TSTP Solution File: NUM283-1.005 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : NUM283-1.005 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n009.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 Jul 27 13:07:57 EDT 2022

% Result   : Unsatisfiable 1.93s 2.10s
% Output   : Refutation 1.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   47 (  44 unt;   0 nHn;  21 RR)
%            Number of literals    :   52 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :  121 (  22 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   :   37 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ sum(A,B,C)
    | sum(A,s(B),s(C)) ),
    file('NUM283-1.005.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ sum(A,B,C)
    | ~ product(D,B,A)
    | product(s(D),B,C) ),
    file('NUM283-1.005.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ factorial(A,B)
    | ~ product(s(A),B,C)
    | factorial(s(A),C) ),
    file('NUM283-1.005.p',unknown),
    [] ).

cnf(4,axiom,
    ~ factorial(s(s(s(s(s(n0))))),A),
    file('NUM283-1.005.p',unknown),
    [] ).

cnf(5,axiom,
    sum(A,n0,A),
    file('NUM283-1.005.p',unknown),
    [] ).

cnf(6,axiom,
    product(s(n0),A,A),
    file('NUM283-1.005.p',unknown),
    [] ).

cnf(7,axiom,
    factorial(n0,s(n0)),
    file('NUM283-1.005.p',unknown),
    [] ).

cnf(8,plain,
    sum(A,s(n0),s(A)),
    inference(hyper,[status(thm)],[5,1]),
    [iquote('hyper,5,1')] ).

cnf(9,plain,
    factorial(s(n0),s(n0)),
    inference(hyper,[status(thm)],[6,3,7]),
    [iquote('hyper,6,3,7')] ).

cnf(11,plain,
    product(s(s(n0)),s(n0),s(s(n0))),
    inference(hyper,[status(thm)],[8,2,6]),
    [iquote('hyper,8,2,6')] ).

cnf(12,plain,
    sum(A,s(s(n0)),s(s(A))),
    inference(hyper,[status(thm)],[8,1]),
    [iquote('hyper,8,1')] ).

cnf(15,plain,
    product(s(s(n0)),s(s(n0)),s(s(s(s(n0))))),
    inference(hyper,[status(thm)],[12,2,6]),
    [iquote('hyper,12,2,6')] ).

cnf(16,plain,
    sum(A,s(s(s(n0))),s(s(s(A)))),
    inference(hyper,[status(thm)],[12,1]),
    [iquote('hyper,12,1')] ).

cnf(18,plain,
    factorial(s(s(n0)),s(s(n0))),
    inference(hyper,[status(thm)],[11,3,9]),
    [iquote('hyper,11,3,9')] ).

cnf(20,plain,
    product(s(s(s(n0))),s(s(n0)),s(s(s(s(s(s(n0))))))),
    inference(hyper,[status(thm)],[15,2,12]),
    [iquote('hyper,15,2,12')] ).

cnf(23,plain,
    sum(A,s(s(s(s(n0)))),s(s(s(s(A))))),
    inference(hyper,[status(thm)],[16,1]),
    [iquote('hyper,16,1')] ).

cnf(28,plain,
    sum(A,s(s(s(s(s(n0))))),s(s(s(s(s(A)))))),
    inference(hyper,[status(thm)],[23,1]),
    [iquote('hyper,23,1')] ).

cnf(31,plain,
    factorial(s(s(s(n0))),s(s(s(s(s(s(n0))))))),
    inference(hyper,[status(thm)],[20,3,18]),
    [iquote('hyper,20,3,18')] ).

cnf(35,plain,
    sum(A,s(s(s(s(s(s(n0)))))),s(s(s(s(s(s(A))))))),
    inference(hyper,[status(thm)],[28,1]),
    [iquote('hyper,28,1')] ).

cnf(40,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))))))))))))),
    inference(hyper,[status(thm)],[35,2,6]),
    [iquote('hyper,35,2,6')] ).

cnf(41,plain,
    sum(A,s(s(s(s(s(s(s(n0))))))),s(s(s(s(s(s(s(A)))))))),
    inference(hyper,[status(thm)],[35,1]),
    [iquote('hyper,35,1')] ).

cnf(48,plain,
    sum(A,s(s(s(s(s(s(s(s(n0)))))))),s(s(s(s(s(s(s(s(A))))))))),
    inference(hyper,[status(thm)],[41,1]),
    [iquote('hyper,41,1')] ).

cnf(54,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))))))))))))))))))),
    inference(hyper,[status(thm)],[40,2,35]),
    [iquote('hyper,40,2,35')] ).

cnf(56,plain,
    sum(A,s(s(s(s(s(s(s(s(s(n0))))))))),s(s(s(s(s(s(s(s(s(A)))))))))),
    inference(hyper,[status(thm)],[48,1]),
    [iquote('hyper,48,1')] ).

