TSTP Solution File: SYN084+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n005.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 13:23:32 EDT 2022

% Result   : Theorem 1.67s 1.89s
% Output   : Refutation 1.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   24 (   8 unt;  12 nHn;  21 RR)
%            Number of literals    :   52 (   0 equ;  15 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :    7 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( big_p(A)
    | big_p(f(f(A)))
    | ~ big_p(a)
    | big_p(B)
    | big_p(f(f(B))) ),
    file('SYN084+1.p',unknown),
    [] ).

cnf(2,plain,
    ( big_p(A)
    | big_p(f(f(A)))
    | ~ big_p(a) ),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[1])])]),
    [iquote('copy,1,factor_simp,factor_simp')] ).

cnf(3,axiom,
    ( ~ big_p(f(A))
    | big_p(f(f(A)))
    | ~ big_p(a)
    | ~ big_p(f(B))
    | big_p(f(f(B))) ),
    file('SYN084+1.p',unknown),
    [] ).

cnf(4,plain,
    ( ~ big_p(f(A))
    | big_p(f(f(A)))
    | ~ big_p(a) ),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[3])])]),
    [iquote('copy,3,factor_simp,factor_simp')] ).

cnf(5,axiom,
    ( ~ big_p(dollar_c1)
    | big_p(f(dollar_c1))
    | ~ big_p(dollar_c2)
    | big_p(f(dollar_c2)) ),
    file('SYN084+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ big_p(dollar_c1)
    | big_p(f(dollar_c1))
    | ~ big_p(f(f(dollar_c2))) ),
    file('SYN084+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ big_p(f(f(dollar_c1)))
    | ~ big_p(dollar_c2)
    | big_p(f(dollar_c2)) ),
    file('SYN084+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ big_p(f(f(dollar_c1)))
    | ~ big_p(f(f(dollar_c2))) ),
    file('SYN084+1.p',unknown),
    [] ).

cnf(9,axiom,
    big_p(a),
    file('SYN084+1.p',unknown),
    [] ).

cnf(10,plain,
    ( big_p(A)
    | big_p(f(f(A))) ),
    inference(hyper,[status(thm)],[9,2]),
    [iquote('hyper,9,2')] ).

cnf(22,plain,
    ( big_p(dollar_c2)
    | big_p(dollar_c1) ),
    inference(hyper,[status(thm)],[10,8,10]),
    [iquote('hyper,10,8,10')] ).

cnf(24,plain,
    ( big_p(dollar_c1)
    | big_p(f(dollar_c2)) ),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,7,10])]),
    [iquote('hyper,22,7,10,factor_simp')] ).

cnf(25,plain,
    ( big_p(dollar_c2)
    | big_p(f(dollar_c1)) ),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,6,10])]),
    [iquote('hyper,22,6,10,factor_simp')] ).

cnf(28,plain,
    ( big_p(dollar_c1)
    | big_p(f(f(dollar_c2))) ),
    inference(hyper,[status(thm)],[24,4,9]),
    [iquote('hyper,24,4,9')] ).

cnf(29,plain,
    ( big_p(f(dollar_c1))
    | big_p(f(dollar_c2)) ),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[25,5,24])])]),
    [iquote('hyper,25,5,24,factor_simp,factor_simp')] ).

cnf(31,plain,
    ( big_p(dollar_c2)
    | big_p(f(f(dollar_c1))) ),
    inference(hyper,[status(thm)],[25,4,9]),
    [iquote('hyper,25,4,9')] ).

cnf(35,plain,
    big_p(dollar_c1),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[28,8,10])]),
    [iquote('hyper,28,8,10,factor_simp')] ).

cnf(37,plain,
    ( big_p(f(dollar_c2))
    | big_p(f(f(dollar_c1))) ),
    inference(hyper,[status(thm)],[29,4,9]),
    [iquote('hyper,29,4,9')] ).

cnf(40,plain,
    big_p(dollar_c2),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[31,8,10])]),
    [iquote('hyper,31,8,10,factor_simp')] ).

