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  
%------------------------------------------------------------------------------