TSTP Solution File: SYN334+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SYN334+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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 13:24:16 EDT 2022

% Result   : Theorem 1.96s 2.16s
% Output   : Refutation 1.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (   3 unt;   8 nHn;   6 RR)
%            Number of literals    :   33 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   24 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ big_f(A,B)
    | ~ big_f(A,dollar_f1(A,B))
    | big_g(B,dollar_f1(A,B)) ),
    file('SYN334+1.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ big_f(A,B)
    | big_f(A,dollar_f1(A,B))
    | ~ big_g(B,dollar_f1(A,B)) ),
    file('SYN334+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ big_f(A,B)
    | ~ big_f(dollar_f1(A,B),dollar_f1(A,B))
    | big_g(dollar_f1(A,B),dollar_f1(A,B)) ),
    file('SYN334+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( big_f(A,B)
    | ~ big_g(dollar_f1(A,B),dollar_f1(A,B)) ),
    file('SYN334+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ big_g(A,B)
    | ~ big_g(dollar_f1(A,B),dollar_f1(A,B)) ),
    file('SYN334+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( big_f(A,B)
    | big_f(dollar_f1(A,B),dollar_f1(A,B)) ),
    file('SYN334+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( big_g(A,B)
    | big_g(dollar_f1(A,B),dollar_f1(A,B)) ),
    file('SYN334+1.p',unknown),
    [] ).

cnf(15,plain,
    ( big_g(A,B)
    | big_f(A,B) ),
    inference(hyper,[status(thm)],[7,4]),
    [iquote('hyper,7,4')] ).

cnf(18,plain,
    ( big_f(A,dollar_f1(B,A))
    | big_f(B,dollar_f1(B,A))
    | big_f(dollar_f1(B,A),dollar_f1(B,A)) ),
    inference(hyper,[status(thm)],[15,2,6]),
    [iquote('hyper,15,2,6')] ).

cnf(19,plain,
    ( big_f(A,dollar_f1(A,A))
    | big_f(dollar_f1(A,A),dollar_f1(A,A)) ),
    inference(factor,[status(thm)],[18]),
    [iquote('factor,18.1.2')] ).

cnf(25,plain,
    ( big_f(dollar_f1(A,A),dollar_f1(A,A))
    | big_g(A,dollar_f1(A,A)) ),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,1,6])]),
    [iquote('hyper,19,1,6,factor_simp')] ).

cnf(31,plain,
    ( big_f(dollar_f1(A,A),dollar_f1(A,A))
    | big_f(dollar_f1(A,dollar_f1(A,A)),dollar_f1(A,dollar_f1(A,A))) ),
    inference(hyper,[status(thm)],[25,5,15]),
    [iquote('hyper,25,5,15')] ).

cnf(131,plain,
    ( big_f(dollar_f1(A,A),dollar_f1(A,A))
    | big_g(dollar_f1(A,dollar_f1(A,A)),dollar_f1(A,dollar_f1(A,A))) ),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[31,3,19])]),
    [iquote('hyper,31,3,19,factor_simp')] ).

cnf(139,plain,
    big_f(dollar_f1(A,A),dollar_f1(A,A)),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[131,5,25])]),
    [iquote('hyper,131,5,25,factor_simp')] ).

cnf(140,plain,
    big_g(dollar_f1(dollar_f1(A,A),dollar_f1(A,A)),dollar_f1(dollar_f1(A,A),dollar_f1(A,A))),
    inference(hyper,[status(thm)],[139,3,139]),
    [iquote('hyper,139,3,139')] ).

