TSTP Solution File: COL066-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : COL066-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n012.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 12:48:10 EDT 2022

% Result   : Unsatisfiable 1.68s 1.91s
% Output   : Refutation 1.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   7 unt;   0 nHn;   4 RR)
%            Number of literals    :    7 (   6 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
    file('COL066-2.p',unknown),
    [] ).

cnf(2,axiom,
    A = A,
    file('COL066-2.p',unknown),
    [] ).

cnf(6,axiom,
    apply(apply(apply(q,A),B),C) = apply(B,apply(A,C)),
    file('COL066-2.p',unknown),
    [] ).

cnf(7,axiom,
    apply(apply(w,A),B) = apply(apply(A,B),B),
    file('COL066-2.p',unknown),
    [] ).

cnf(8,plain,
    apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6]),
    [iquote('back_demod,1,demod,6')] ).

cnf(64,plain,
    apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,7]),6,6,6,6,6]),
    [iquote('para_into,8.1.1.1.1.1,7.1.1,demod,6,6,6,6,6')] ).

cnf(65,plain,
    $false,
    inference(binary,[status(thm)],[64,2]),
    [iquote('binary,64.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : COL066-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n012.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 02:20:20 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.68/1.91  ----- Otter 3.3f, August 2004 -----
% 1.68/1.91  The process was started by sandbox2 on n012.cluster.edu,
% 1.68/1.91  Wed Jul 27 02:20:20 2022
% 1.68/1.91  The command was "./otter".  The process ID is 4438.
% 1.68/1.91  
% 1.68/1.91  set(prolog_style_variables).
% 1.68/1.91  set(auto).
% 1.68/1.91     dependent: set(auto1).
% 1.68/1.91     dependent: set(process_input).
% 1.68/1.91     dependent: clear(print_kept).
% 1.68/1.91     dependent: clear(print_new_demod).
% 1.68/1.91     dependent: clear(print_back_demod).
% 1.68/1.91     dependent: clear(print_back_sub).
% 1.68/1.91     dependent: set(control_memory).
% 1.68/1.91     dependent: assign(max_mem, 12000).
% 1.68/1.91     dependent: assign(pick_given_ratio, 4).
% 1.68/1.91     dependent: assign(stats_level, 1).
% 1.68/1.91     dependent: assign(max_seconds, 10800).
% 1.68/1.91  clear(print_given).
% 1.68/1.91  
% 1.68/1.91  list(usable).
% 1.68/1.91  0 [] A=A.
% 1.68/1.91  0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.68/1.91  0 [] apply(apply(apply(q,X),Y),Z)=apply(Y,apply(X,Z)).
% 1.68/1.91  0 [] apply(apply(w,X),Y)=apply(apply(X,Y),Y).
% 1.68/1.91  0 [] apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z)!=apply(apply(x,y),apply(apply(x,y),z)).
% 1.68/1.91  end_of_list.
% 1.68/1.91  
% 1.68/1.91  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.91  
% 1.68/1.91  All clauses are units, and equality is present; the
% 1.68/1.91  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.91  
% 1.68/1.91     dependent: set(knuth_bendix).
% 1.68/1.91     dependent: set(anl_eq).
% 1.68/1.91     dependent: set(para_from).
% 1.68/1.91     dependent: set(para_into).
% 1.68/1.91     dependent: clear(para_from_right).
% 1.68/1.91     dependent: clear(para_into_right).
% 1.68/1.91     dependent: set(para_from_vars).
% 1.68/1.91     dependent: set(eq_units_both_ways).
% 1.68/1.91     dependent: set(dynamic_demod_all).
% 1.68/1.91     dependent: set(dynamic_demod).
% 1.68/1.91     dependent: set(order_eq).
% 1.68/1.91     dependent: set(back_demod).
% 1.68/1.91     dependent: set(lrpo).
% 1.68/1.91  
% 1.68/1.91  ------------> process usable:
% 1.68/1.91  ** KEPT (pick-wt=29): 1 [] apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z)!=apply(apply(x,y),apply(apply(x,y),z)).
% 1.68/1.91  
% 1.68/1.91  ------------> process sos:
% 1.68/1.91  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.68/1.91  ** KEPT (pick-wt=13): 3 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.68/1.91  ---> New Demodulator: 4 [new_demod,3] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.68/1.91  ** KEPT (pick-wt=13): 5 [] apply(apply(apply(q,A),B),C)=apply(B,apply(A,C)).
% 1.68/1.91  ---> New Demodulator: 6 [new_demod,5] apply(apply(apply(q,A),B),C)=apply(B,apply(A,C)).
% 1.68/1.91  ** KEPT (pick-wt=11): 7 [] apply(apply(w,A),B)=apply(apply(A,B),B).
% 1.68/1.91    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.68/1.91  >>>> Starting back demodulation with 4.
% 1.68/1.91  >>>> Starting back demodulation with 6.
% 1.68/1.91      >> back demodulating 1 with 6.
% 1.68/1.91  ** KEPT (pick-wt=11): 9 [copy,7,flip.1] apply(apply(A,B),B)=apply(apply(w,A),B).
% 1.68/1.91    Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] apply(apply(w,A),B)=apply(apply(A,B),B).
% 1.68/1.91  
% 1.68/1.91  ======= end of input processing =======
% 1.68/1.91  
% 1.68/1.91  =========== start of search ===========
% 1.68/1.91  
% 1.68/1.91  -------- PROOF -------- 
% 1.68/1.91  
% 1.68/1.91  ----> UNIT CONFLICT at   0.00 sec ----> 65 [binary,64.1,2.1] $F.
% 1.68/1.91  
% 1.68/1.91  Length of proof is 2.  Level of proof is 2.
% 1.68/1.91  
% 1.68/1.91  ---------------- PROOF ----------------
% 1.68/1.91  % SZS status Unsatisfiable
% 1.68/1.91  % SZS output start Refutation
% See solution above
% 1.68/1.91  ------------ end of proof -------------
% 1.68/1.91  
% 1.68/1.91  
% 1.68/1.91  Search stopped by max_proofs option.
% 1.68/1.91  
% 1.68/1.91  
% 1.68/1.91  Search stopped by max_proofs option.
% 1.68/1.91  
% 1.68/1.91  ============ end of search ============
% 1.68/1.91  
% 1.68/1.91  -------------- statistics -------------
% 1.68/1.91  clauses given                 11
% 1.68/1.91  clauses generated             74
% 1.68/1.91  clauses kept                  48
% 1.68/1.91  clauses forward subsumed      61
% 1.68/1.91  clauses back subsumed          0
% 1.68/1.91  Kbytes malloced              976
% 1.68/1.91  
% 1.68/1.91  ----------- times (seconds) -----------
% 1.68/1.91  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.68/1.91  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.68/1.91  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.68/1.91  
% 1.68/1.91  That finishes the proof of the theorem.
% 1.68/1.91  
% 1.68/1.91  Process 4438 finished Wed Jul 27 02:20:22 2022
% 1.68/1.91  Otter interrupted
% 1.68/1.91  PROOF FOUND
%------------------------------------------------------------------------------