TSTP Solution File: SYN349+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SYN349+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 13:24:19 EDT 2022

% Result   : Theorem 1.65s 1.87s
% Output   : Refutation 1.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   15 (   4 unt;   6 nHn;   9 RR)
%            Number of literals    :   37 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :   20 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ big_f(A,dollar_f1(A,B))
    | big_f(dollar_f2(A),dollar_f1(A,B)) ),
    file('SYN349+1.p',unknown),
    [] ).

cnf(2,axiom,
    ( big_f(A,dollar_f1(A,B))
    | ~ big_f(dollar_f2(A),dollar_f1(A,B)) ),
    file('SYN349+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ big_f(A,dollar_f1(A,B))
    | big_f(dollar_f1(A,B),B)
    | ~ big_f(B,dollar_f1(A,B))
    | big_f(dollar_f1(A,B),dollar_f2(A)) ),
    file('SYN349+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( big_f(A,dollar_f1(A,B))
    | ~ big_f(dollar_f1(A,B),B)
    | big_f(B,dollar_f1(A,B))
    | ~ big_f(dollar_f1(A,B),dollar_f2(A)) ),
    file('SYN349+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ big_f(A,dollar_f1(A,B))
    | ~ big_f(dollar_f1(A,B),B)
    | ~ big_f(B,dollar_f1(A,B))
    | ~ big_f(dollar_f1(A,B),dollar_f2(A)) ),
    file('SYN349+1.p',unknown),
    [] ).

cnf(11,plain,
    ( ~ big_f(A,dollar_f1(A,dollar_f2(A)))
    | big_f(dollar_f1(A,dollar_f2(A)),dollar_f2(A))
    | ~ big_f(dollar_f2(A),dollar_f1(A,dollar_f2(A))) ),
    inference(factor,[status(thm)],[4]),
    [iquote('factor,4.2.4')] ).

cnf(13,plain,
    ( big_f(A,dollar_f1(A,dollar_f2(A)))
    | ~ big_f(dollar_f1(A,dollar_f2(A)),dollar_f2(A))
    | big_f(dollar_f2(A),dollar_f1(A,dollar_f2(A))) ),
    inference(factor,[status(thm)],[7]),
    [iquote('factor,7.2.4')] ).

cnf(15,plain,
    ( ~ big_f(A,dollar_f1(A,dollar_f2(A)))
    | ~ big_f(dollar_f1(A,dollar_f2(A)),dollar_f2(A))
    | ~ big_f(dollar_f2(A),dollar_f1(A,dollar_f2(A))) ),
    inference(factor,[status(thm)],[9]),
    [iquote('factor,9.2.4')] ).

cnf(16,axiom,
    ( big_f(A,dollar_f1(A,B))
    | big_f(dollar_f1(A,B),B)
    | big_f(B,dollar_f1(A,B))
    | big_f(dollar_f1(A,B),dollar_f2(A)) ),
    file('SYN349+1.p',unknown),
    [] ).

cnf(20,plain,
    ( big_f(A,dollar_f1(A,dollar_f2(A)))
    | big_f(dollar_f1(A,dollar_f2(A)),dollar_f2(A)) ),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[16,2])])]),
    [iquote('hyper,16,2,factor_simp,factor_simp')] ).

cnf(22,plain,
    ( big_f(A,dollar_f1(A,dollar_f2(A)))
    | big_f(dollar_f2(A),dollar_f1(A,dollar_f2(A))) ),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[20,13])]),
    [iquote('hyper,20,13,factor_simp')] ).

cnf(23,plain,
    big_f(dollar_f2(A),dollar_f1(A,dollar_f2(A))),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,1])]),
    [iquote('hyper,22,1,factor_simp')] ).

cnf(24,plain,
    big_f(A,dollar_f1(A,dollar_f2(A))),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,2])]),
    [iquote('hyper,22,2,factor_simp')] ).

cnf(25,plain,
    big_f(dollar_f1(A,dollar_f2(A)),dollar_f2(A)),
    inference(hyper,[status(thm)],[23,11,24]),
    [iquote('hyper,23,11,24')] ).

