TSTP Solution File: SYN328+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SYN328+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n026.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 13:24:15 EDT 2022

% Result   : Theorem 1.98s 2.16s
% Output   : Refutation 1.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   32 (  12 unt;  14 nHn;   8 RR)
%            Number of literals    :   59 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-1 aty)
%            Number of variables   :   31 (  11 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ big_g(dollar_f2(A))
    | big_f(A) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ big_f(dollar_f2(A))
    | big_g(dollar_f2(A))
    | ~ big_f(A) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ big_h(dollar_f2(A))
    | big_g(A) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ big_f(dollar_f2(A))
    | big_h(dollar_f2(A))
    | ~ big_g(A) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ big_f(dollar_f2(A))
    | big_g(dollar_f2(A))
    | big_h(A) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ big_h(dollar_f2(A))
    | big_h(A) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ big_f(dollar_f1(A))
    | ~ big_g(dollar_f1(A))
    | ~ big_h(dollar_f1(A)) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( big_f(dollar_f2(A))
    | big_f(A) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( big_f(dollar_f2(A))
    | big_g(A) ),
    file('SYN328+1.p',unknown),
    [] ).

cnf(12,plain,
    ( big_f(A)
    | big_g(dollar_f2(A))
    | big_h(A) ),
    inference(hyper,[status(thm)],[10,5]),
    [iquote('hyper,10,5')] ).

cnf(13,plain,
    ( big_f(dollar_f2(dollar_f2(A)))
    | big_f(A) ),
    inference(hyper,[status(thm)],[11,1]),
    [iquote('hyper,11,1')] ).

cnf(20,plain,
    ( big_f(dollar_f2(A))
    | big_g(dollar_f2(dollar_f2(A)))
    | big_h(A) ),
    inference(hyper,[status(thm)],[12,6]),
    [iquote('hyper,12,6')] ).

cnf(22,plain,
    ( big_f(dollar_f2(dollar_f1(A)))
    | big_g(dollar_f2(dollar_f2(dollar_f1(A)))) ),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[20,9,10,11])])]),
    [iquote('hyper,20,9,10,11,factor_simp,factor_simp')] ).

cnf(24,plain,
    ( big_f(dollar_f2(dollar_f2(A)))
    | big_g(dollar_f2(dollar_f2(dollar_f2(A))))
    | big_g(A) ),
    inference(hyper,[status(thm)],[20,3]),
    [iquote('hyper,20,3')] ).

cnf(27,plain,
    big_f(dollar_f2(dollar_f1(A))),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,1])]),
    [iquote('hyper,22,1,factor_simp')] ).

cnf(36,plain,
    ( big_f(dollar_f2(dollar_f2(A)))
    | big_g(A) ),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[24,1])]),
    [iquote('hyper,24,1,factor_simp')] ).

cnf(41,plain,
    ( big_f(dollar_f2(dollar_f2(A)))
    | big_h(dollar_f2(A)) ),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[36,4,10])]),
    [iquote('hyper,36,4,10,factor_simp')] ).

cnf(42,plain,
    ( big_f(dollar_f2(dollar_f2(dollar_f2(A))))
    | big_f(A) ),
    inference(hyper,[status(thm)],[36,1]),
    [iquote('hyper,36,1')] ).

cnf(44,plain,
    ( big_f(dollar_f2(dollar_f2(A)))
    | big_h(A) ),
    inference(hyper,[status(thm)],[41,6]),
    [iquote('hyper,41,6')] ).

cnf(47,plain,
    big_f(dollar_f2(dollar_f2(dollar_f1(A)))),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[44,9,13,36])])]),
    [iquote('hyper,44,9,13,36,factor_simp,factor_simp')] ).

cnf(48,plain,
    ( big_f(dollar_f2(dollar_f2(dollar_f2(A))))
    | big_h(A) ),
    inference(hyper,[status(thm)],[44,6]),
    [iquote('hyper,44,6')] ).

cnf(49,plain,
    ( big_f(dollar_f2(dollar_f2(dollar_f2(A))))
    | big_g(A) ),
    inference(hyper,[status(thm)],[44,3]),
    [iquote('hyper,44,3')] ).

cnf(51,plain,
    big_g(dollar_f2(dollar_f2(dollar_f1(A)))),
    inference(hyper,[status(thm)],[47,2,27]),
    [iquote('hyper,47,2,27')] ).