cnf(154,plain,
    $false,
    inference(hyper,[status(thm)],[140,5,140]),
    [iquote('hyper,140,5,140')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYN334+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 11:31:18 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.96/2.16  ----- Otter 3.3f, August 2004 -----
% 1.96/2.16  The process was started by sandbox2 on n023.cluster.edu,
% 1.96/2.16  Wed Jul 27 11:31:18 2022
% 1.96/2.16  The command was "./otter".  The process ID is 9921.
% 1.96/2.16  
% 1.96/2.16  set(prolog_style_variables).
% 1.96/2.16  set(auto).
% 1.96/2.16     dependent: set(auto1).
% 1.96/2.16     dependent: set(process_input).
% 1.96/2.16     dependent: clear(print_kept).
% 1.96/2.16     dependent: clear(print_new_demod).
% 1.96/2.16     dependent: clear(print_back_demod).
% 1.96/2.16     dependent: clear(print_back_sub).
% 1.96/2.16     dependent: set(control_memory).
% 1.96/2.16     dependent: assign(max_mem, 12000).
% 1.96/2.16     dependent: assign(pick_given_ratio, 4).
% 1.96/2.16     dependent: assign(stats_level, 1).
% 1.96/2.16     dependent: assign(max_seconds, 10800).
% 1.96/2.16  clear(print_given).
% 1.96/2.16  
% 1.96/2.16  formula_list(usable).
% 1.96/2.16  -(exists X Y all Z ((big_f(X,Y)-> (big_f(X,Z)<->big_g(Y,Z)))-> ((big_f(X,Y)<-> (big_f(Z,Z)->big_g(Z,Z)))-> (big_g(X,Y)<->big_g(Z,Z))))).
% 1.96/2.16  end_of_list.
% 1.96/2.16  
% 1.96/2.16  -------> usable clausifies to:
% 1.96/2.16  
% 1.96/2.16  list(usable).
% 1.96/2.16  0 [] -big_f(X,Y)| -big_f(X,$f1(X,Y))|big_g(Y,$f1(X,Y)).
% 1.96/2.16  0 [] -big_f(X,Y)|big_f(X,$f1(X,Y))| -big_g(Y,$f1(X,Y)).
% 1.96/2.16  0 [] -big_f(X,Y)| -big_f($f1(X,Y),$f1(X,Y))|big_g($f1(X,Y),$f1(X,Y)).
% 1.96/2.16  0 [] big_f(X,Y)|big_f($f1(X,Y),$f1(X,Y)).
% 1.96/2.16  0 [] big_f(X,Y)| -big_g($f1(X,Y),$f1(X,Y)).
% 1.96/2.16  0 [] big_g(X,Y)|big_g($f1(X,Y),$f1(X,Y)).
% 1.96/2.16  0 [] -big_g(X,Y)| -big_g($f1(X,Y),$f1(X,Y)).
% 1.96/2.16  end_of_list.
% 1.96/2.16  
% 1.96/2.16  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.96/2.16  
% 1.96/2.16  This is a non-Horn set without equality.  The strategy will
% 1.96/2.16  be ordered hyper_res, unit deletion, and factoring, with
% 1.96/2.16  satellites in sos and with nuclei in usable.
% 1.96/2.16  
% 1.96/2.16     dependent: set(hyper_res).
% 1.96/2.16     dependent: set(factor).
% 1.96/2.16     dependent: set(unit_deletion).
% 1.96/2.16  
% 1.96/2.16  ------------> process usable:
% 1.96/2.16  ** KEPT (pick-wt=13): 1 [] -big_f(A,B)| -big_f(A,$f1(A,B))|big_g(B,$f1(A,B)).
% 1.96/2.16  ** KEPT (pick-wt=13): 2 [] -big_f(A,B)|big_f(A,$f1(A,B))| -big_g(B,$f1(A,B)).
% 1.96/2.16  ** KEPT (pick-wt=17): 3 [] -big_f(A,B)| -big_f($f1(A,B),$f1(A,B))|big_g($f1(A,B),$f1(A,B)).
% 1.96/2.16  ** KEPT (pick-wt=10): 4 [] big_f(A,B)| -big_g($f1(A,B),$f1(A,B)).
% 1.96/2.16  ** KEPT (pick-wt=10): 5 [] -big_g(A,B)| -big_g($f1(A,B),$f1(A,B)).
% 1.96/2.16  
% 1.96/2.16  ------------> process sos:
% 1.96/2.16  ** KEPT (pick-wt=10): 6 [] big_f(A,B)|big_f($f1(A,B),$f1(A,B)).
% 1.96/2.16  ** KEPT (pick-wt=10): 7 [] big_g(A,B)|big_g($f1(A,B),$f1(A,B)).
% 1.96/2.16  
% 1.96/2.16  ======= end of input processing =======
% 1.96/2.16  
% 1.96/2.16  =========== start of search ===========
% 1.96/2.16  
% 1.96/2.16  -------- PROOF -------- 
% 1.96/2.16  
% 1.96/2.16  -----> EMPTY CLAUSE at   0.03 sec ----> 154 [hyper,140,5,140] $F.
% 1.96/2.16  
% 1.96/2.16  Length of proof is 8.  Level of proof is 8.
% 1.96/2.16  
% 1.96/2.16  ---------------- PROOF ----------------
% 1.96/2.16  % SZS status Theorem
% 1.96/2.16  % SZS output start Refutation
% See solution above
% 1.96/2.16  ------------ end of proof -------------
% 1.96/2.16  
% 1.96/2.16  
% 1.96/2.16  Search stopped by max_proofs option.
% 1.96/2.16  
% 1.96/2.16  
% 1.96/2.16  Search stopped by max_proofs option.
% 1.96/2.16  
% 1.96/2.16  ============ end of search ============
% 1.96/2.16  
% 1.96/2.16  -------------- statistics -------------
% 1.96/2.16  clauses given                 23
% 1.96/2.16  clauses generated            442
% 1.96/2.16  clauses kept                 153
% 1.96/2.16  clauses forward subsumed     295
% 1.96/2.16  clauses back subsumed        105
% 1.96/2.16  Kbytes malloced             2929
% 1.96/2.16  
% 1.96/2.16  ----------- times (seconds) -----------
% 1.96/2.16  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 1.96/2.16  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.96/2.16  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.96/2.16  
% 1.96/2.16  That finishes the proof of the theorem.
% 1.96/2.16  
% 1.96/2.16  Process 9921 finished Wed Jul 27 11:31:20 2022
% 1.96/2.16  Otter interrupted
% 1.96/2.16  PROOF FOUND
%------------------------------------------------------------------------------