TSTP Solution File: COL003-13 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : COL003-13 : TPTP v8.1.0. Released v2.1.0.
% 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 12:47:57 EDT 2022

% Result   : Unsatisfiable 1.80s 2.02s
% Output   : Refutation 1.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   15 (  15 unt;   0 nHn;   5 RR)
%            Number of literals    :   15 (  14 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
    file('COL003-13.p',unknown),
    [] ).

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

cnf(5,axiom,
    apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
    file('COL003-13.p',unknown),
    [] ).

cnf(6,axiom,
    apply(apply(w,A),B) = apply(apply(A,B),B),
    file('COL003-13.p',unknown),
    [] ).

cnf(7,axiom,
    strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),
    file('COL003-13.p',unknown),
    [] ).

cnf(8,plain,
    apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)) = strong_fixed_point,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
    [iquote('copy,7,flip.1')] ).

cnf(10,plain,
    apply(apply(A,B),B) = apply(apply(w,A),B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
    [iquote('copy,6,flip.1')] ).

cnf(12,plain,
    apply(apply(apply(w,A),B),B) = apply(apply(w,apply(A,B)),B),
    inference(para_into,[status(thm),theory(equality)],[10,10]),
    [iquote('para_into,10.1.1.1,10.1.1')] ).

cnf(15,plain,
    apply(apply(A,A),A) = apply(apply(w,w),A),
    inference(para_into,[status(thm),theory(equality)],[10,6]),
    [iquote('para_into,10.1.1,6.1.1')] ).

cnf(28,plain,
    apply(apply(w,apply(b,A)),B) = apply(A,apply(B,B)),
    inference(para_into,[status(thm),theory(equality)],[5,10]),
    [iquote('para_into,4.1.1,10.1.1')] ).

cnf(49,plain,
    apply(apply(A,apply(apply(w,apply(b,A)),apply(w,apply(b,A)))),apply(w,apply(b,A))) = apply(apply(w,w),apply(w,apply(b,A))),
    inference(para_from,[status(thm),theory(equality)],[28,15]),
    [iquote('para_from,28.1.1,15.1.1.1')] ).

cnf(104,plain,
    apply(apply(w,w),apply(w,apply(b,apply(b,A)))) = apply(strong_fixed_point,A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,5]),5,5])]),
    [iquote('para_from,8.1.1,4.1.1.1,demod,5,5,flip.1')] ).

cnf(163,plain,
    apply(apply(w,apply(A,apply(w,A))),apply(w,A)) = apply(apply(w,w),apply(w,A)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,15])]),
    [iquote('para_into,11.1.1,15.1.1,flip.1')] ).

cnf(1263,plain,
    apply(A,apply(strong_fixed_point,A)) = apply(strong_fixed_point,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,5]),12,163,104,104]),
    [iquote('para_into,49.1.1,4.1.1,demod,12,163,104,104')] ).