cnf(63,plain,
    sum(A,s(s(s(s(s(s(s(s(s(s(n0)))))))))),s(s(s(s(s(s(s(s(s(s(A))))))))))),
    inference(hyper,[status(thm)],[56,1]),
    [iquote('hyper,56,1')] ).

cnf(71,plain,
    sum(A,s(s(s(s(s(s(s(s(s(s(s(n0))))))))))),s(s(s(s(s(s(s(s(s(s(s(A)))))))))))),
    inference(hyper,[status(thm)],[63,1]),
    [iquote('hyper,63,1')] ).

cnf(77,plain,
    sum(A,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(A))))))))))))),
    inference(hyper,[status(thm)],[71,1]),
    [iquote('hyper,71,1')] ).

cnf(78,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))))))))))))))))))))))))),
    inference(hyper,[status(thm)],[54,2,35]),
    [iquote('hyper,54,2,35')] ).

cnf(87,plain,
    sum(A,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(A)))))))))))))),
    inference(hyper,[status(thm)],[77,1]),
    [iquote('hyper,77,1')] ).

cnf(94,plain,
    sum(A,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(A))))))))))))))),
    inference(hyper,[status(thm)],[87,1]),
    [iquote('hyper,87,1')] ).

cnf(102,plain,
    sum(A,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(A)))))))))))))))),
    inference(hyper,[status(thm)],[94,1]),
    [iquote('hyper,94,1')] ).

cnf(111,plain,
    sum(A,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(A))))))))))))))))),
    inference(hyper,[status(thm)],[102,1]),
    [iquote('hyper,102,1')] ).

cnf(112,plain,
    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(hyper,[status(thm)],[78,3,31]),
    [iquote('hyper,78,3,31')] ).

cnf(121,plain,
    sum(A,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(A)))))))))))))))))),
    inference(hyper,[status(thm)],[111,1]),
    [iquote('hyper,111,1')] ).

cnf(128,plain,
    sum(A,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(A))))))))))))))))))),
    inference(hyper,[status(thm)],[121,1]),
    [iquote('hyper,121,1')] ).

cnf(138,plain,
    sum(A,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(A)))))))))))))))))))),
    inference(hyper,[status(thm)],[128,1]),
    [iquote('hyper,128,1')] ).

cnf(145,plain,
    sum(A,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(A))))))))))))))))))))),
    inference(hyper,[status(thm)],[138,1]),
    [iquote('hyper,138,1')] ).

cnf(154,plain,
    sum(A,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(A)))))))))))))))))))))),
    inference(hyper,[status(thm)],[145,1]),
    [iquote('hyper,145,1')] ).

cnf(164,plain,
    sum(A,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(A))))))))))))))))))))))),
    inference(hyper,[status(thm)],[154,1]),
    [iquote('hyper,154,1')] ).

cnf(173,plain,
    sum(A,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(A)))))))))))))))))))))))),
    inference(hyper,[status(thm)],[164,1]),
    [iquote('hyper,164,1')] ).

cnf(179,plain,
    sum(A,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(A))))))))))))))))))))))))),
    inference(hyper,[status(thm)],[173,1]),
    [iquote('hyper,173,1')] ).

cnf(191,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))))))))))))))))))))))))))))))))))))))))))))))))),
    inference(hyper,[status(thm)],[179,2,6]),
    [iquote('hyper,179,2,6')] ).

cnf(274,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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
    inference(hyper,[status(thm)],[191,2,179]),
    [iquote('hyper,191,2,179')] ).

cnf(385,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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
    inference(hyper,[status(thm)],[274,2,179]),
    [iquote('hyper,274,2,179')] ).

cnf(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)))))))))))))))))))))))),s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(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(hyper,[status(thm)],[385,2,179]),
    [iquote('hyper,385,2,179')] ).

cnf(720,plain,
    factorial(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(hyper,[status(thm)],[528,3,112]),
    [iquote('hyper,528,3,112')] ).

