TSTP Solution File: COL009-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : COL009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n028.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 12:47:59 EDT 2022

% Result   : Unsatisfiable 1.65s 1.89s
% Output   : Refutation 1.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   3 RR)
%            Number of literals    :    9 (   8 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   19 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    A != apply(combinator,A),
    file('COL009-1.p',unknown),
    [] ).

cnf(2,plain,
    apply(combinator,A) != A,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
    [iquote('copy,1,flip.1')] ).

cnf(4,axiom,
    apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
    file('COL009-1.p',unknown),
    [] ).

cnf(6,axiom,
    apply(apply(l2,A),B) = apply(B,apply(A,A)),
    file('COL009-1.p',unknown),
    [] ).

cnf(7,plain,
    apply(A,apply(B,B)) = apply(apply(l2,B),A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
    [iquote('copy,6,flip.1')] ).

cnf(22,plain,
    apply(apply(l2,A),apply(apply(b,B),C)) = apply(B,apply(C,apply(A,A))),
    inference(para_into,[status(thm),theory(equality)],[4,7]),
    [iquote('para_into,4.1.1,7.1.1')] ).

cnf(23,plain,
    apply(A,apply(B,apply(C,C))) = apply(apply(l2,C),apply(apply(b,A),B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
    [iquote('copy,22,flip.1')] ).

cnf(521,plain,
    apply(A,apply(B,apply(C,apply(D,apply(apply(b,C),D))))) = apply(apply(l2,apply(apply(b,C),D)),apply(apply(b,A),B)),
    inference(para_into,[status(thm),theory(equality)],[23,4]),
    [iquote('para_into,23.1.1.2.2,4.1.1')] ).

cnf(522,plain,
    $false,
    inference(binary,[status(thm)],[521,2]),
    [iquote('binary,521.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : COL009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n028.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 02:32:48 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.65/1.89  ----- Otter 3.3f, August 2004 -----
% 1.65/1.89  The process was started by sandbox on n028.cluster.edu,
% 1.65/1.89  Wed Jul 27 02:32:48 2022
% 1.65/1.89  The command was "./otter".  The process ID is 13234.
% 1.65/1.89  
% 1.65/1.89  set(prolog_style_variables).
% 1.65/1.89  set(auto).
% 1.65/1.89     dependent: set(auto1).
% 1.65/1.89     dependent: set(process_input).
% 1.65/1.89     dependent: clear(print_kept).
% 1.65/1.89     dependent: clear(print_new_demod).
% 1.65/1.89     dependent: clear(print_back_demod).
% 1.65/1.89     dependent: clear(print_back_sub).
% 1.65/1.89     dependent: set(control_memory).
% 1.65/1.89     dependent: assign(max_mem, 12000).
% 1.65/1.89     dependent: assign(pick_given_ratio, 4).
% 1.65/1.89     dependent: assign(stats_level, 1).
% 1.65/1.89     dependent: assign(max_seconds, 10800).
% 1.65/1.89  clear(print_given).
% 1.65/1.89  
% 1.65/1.89  list(usable).
% 1.65/1.89  0 [] A=A.
% 1.65/1.89  0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.65/1.89  0 [] apply(apply(l2,X),Y)=apply(Y,apply(X,X)).
% 1.65/1.89  0 [] Y!=apply(combinator,Y).
% 1.65/1.89  end_of_list.
% 1.65/1.89  
% 1.65/1.89  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.65/1.89  
% 1.65/1.89  All clauses are units, and equality is present; the
% 1.65/1.89  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.65/1.89  
% 1.65/1.89     dependent: set(knuth_bendix).
% 1.65/1.89     dependent: set(anl_eq).
% 1.65/1.89     dependent: set(para_from).
% 1.65/1.89     dependent: set(para_into).
% 1.65/1.89     dependent: clear(para_from_right).
% 1.65/1.89     dependent: clear(para_into_right).
% 1.65/1.89     dependent: set(para_from_vars).
% 1.65/1.89     dependent: set(eq_units_both_ways).
% 1.65/1.89     dependent: set(dynamic_demod_all).
% 1.65/1.89     dependent: set(dynamic_demod).
% 1.65/1.89     dependent: set(order_eq).
% 1.65/1.89     dependent: set(back_demod).
% 1.65/1.89     dependent: set(lrpo).
% 1.65/1.89  
% 1.65/1.89  ------------> process usable:
% 1.65/1.89  ** KEPT (pick-wt=5): 2 [copy,1,flip.1] apply(combinator,A)!=A.
% 1.65/1.89  
% 1.65/1.89  ------------> process sos:
% 1.65/1.89  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.65/1.89  ** KEPT (pick-wt=13): 4 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.65/1.89  ---> New Demodulator: 5 [new_demod,4] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.65/1.89  ** KEPT (pick-wt=11): 6 [] apply(apply(l2,A),B)=apply(B,apply(A,A)).
% 1.65/1.89    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.65/1.89  >>>> Starting back demodulation with 5.
% 1.65/1.89  ** KEPT (pick-wt=11): 7 [copy,6,flip.1] apply(A,apply(B,B))=apply(apply(l2,B),A).
% 1.65/1.89    Following clause subsumed by 6 during input processing: 0 [copy,7,flip.1] apply(apply(l2,A),B)=apply(B,apply(A,A)).
% 1.65/1.89  
% 1.65/1.89  ======= end of input processing =======
% 1.65/1.89  
% 1.65/1.89  =========== start of search ===========
% 1.65/1.89  
% 1.65/1.89  -------- PROOF -------- 
% 1.65/1.89  
% 1.65/1.89  ----> UNIT CONFLICT at   0.04 sec ----> 522 [binary,521.1,2.1] $F.
% 1.65/1.89  
% 1.65/1.89  Length of proof is 5.  Level of proof is 4.
% 1.65/1.89  
% 1.65/1.89  ---------------- PROOF ----------------
% 1.65/1.89  % SZS status Unsatisfiable
% 1.65/1.89  % SZS output start Refutation
% See solution above
% 1.65/1.89  ------------ end of proof -------------
% 1.65/1.89  
% 1.65/1.89  
% 1.65/1.89  Search stopped by max_proofs option.
% 1.65/1.89  
% 1.65/1.89  
% 1.65/1.89  Search stopped by max_proofs option.
% 1.65/1.89  
% 1.65/1.89  ============ end of search ============
% 1.65/1.89  
% 1.65/1.89  -------------- statistics -------------
% 1.65/1.89  clauses given                 27
% 1.65/1.89  clauses generated            569
% 1.65/1.89  clauses kept                 466
% 1.65/1.89  clauses forward subsumed     566
% 1.65/1.89  clauses back subsumed          9
% 1.65/1.89  Kbytes malloced             1953
% 1.65/1.89  
% 1.65/1.89  ----------- times (seconds) -----------
% 1.65/1.89  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.65/1.89  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.65/1.89  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.65/1.89  
% 1.65/1.89  That finishes the proof of the theorem.
% 1.65/1.89  
% 1.65/1.89  Process 13234 finished Wed Jul 27 02:32:50 2022
% 1.65/1.89  Otter interrupted
% 1.65/1.89  PROOF FOUND
%------------------------------------------------------------------------------