cnf(59,plain,
    big_f(dollar_f2(dollar_f2(dollar_f2(dollar_f1(A))))),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[49,9,42,48])])]),
    [iquote('hyper,49,9,42,48,factor_simp,factor_simp')] ).

cnf(62,plain,
    big_h(dollar_f2(dollar_f2(dollar_f2(dollar_f1(A))))),
    inference(hyper,[status(thm)],[59,4,51]),
    [iquote('hyper,59,4,51')] ).

cnf(64,plain,
    big_h(dollar_f2(dollar_f2(dollar_f1(A)))),
    inference(hyper,[status(thm)],[62,6]),
    [iquote('hyper,62,6')] ).

cnf(66,plain,
    big_h(dollar_f2(dollar_f1(A))),
    inference(hyper,[status(thm)],[64,6]),
    [iquote('hyper,64,6')] ).

cnf(67,plain,
    big_g(dollar_f2(dollar_f1(A))),
    inference(hyper,[status(thm)],[64,3]),
    [iquote('hyper,64,3')] ).

cnf(68,plain,
    big_h(dollar_f1(A)),
    inference(hyper,[status(thm)],[66,6]),
    [iquote('hyper,66,6')] ).

cnf(69,plain,
    big_g(dollar_f1(A)),
    inference(hyper,[status(thm)],[66,3]),
    [iquote('hyper,66,3')] ).

cnf(70,plain,
    big_f(dollar_f1(A)),
    inference(hyper,[status(thm)],[67,1]),
    [iquote('hyper,67,1')] ).