cnf(1265,plain,
    $false,
    inference(binary,[status(thm)],[1263,2]),
    [iquote('binary,1263.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : COL003-13 : TPTP v8.1.0. Released v2.1.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n005.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 02:24:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.72/1.99  ----- Otter 3.3f, August 2004 -----
% 1.72/1.99  The process was started by sandbox2 on n005.cluster.edu,
% 1.72/1.99  Wed Jul 27 02:24:35 2022
% 1.72/1.99  The command was "./otter".  The process ID is 24000.
% 1.72/1.99  
% 1.72/1.99  set(prolog_style_variables).
% 1.72/1.99  set(auto).
% 1.72/1.99     dependent: set(auto1).
% 1.72/1.99     dependent: set(process_input).
% 1.72/1.99     dependent: clear(print_kept).
% 1.72/1.99     dependent: clear(print_new_demod).
% 1.72/1.99     dependent: clear(print_back_demod).
% 1.72/1.99     dependent: clear(print_back_sub).
% 1.72/1.99     dependent: set(control_memory).
% 1.72/1.99     dependent: assign(max_mem, 12000).
% 1.72/1.99     dependent: assign(pick_given_ratio, 4).
% 1.72/1.99     dependent: assign(stats_level, 1).
% 1.72/1.99     dependent: assign(max_seconds, 10800).
% 1.72/1.99  clear(print_given).
% 1.72/1.99  
% 1.72/1.99  list(usable).
% 1.72/1.99  0 [] A=A.
% 1.72/1.99  0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.72/1.99  0 [] apply(apply(w,X),Y)=apply(apply(X,Y),Y).
% 1.72/1.99  0 [] strong_fixed_point=apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)).
% 1.72/1.99  0 [] apply(strong_fixed_point,fixed_pt)!=apply(fixed_pt,apply(strong_fixed_point,fixed_pt)).
% 1.72/1.99  end_of_list.
% 1.72/1.99  
% 1.72/1.99  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.72/1.99  
% 1.72/1.99  All clauses are units, and equality is present; the
% 1.72/1.99  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.72/1.99  
% 1.72/1.99     dependent: set(knuth_bendix).
% 1.72/1.99     dependent: set(anl_eq).
% 1.72/1.99     dependent: set(para_from).
% 1.72/1.99     dependent: set(para_into).
% 1.72/1.99     dependent: clear(para_from_right).
% 1.72/1.99     dependent: clear(para_into_right).
% 1.72/1.99     dependent: set(para_from_vars).
% 1.72/1.99     dependent: set(eq_units_both_ways).
% 1.72/1.99     dependent: set(dynamic_demod_all).
% 1.72/1.99     dependent: set(dynamic_demod).
% 1.72/1.99     dependent: set(order_eq).
% 1.72/1.99     dependent: set(back_demod).
% 1.72/1.99     dependent: set(lrpo).
% 1.72/1.99  
% 1.72/1.99  ------------> process usable:
% 1.72/1.99  ** KEPT (pick-wt=9): 2 [copy,1,flip.1] apply(fixed_pt,apply(strong_fixed_point,fixed_pt))!=apply(strong_fixed_point,fixed_pt).
% 1.72/1.99  
% 1.72/1.99  ------------> process sos:
% 1.72/1.99  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.72/1.99  ** KEPT (pick-wt=13): 4 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.72/1.99  ---> New Demodulator: 5 [new_demod,4] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.72/1.99  ** KEPT (pick-wt=11): 6 [] apply(apply(w,A),B)=apply(apply(A,B),B).
% 1.72/1.99  ** KEPT (pick-wt=17): 8 [copy,7,flip.1] apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))=strong_fixed_point.
% 1.72/1.99  ---> New Demodulator: 9 [new_demod,8] apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))=strong_fixed_point.
% 1.72/1.99    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.72/1.99  >>>> Starting back demodulation with 5.
% 1.72/1.99  ** KEPT (pick-wt=11): 10 [copy,6,flip.1] apply(apply(A,B),B)=apply(apply(w,A),B).
% 1.72/1.99  >>>> Starting back demodulation with 9.
% 1.72/1.99    Following clause subsumed by 6 during input processing: 0 [copy,10,flip.1] apply(apply(w,A),B)=apply(apply(A,B),B).
% 1.72/1.99  
% 1.72/1.99  ======= end of input processing =======
% 1.72/1.99  
% 1.72/1.99  =========== start of search ===========
% 1.72/1.99  WARNING, demod_limit (given clause 46): 0 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% 1.80/2.01  WARNING, demod_limit stopped the demodulation of a clause.
% 1.80/2.01  This warning will not be repeated.
% 1.80/2.01  
% 1.80/2.01  
% 1.80/2.01  
% 1.80/2.01  Resetting weight limit to 19.
% 1.80/2.01  
% 1.80/2.01  ,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(apply(w,b),apply(w,b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))=apply(apply(w,apply(apply(w,b),apply(w,w))),apply(w,b)).
% 1.80/2.02  
% 1.80/2.02  Resetting weight limit to 19.
% 1.80/2.02  
% 1.80/2.02  sos_size=693
% 1.80/2.02  
% 1.80/2.02  -------- PROOF -------- 
% 1.80/2.02  
% 1.80/2.02  ----> UNIT CONFLICT at   0.12 sec ----> 1265 [binary,1263.1,2.1] $F.
% 1.80/2.02  
% 1.80/2.02  Length of proof is 10.  Level of proof is 4.
% 1.80/2.02  
% 1.80/2.02  ---------------- PROOF ----------------
% 1.80/2.02  % SZS status Unsatisfiable
% 1.80/2.02  % SZS output start Refutation
% See solution above
% 1.80/2.02  ------------ end of proof -------------
% 1.80/2.02  
% 1.80/2.02  
% 1.80/2.02  Search stopped by max_proofs option.
% 1.80/2.02  
% 1.80/2.02  
% 1.80/2.02  Search stopped by max_proofs option.
% 1.80/2.02  
% 1.80/2.02  ============ end of search ============
% 1.80/2.02  
% 1.80/2.02  -------------- statistics -------------
% 1.80/2.02  clauses given                 51
% 1.80/2.02  clauses generated           1418
% 1.80/2.02  clauses kept                 865
% 1.80/2.02  clauses forward subsumed    1047
% 1.80/2.02  clauses back subsumed         26
% 1.80/2.02  Kbytes malloced             5859
% 1.80/2.02  
% 1.80/2.02  ----------- times (seconds) -----------
% 1.80/2.02  user CPU time          0.12          (0 hr, 0 min, 0 sec)
% 1.80/2.02  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 1.80/2.02  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.80/2.02  
% 1.80/2.02  That finishes the proof of the theorem.
% 1.80/2.02  
% 1.80/2.02  Process 24000 finished Wed Jul 27 02:24:37 2022
% 1.80/2.02  Otter interrupted
% 1.80/2.02  PROOF FOUND
%------------------------------------------------------------------------------