cnf(27,plain,
    $false,
    inference(hyper,[status(thm)],[25,15,24,23]),
    [iquote('hyper,25,15,24,23')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN349+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n005.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Jul 27 11:10:05 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 1.65/1.87  ----- Otter 3.3f, August 2004 -----
% 1.65/1.87  The process was started by sandbox on n005.cluster.edu,
% 1.65/1.87  Wed Jul 27 11:10:05 2022
% 1.65/1.87  The command was "./otter".  The process ID is 24403.
% 1.65/1.87  
% 1.65/1.87  set(prolog_style_variables).
% 1.65/1.87  set(auto).
% 1.65/1.87     dependent: set(auto1).
% 1.65/1.87     dependent: set(process_input).
% 1.65/1.87     dependent: clear(print_kept).
% 1.65/1.87     dependent: clear(print_new_demod).
% 1.65/1.87     dependent: clear(print_back_demod).
% 1.65/1.87     dependent: clear(print_back_sub).
% 1.65/1.87     dependent: set(control_memory).
% 1.65/1.87     dependent: assign(max_mem, 12000).
% 1.65/1.87     dependent: assign(pick_given_ratio, 4).
% 1.65/1.87     dependent: assign(stats_level, 1).
% 1.65/1.87     dependent: assign(max_seconds, 10800).
% 1.65/1.87  clear(print_given).
% 1.65/1.87  
% 1.65/1.87  formula_list(usable).
% 1.65/1.87  -(exists X1 all X2 exists X3 all X4 ((big_f(X1,X4)<->big_f(X2,X4))-> (((big_f(X1,X4)<->big_f(X4,X3))<->big_f(X3,X4))<->big_f(X4,X2)))).
% 1.65/1.87  end_of_list.
% 1.65/1.87  
% 1.65/1.87  -------> usable clausifies to:
% 1.65/1.87  
% 1.65/1.87  list(usable).
% 1.65/1.87  0 [] -big_f(X1,$f1(X1,X3))|big_f($f2(X1),$f1(X1,X3)).
% 1.65/1.87  0 [] big_f(X1,$f1(X1,X3))| -big_f($f2(X1),$f1(X1,X3)).
% 1.65/1.87  0 [] big_f(X1,$f1(X1,X3))|big_f($f1(X1,X3),X3)|big_f(X3,$f1(X1,X3))|big_f($f1(X1,X3),$f2(X1)).
% 1.65/1.87  0 [] -big_f(X1,$f1(X1,X3))| -big_f($f1(X1,X3),X3)|big_f(X3,$f1(X1,X3))|big_f($f1(X1,X3),$f2(X1)).
% 1.65/1.87  0 [] -big_f(X1,$f1(X1,X3))|big_f($f1(X1,X3),X3)| -big_f(X3,$f1(X1,X3))|big_f($f1(X1,X3),$f2(X1)).
% 1.65/1.87  0 [] big_f(X1,$f1(X1,X3))| -big_f($f1(X1,X3),X3)| -big_f(X3,$f1(X1,X3))|big_f($f1(X1,X3),$f2(X1)).
% 1.65/1.87  0 [] -big_f(X1,$f1(X1,X3))|big_f($f1(X1,X3),X3)|big_f(X3,$f1(X1,X3))| -big_f($f1(X1,X3),$f2(X1)).
% 1.65/1.87  0 [] big_f(X1,$f1(X1,X3))| -big_f($f1(X1,X3),X3)|big_f(X3,$f1(X1,X3))| -big_f($f1(X1,X3),$f2(X1)).
% 1.65/1.87  0 [] big_f(X1,$f1(X1,X3))|big_f($f1(X1,X3),X3)| -big_f(X3,$f1(X1,X3))| -big_f($f1(X1,X3),$f2(X1)).
% 1.65/1.87  0 [] -big_f(X1,$f1(X1,X3))| -big_f($f1(X1,X3),X3)| -big_f(X3,$f1(X1,X3))| -big_f($f1(X1,X3),$f2(X1)).
% 1.65/1.87  end_of_list.
% 1.65/1.87  
% 1.65/1.87  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.65/1.87  
% 1.65/1.87  This is a non-Horn set without equality.  The strategy will
% 1.65/1.87  be ordered hyper_res, unit deletion, and factoring, with
% 1.65/1.87  satellites in sos and with nuclei in usable.
% 1.65/1.87  
% 1.65/1.87     dependent: set(hyper_res).
% 1.65/1.87     dependent: set(factor).