cnf(71,plain,
    $false,
    inference(hyper,[status(thm)],[70,9,69,68]),
    [iquote('hyper,70,9,69,68')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SYN328+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n026.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 11:37:39 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.98/2.16  ----- Otter 3.3f, August 2004 -----
% 1.98/2.16  The process was started by sandbox2 on n026.cluster.edu,
% 1.98/2.16  Wed Jul 27 11:37:39 2022
% 1.98/2.16  The command was "./otter".  The process ID is 31009.
% 1.98/2.16  
% 1.98/2.16  set(prolog_style_variables).
% 1.98/2.16  set(auto).
% 1.98/2.16     dependent: set(auto1).
% 1.98/2.16     dependent: set(process_input).
% 1.98/2.16     dependent: clear(print_kept).
% 1.98/2.16     dependent: clear(print_new_demod).
% 1.98/2.16     dependent: clear(print_back_demod).
% 1.98/2.16     dependent: clear(print_back_sub).
% 1.98/2.16     dependent: set(control_memory).
% 1.98/2.16     dependent: assign(max_mem, 12000).
% 1.98/2.16     dependent: assign(pick_given_ratio, 4).
% 1.98/2.16     dependent: assign(stats_level, 1).
% 1.98/2.16     dependent: assign(max_seconds, 10800).
% 1.98/2.16  clear(print_given).
% 1.98/2.16  
% 1.98/2.16  formula_list(usable).
% 1.98/2.16  -(exists X all Y Z (((big_f(Y)->big_g(Y))<->big_f(X))-> (((big_f(Y)->big_h(Y))<->big_g(X))-> ((((big_f(Y)->big_g(Y))->big_h(Y))<->big_h(X))->big_f(Z)&big_g(Z)&big_h(Z))))).
% 1.98/2.16  end_of_list.
% 1.98/2.16  
% 1.98/2.16  -------> usable clausifies to:
% 1.98/2.16  
% 1.98/2.16  list(usable).
% 1.98/2.16  0 [] big_f($f2(X))|big_f(X).
% 1.98/2.16  0 [] -big_g($f2(X))|big_f(X).
% 1.98/2.16  0 [] -big_f($f2(X))|big_g($f2(X))| -big_f(X).
% 1.98/2.16  0 [] big_f($f2(X))|big_g(X).
% 1.98/2.16  0 [] -big_h($f2(X))|big_g(X).
% 1.98/2.16  0 [] -big_f($f2(X))|big_h($f2(X))| -big_g(X).
% 1.98/2.16  0 [] -big_f($f2(X))|big_g($f2(X))|big_h(X).
% 1.98/2.16  0 [] -big_h($f2(X))|big_h(X).
% 1.98/2.16  0 [] big_f($f2(X))|big_h($f2(X))| -big_h(X).
% 1.98/2.16  0 [] -big_g($f2(X))|big_h($f2(X))| -big_h(X).
% 1.98/2.16  0 [] -big_f($f1(X))| -big_g($f1(X))| -big_h($f1(X)).
% 1.98/2.16  end_of_list.
% 1.98/2.16  
% 1.98/2.16  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.98/2.16  
% 1.98/2.16  This is a non-Horn set without equality.  The strategy will
% 1.98/2.16  be ordered hyper_res, unit deletion, and factoring, with
% 1.98/2.16  satellites in sos and with nuclei in usable.
% 1.98/2.16  
% 1.98/2.16     dependent: set(hyper_res).
% 1.98/2.16     dependent: set(factor).
% 1.98/2.16     dependent: set(unit_deletion).
% 1.98/2.16  
% 1.98/2.16  ------------> process usable:
% 1.98/2.16  ** KEPT (pick-wt=5): 1 [] -big_g($f2(A))|big_f(A).
% 1.98/2.16  ** KEPT (pick-wt=8): 2 [] -big_f($f2(A))|big_g($f2(A))| -big_f(A).
% 1.98/2.16  ** KEPT (pick-wt=5): 3 [] -big_h($f2(A))|big_g(A).
% 1.98/2.16  ** KEPT (pick-wt=8): 4 [] -big_f($f2(A))|big_h($f2(A))| -big_g(A).
% 1.98/2.16  ** KEPT (pick-wt=8): 5 [] -big_f($f2(A))|big_g($f2(A))|big_h(A).
% 1.98/2.16  ** KEPT (pick-wt=5): 6 [] -big_h($f2(A))|big_h(A).
% 1.98/2.16  ** KEPT (pick-wt=8): 7 [] big_f($f2(A))|big_h($f2(A))| -big_h(A).
% 1.98/2.16  ** KEPT (pick-wt=8): 8 [] -big_g($f2(A))|big_h($f2(A))| -big_h(A).
% 1.98/2.16  ** KEPT (pick-wt=9): 9 [] -big_f($f1(A))| -big_g($f1(A))| -big_h($f1(A)).
% 1.98/2.16  
% 1.98/2.16  ------------> process sos:
% 1.98/2.16  ** KEPT (pick-wt=5): 10 [] big_f($f2(A))|big_f(A).
% 1.98/2.16  ** KEPT (pick-wt=5): 11 [] big_f($f2(A))|big_g(A).
% 1.98/2.16  
% 1.98/2.16  ======= end of input processing =======
% 1.98/2.16  
% 1.98/2.16  =========== start of search ===========
% 1.98/2.16  
% 1.98/2.16  -------- PROOF -------- 
% 1.98/2.16  
% 1.98/2.16  -----> EMPTY CLAUSE at   0.01 sec ----> 71 [hyper,70,9,69,68] $F.
% 1.98/2.16  
% 1.98/2.16  Length of proof is 22.  Level of proof is 12.
% 1.98/2.16  
% 1.98/2.16  ---------------- PROOF ----------------
% 1.98/2.16  % SZS status Theorem
% 1.98/2.16  % SZS output start Refutation
% See solution above
% 1.98/2.16  ------------ end of proof -------------
% 1.98/2.16  
% 1.98/2.16  
% 1.98/2.16  Search stopped by max_proofs option.
% 1.98/2.16  
% 1.98/2.16  
% 1.98/2.16  Search stopped by max_proofs option.
% 1.98/2.16  
% 1.98/2.16  ============ end of search ============
% 1.98/2.16  
% 1.98/2.16  -------------- statistics -------------
% 1.98/2.16  clauses given                 33
% 1.98/2.16  clauses generated            394
% 1.98/2.16  clauses kept                  70
% 1.98/2.16  clauses forward subsumed     334
% 1.98/2.16  clauses back subsumed         30
% 1.98/2.16  Kbytes malloced              976
% 1.98/2.16  
% 1.98/2.16  ----------- times (seconds) -----------
% 1.98/2.16  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.98/2.16  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.98/2.16  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.98/2.16  
% 1.98/2.16  That finishes the proof of the theorem.
% 1.98/2.16  
% 1.98/2.16  Process 31009 finished Wed Jul 27 11:37:41 2022
% 1.98/2.16  Otter interrupted
% 1.98/2.16  PROOF FOUND
%------------------------------------------------------------------------------