| 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ),
inference(instantiation,[status(thm)],[c_626]) ).
cnf(c_686,plain,
( ~ 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
| 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ),
inference(instantiation,[status(thm)],[c_636]) ).
cnf(c_697,plain,
( ~ 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
| 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ),
inference(instantiation,[status(thm)],[c_647]) ).
cnf(c_708,plain,
~ 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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
inference(instantiation,[status(thm)],[c_603]) ).
cnf(c_721,plain,
sum(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(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(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))))))))))))))))))))))))))))))))))))))))))))))))),
inference(instantiation,[status(thm)],[c_453]) ).
cnf(c_722,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_721,c_708,c_697,c_686,c_676,c_668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM283-1.005 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 14:50:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.09/1.17 % SZS status Started for theBenchmark.p
% 4.09/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 4.09/1.17
% 4.09/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 4.09/1.17
% 4.09/1.17 ------ iProver source info
% 4.09/1.17
% 4.09/1.17 git: date: 2023-05-31 18:12:56 +0000
% 4.09/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 4.09/1.17 git: non_committed_changes: false
% 4.09/1.17 git: last_make_outside_of_git: false
% 4.09/1.17
% 4.09/1.17 ------ Parsing...successful
% 4.09/1.17
% 4.09/1.17
% 4.09/1.17
% 4.09/1.17 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 4.09/1.17
% 4.09/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.09/1.17 ------ Proving...
% 4.09/1.17 ------ Problem Properties
% 4.09/1.17
% 4.09/1.17
% 4.09/1.17 clauses 7
% 4.09/1.17 conjectures 1
% 4.09/1.17 EPR 1
% 4.09/1.17 Horn 7
% 4.09/1.17 unary 4
% 4.09/1.17 binary 1
% 4.09/1.17 lits 12
% 4.09/1.17 lits eq 0
% 4.09/1.17 fd_pure 0
% 4.09/1.17 fd_pseudo 0
% 4.09/1.17 fd_cond 0
% 4.09/1.17 fd_pseudo_cond 0
% 4.09/1.17 AC symbols 0
% 4.09/1.17
% 4.09/1.17 ------ Input Options Time Limit: Unbounded
% 4.09/1.17
% 4.09/1.17
% 4.09/1.17 ------
% 4.09/1.17 Current options:
% 4.09/1.17 ------
% 4.09/1.17
% 4.09/1.17
% 4.09/1.17
% 4.09/1.17
% 4.09/1.17 ------ Proving...
% 4.09/1.17
% 4.09/1.17
% 4.09/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 4.09/1.17
% 4.09/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.09/1.18
% 4.09/1.18
%------------------------------------------------------------------------------