% 1.65/1.87     dependent: set(unit_deletion).
% 1.65/1.87  
% 1.65/1.87  ------------> process usable:
% 1.65/1.87  ** KEPT (pick-wt=11): 1 [] -big_f(A,$f1(A,B))|big_f($f2(A),$f1(A,B)).
% 1.65/1.87  ** KEPT (pick-wt=11): 2 [] big_f(A,$f1(A,B))| -big_f($f2(A),$f1(A,B)).
% 1.65/1.87  ** KEPT (pick-wt=21): 3 [] -big_f(A,$f1(A,B))| -big_f($f1(A,B),B)|big_f(B,$f1(A,B))|big_f($f1(A,B),$f2(A)).
% 1.65/1.87  ** KEPT (pick-wt=21): 4 [] -big_f(A,$f1(A,B))|big_f($f1(A,B),B)| -big_f(B,$f1(A,B))|big_f($f1(A,B),$f2(A)).
% 1.65/1.87  ** KEPT (pick-wt=21): 5 [] big_f(A,$f1(A,B))| -big_f($f1(A,B),B)| -big_f(B,$f1(A,B))|big_f($f1(A,B),$f2(A)).
% 1.65/1.87  ** KEPT (pick-wt=21): 6 [] -big_f(A,$f1(A,B))|big_f($f1(A,B),B)|big_f(B,$f1(A,B))| -big_f($f1(A,B),$f2(A)).
% 1.65/1.87  ** KEPT (pick-wt=21): 7 [] big_f(A,$f1(A,B))| -big_f($f1(A,B),B)|big_f(B,$f1(A,B))| -big_f($f1(A,B),$f2(A)).
% 1.65/1.87  ** KEPT (pick-wt=21): 8 [] big_f(A,$f1(A,B))|big_f($f1(A,B),B)| -big_f(B,$f1(A,B))| -big_f($f1(A,B),$f2(A)).
% 1.65/1.87  ** KEPT (pick-wt=21): 9 [] -big_f(A,$f1(A,B))| -big_f($f1(A,B),B)| -big_f(B,$f1(A,B))| -big_f($f1(A,B),$f2(A)).
% 1.65/1.87  
% 1.65/1.87  ------------> process sos:
% 1.65/1.87  ** KEPT (pick-wt=21): 16 [] big_f(A,$f1(A,B))|big_f($f1(A,B),B)|big_f(B,$f1(A,B))|big_f($f1(A,B),$f2(A)).
% 1.65/1.87  
% 1.65/1.87  ======= end of input processing =======
% 1.65/1.87  
% 1.65/1.87  =========== start of search ===========
% 1.65/1.87  
% 1.65/1.87  -------- PROOF -------- 
% 1.65/1.87  
% 1.65/1.87  -----> EMPTY CLAUSE at   0.02 sec ----> 27 [hyper,25,15,24,23] $F.
% 1.65/1.87  
% 1.65/1.87  Length of proof is 8.  Level of proof is 4.
% 1.65/1.87  
% 1.65/1.87  ---------------- PROOF ----------------
% 1.65/1.87  % SZS status Theorem
% 1.65/1.87  % SZS output start Refutation
% See solution above
% 1.65/1.87  ------------ end of proof -------------
% 1.65/1.87  
% 1.65/1.87  
% 1.65/1.87  Search stopped by max_proofs option.
% 1.65/1.87  
% 1.65/1.87  
% 1.65/1.87  Search stopped by max_proofs option.
% 1.65/1.87  
% 1.65/1.87  ============ end of search ============
% 1.65/1.87  
% 1.65/1.87  -------------- statistics -------------
% 1.65/1.87  clauses given                  7
% 1.65/1.87  clauses generated            380
% 1.65/1.87  clauses kept                  26
% 1.65/1.87  clauses forward subsumed     363
% 1.65/1.87  clauses back subsumed          8
% 1.65/1.87  Kbytes malloced              976
% 1.65/1.87  
% 1.65/1.87  ----------- times (seconds) -----------
% 1.65/1.87  user CPU time          0.02          (0 hr, 0 min, 0 sec)
% 1.65/1.87  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.65/1.87  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.65/1.87  
% 1.65/1.87  That finishes the proof of the theorem.
% 1.65/1.87  
% 1.65/1.87  Process 24403 finished Wed Jul 27 11:10:07 2022
% 1.65/1.87  Otter interrupted
% 1.65/1.87  PROOF FOUND
%------------------------------------------------------------------------------