cnf(55,plain,
    big_p(f(dollar_c2)),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[37,7,40])]),
    [iquote('hyper,37,7,40,factor_simp')] ).

cnf(58,plain,
    big_p(f(f(dollar_c2))),
    inference(hyper,[status(thm)],[55,4,9]),
    [iquote('hyper,55,4,9')] ).

cnf(68,plain,
    big_p(f(dollar_c1)),
    inference(hyper,[status(thm)],[58,6,35]),
    [iquote('hyper,58,6,35')] ).

cnf(70,plain,
    big_p(f(f(dollar_c1))),
    inference(hyper,[status(thm)],[68,4,9]),
    [iquote('hyper,68,4,9')] ).

cnf(71,plain,
    $false,
    inference(hyper,[status(thm)],[70,8,58]),
    [iquote('hyper,70,8,58')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n005.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 10:57:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.67/1.89  ----- Otter 3.3f, August 2004 -----
% 1.67/1.89  The process was started by sandbox on n005.cluster.edu,
% 1.67/1.89  Wed Jul 27 10:57:35 2022
% 1.67/1.89  The command was "./otter".  The process ID is 12229.
% 1.67/1.89  
% 1.67/1.89  set(prolog_style_variables).
% 1.67/1.89  set(auto).
% 1.67/1.89     dependent: set(auto1).
% 1.67/1.89     dependent: set(process_input).
% 1.67/1.89     dependent: clear(print_kept).
% 1.67/1.89     dependent: clear(print_new_demod).
% 1.67/1.89     dependent: clear(print_back_demod).
% 1.67/1.89     dependent: clear(print_back_sub).
% 1.67/1.89     dependent: set(control_memory).
% 1.67/1.89     dependent: assign(max_mem, 12000).
% 1.67/1.89     dependent: assign(pick_given_ratio, 4).
% 1.67/1.89     dependent: assign(stats_level, 1).
% 1.67/1.89     dependent: assign(max_seconds, 10800).
% 1.67/1.89  clear(print_given).
% 1.67/1.89  
% 1.67/1.89  formula_list(usable).
% 1.67/1.89  -((all X (big_p(a)& (big_p(X)->big_p(f(X)))->big_p(f(f(X)))))<-> (all X1 ((-big_p(a)|big_p(X1)|big_p(f(f(X1))))& (-big_p(a)| -big_p(f(X1))|big_p(f(f(X1))))))).
% 1.67/1.89  end_of_list.
% 1.67/1.89  
% 1.67/1.89  -------> usable clausifies to:
% 1.67/1.89  
% 1.67/1.89  list(usable).
% 1.67/1.89  0 [] big_p(X)|big_p(f(f(X)))| -big_p(a)|big_p(X1)|big_p(f(f(X1))).
% 1.67/1.89  0 [] big_p(X)|big_p(f(f(X)))| -big_p(a)| -big_p(f(X1))|big_p(f(f(X1))).
% 1.67/1.89  0 [] -big_p(f(X))|big_p(f(f(X)))| -big_p(a)|big_p(X1)|big_p(f(f(X1))).
% 1.67/1.89  0 [] -big_p(f(X))|big_p(f(f(X)))| -big_p(a)| -big_p(f(X1))|big_p(f(f(X1))).
% 1.67/1.89  0 [] big_p(a).
% 1.67/1.89  0 [] -big_p($c1)|big_p(f($c1))| -big_p($c2)|big_p(f($c2)).
% 1.67/1.89  0 [] -big_p($c1)|big_p(f($c1))| -big_p(f(f($c2))).
% 1.67/1.89  0 [] -big_p(f(f($c1)))| -big_p($c2)|big_p(f($c2)).
% 1.67/1.89  0 [] -big_p(f(f($c1)))| -big_p(f(f($c2))).
% 1.67/1.89  end_of_list.
% 1.67/1.89  
% 1.67/1.89  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.67/1.89  
% 1.67/1.89  This is a non-Horn set without equality.  The strategy will
% 1.67/1.89  be ordered hyper_res, unit deletion, and factoring, with