cnf(721,plain,
    $false,
    inference(binary,[status(thm)],[720,4]),
    [iquote('binary,720.1,4.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM283-1.005 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : otter-tptp-script %s
% 0.13/0.35  % Computer : n009.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Jul 27 09:47:21 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.93/2.10  ----- Otter 3.3f, August 2004 -----
% 1.93/2.10  The process was started by sandbox on n009.cluster.edu,
% 1.93/2.10  Wed Jul 27 09:47:21 2022
% 1.93/2.10  The command was "./otter".  The process ID is 31208.
% 1.93/2.10  
% 1.93/2.10  set(prolog_style_variables).
% 1.93/2.10  set(auto).
% 1.93/2.10     dependent: set(auto1).
% 1.93/2.10     dependent: set(process_input).
% 1.93/2.10     dependent: clear(print_kept).
% 1.93/2.10     dependent: clear(print_new_demod).
% 1.93/2.10     dependent: clear(print_back_demod).
% 1.93/2.10     dependent: clear(print_back_sub).
% 1.93/2.10     dependent: set(control_memory).
% 1.93/2.10     dependent: assign(max_mem, 12000).
% 1.93/2.10     dependent: assign(pick_given_ratio, 4).
% 1.93/2.10     dependent: assign(stats_level, 1).
% 1.93/2.10     dependent: assign(max_seconds, 10800).
% 1.93/2.10  clear(print_given).
% 1.93/2.10  
% 1.93/2.10  list(usable).
% 1.93/2.10  0 [] sum(X,n0,X).
% 1.93/2.10  0 [] -sum(X,Y,Z)|sum(X,s(Y),s(Z)).
% 1.93/2.10  0 [] product(s(n0),X,X).
% 1.93/2.10  0 [] -sum(R,Y,Z)| -product(X,Y,R)|product(s(X),Y,Z).
% 1.93/2.10  0 [] factorial(n0,s(n0)).
% 1.93/2.10  0 [] -factorial(X,Z)| -product(s(X),Z,Y)|factorial(s(X),Y).
% 1.93/2.10  0 [] -factorial(s(s(s(s(s(n0))))),Result).
% 1.93/2.10  end_of_list.
% 1.93/2.10  
% 1.93/2.10  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.93/2.10  
% 1.93/2.10  This is a Horn set without equality.  The strategy will
% 1.93/2.10  be hyperresolution, with satellites in sos and nuclei
% 1.93/2.10  in usable.
% 1.93/2.10  
% 1.93/2.10     dependent: set(hyper_res).
% 1.93/2.10     dependent: clear(order_hyper).
% 1.93/2.10  
% 1.93/2.10  ------------> process usable:
% 1.93/2.10  ** KEPT (pick-wt=10): 1 [] -sum(A,B,C)|sum(A,s(B),s(C)).
% 1.93/2.10  ** KEPT (pick-wt=13): 2 [] -sum(A,B,C)| -product(D,B,A)|product(s(D),B,C).
% 1.93/2.10  ** KEPT (pick-wt=12): 3 [] -factorial(A,B)| -product(s(A),B,C)|factorial(s(A),C).
% 1.93/2.10  ** KEPT (pick-wt=8): 4 [] -factorial(s(s(s(s(s(n0))))),A).
% 1.93/2.10  
% 1.93/2.10  ------------> process sos:
% 1.93/2.10  ** KEPT (pick-wt=4): 5 [] sum(A,n0,A).
% 1.93/2.10  ** KEPT (pick-wt=5): 6 [] product(s(n0),A,A).
% 1.93/2.10  ** KEPT (pick-wt=4): 7 [] factorial(n0,s(n0)).
% 1.93/2.10  
% 1.93/2.10  ======= end of input processing =======
% 1.93/2.10  
% 1.93/2.10  =========== start of search ===========
% 1.93/2.10  
% 1.93/2.10  -------- PROOF -------- 
% 1.93/2.10  
% 1.93/2.10  ----> UNIT CONFLICT at   0.10 sec ----> 721 [binary,720.1,4.1] $F.
% 1.93/2.10  
% 1.93/2.10  Length of proof is 39.  Level of proof is 29.
% 1.93/2.10  
% 1.93/2.10  ---------------- PROOF ----------------
% 1.93/2.10  % SZS status Unsatisfiable
% 1.93/2.10  % SZS output start Refutation
% See solution above
% 1.93/2.10  ------------ end of proof -------------
% 1.93/2.10  
% 1.93/2.10  
% 1.93/2.10  Search stopped by max_proofs option.
% 1.93/2.10  
% 1.93/2.10  
% 1.93/2.10  Search stopped by max_proofs option.
% 1.93/2.10  
% 1.93/2.10  ============ end of search ============
% 1.93/2.10  
% 1.93/2.10  -------------- statistics -------------
% 1.93/2.10  clauses given                641
% 1.93/2.10  clauses generated            713
% 1.93/2.10  clauses kept                 720
% 1.93/2.10  clauses forward subsumed       0
% 1.93/2.10  clauses back subsumed          0
% 1.93/2.10  Kbytes malloced             1953
% 1.93/2.10  
% 1.93/2.10  ----------- times (seconds) -----------
% 1.93/2.10  user CPU time          0.10          (0 hr, 0 min, 0 sec)
% 1.93/2.10  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.93/2.10  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.93/2.10  
% 1.93/2.10  That finishes the proof of the theorem.
% 1.93/2.10  
% 1.93/2.10  Process 31208 finished Wed Jul 27 09:47:23 2022
% 1.93/2.10  Otter interrupted
% 1.93/2.10  PROOF FOUND
%------------------------------------------------------------------------------