% 1.67/1.89  satellites in sos and with nuclei in usable.
% 1.67/1.89  
% 1.67/1.89     dependent: set(hyper_res).
% 1.67/1.89     dependent: set(factor).
% 1.67/1.89     dependent: set(unit_deletion).
% 1.67/1.89  
% 1.67/1.89  ------------> process usable:
% 1.67/1.89  ** KEPT (pick-wt=8): 2 [copy,1,factor_simp,factor_simp] big_p(A)|big_p(f(f(A)))| -big_p(a).
% 1.67/1.89    Following clause subsumed by 2 during input processing: 0 [] big_p(A)|big_p(f(f(A)))| -big_p(a)| -big_p(f(B))|big_p(f(f(B))).
% 1.67/1.89    Following clause subsumed by 2 during input processing: 0 [] -big_p(f(A))|big_p(f(f(A)))| -big_p(a)|big_p(B)|big_p(f(f(B))).
% 1.67/1.89  ** KEPT (pick-wt=9): 4 [copy,3,factor_simp,factor_simp] -big_p(f(A))|big_p(f(f(A)))| -big_p(a).
% 1.67/1.89  ** KEPT (pick-wt=10): 5 [] -big_p($c1)|big_p(f($c1))| -big_p($c2)|big_p(f($c2)).
% 1.67/1.89  ** KEPT (pick-wt=9): 6 [] -big_p($c1)|big_p(f($c1))| -big_p(f(f($c2))).
% 1.67/1.89  ** KEPT (pick-wt=9): 7 [] -big_p(f(f($c1)))| -big_p($c2)|big_p(f($c2)).
% 1.67/1.89  ** KEPT (pick-wt=8): 8 [] -big_p(f(f($c1)))| -big_p(f(f($c2))).
% 1.67/1.89  
% 1.67/1.89  ------------> process sos:
% 1.67/1.89  ** KEPT (pick-wt=2): 9 [] big_p(a).
% 1.67/1.89  
% 1.67/1.89  ======= end of input processing =======
% 1.67/1.89  
% 1.67/1.89  =========== start of search ===========
% 1.67/1.89  
% 1.67/1.89  -------- PROOF -------- 
% 1.67/1.89  
% 1.67/1.89  -----> EMPTY CLAUSE at   0.00 sec ----> 71 [hyper,70,8,58] $F.
% 1.67/1.89  
% 1.67/1.89  Length of proof is 16.  Level of proof is 10.
% 1.67/1.89  
% 1.67/1.89  ---------------- PROOF ----------------
% 1.67/1.89  % SZS status Theorem
% 1.67/1.89  % SZS output start Refutation
% See solution above
% 1.67/1.89  ------------ end of proof -------------
% 1.67/1.89  
% 1.67/1.89  
% 1.67/1.89  Search stopped by max_proofs option.
% 1.67/1.89  
% 1.67/1.89  
% 1.67/1.89  Search stopped by max_proofs option.
% 1.67/1.89  
% 1.67/1.89  ============ end of search ============
% 1.67/1.89  
% 1.67/1.89  -------------- statistics -------------
% 1.67/1.89  clauses given                 19
% 1.67/1.89  clauses generated            161
% 1.67/1.89  clauses kept                  68
% 1.67/1.89  clauses forward subsumed     101
% 1.67/1.89  clauses back subsumed         57
% 1.67/1.89  Kbytes malloced              976
% 1.67/1.89  
% 1.67/1.89  ----------- times (seconds) -----------
% 1.67/1.89  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.67/1.89  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.67/1.89  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.67/1.89  
% 1.67/1.89  That finishes the proof of the theorem.
% 1.67/1.89  
% 1.67/1.89  Process 12229 finished Wed Jul 27 10:57:37 2022
% 1.67/1.89  Otter interrupted
% 1.67/1.89  PROOF FOUND
%------------------------------------------------------------------------------