TSTP Solution File: COL042-6 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : COL042-6 : TPTP v8.1.0. Released v2.1.0.
% 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 12:48:03 EDT 2022

% Result   : Unsatisfiable 1.80s 2.00s
% Output   : Refutation 1.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   17 (  17 unt;   0 nHn;   5 RR)
%            Number of literals    :   17 (  16 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   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   :   25 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
    file('COL042-6.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('COL042-6.p',unknown),
    [] ).

cnf(6,axiom,
    apply(apply(w1,A),B) = apply(apply(B,A),A),
    file('COL042-6.p',unknown),
    [] ).

cnf(7,axiom,
    strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),
    file('COL042-6.p',unknown),
    [] ).

cnf(8,plain,
    apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),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(w1,B),A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
    [iquote('copy,6,flip.1')] ).

cnf(32,plain,
    apply(apply(A,apply(B,C)),C) = apply(apply(w1,C),apply(apply(b,A),B)),
    inference(para_from,[status(thm),theory(equality)],[5,10]),
    [iquote('para_from,4.1.1,10.1.1.1')] ).

cnf(34,plain,
    apply(apply(w1,A),apply(apply(b,B),C)) = apply(apply(B,apply(C,A)),A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),
    [iquote('copy,32,flip.1')] ).

cnf(96,plain,
    apply(apply(w1,w1),apply(apply(b,w1),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(369,plain,
    apply(apply(A,apply(B,A)),apply(B,A)) = apply(apply(w1,A),apply(apply(b,w1),B)),
    inference(para_into,[status(thm),theory(equality)],[32,6]),
    [iquote('para_into,32.1.1,6.1.1')] ).

cnf(370,plain,
    apply(A,apply(apply(B,C),C)) = apply(apply(w1,C),apply(apply(b,apply(b,A)),B)),
    inference(para_into,[status(thm),theory(equality)],[32,5]),
    [iquote('para_into,32.1.1,4.1.1')] ).

cnf(409,plain,
    apply(apply(w1,A),apply(apply(b,apply(b,B)),C)) = apply(B,apply(apply(C,A),A)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[370])]),
    [iquote('copy,370,flip.1')] ).

cnf(674,plain,
    apply(apply(w1,apply(apply(b,apply(b,A)),w1)),w1) = apply(strong_fixed_point,A),
    inference(para_into,[status(thm),theory(equality)],[96,34]),
    [iquote('para_into,95.1.1,34.1.1')] ).

cnf(702,plain,
    apply(apply(w1,apply(apply(b,apply(b,A)),w1)),apply(apply(b,apply(b,A)),w1)) = apply(strong_fixed_point,A),
    inference(para_into,[status(thm),theory(equality)],[674,6]),
    [iquote('para_into,674.1.1,6.1.1')] ).

cnf(1538,plain,
    apply(A,apply(strong_fixed_point,A)) = apply(strong_fixed_point,A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[409,369]),96,702])]),
    [iquote('para_into,409.1.1,369.1.1,demod,96,702,flip.1')] ).

cnf(1540,plain,
    $false,
    inference(binary,[status(thm)],[1538,2]),
    [iquote('binary,1538.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : COL042-6 : TPTP v8.1.0. Released v2.1.0.
% 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 02:32:18 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.80/2.00  ----- Otter 3.3f, August 2004 -----
% 1.80/2.00  The process was started by sandbox on n028.cluster.edu,
% 1.80/2.00  Wed Jul 27 02:32:18 2022
% 1.80/2.00  The command was "./otter".  The process ID is 11479.
% 1.80/2.00  
% 1.80/2.00  set(prolog_style_variables).
% 1.80/2.00  set(auto).
% 1.80/2.00     dependent: set(auto1).
% 1.80/2.00     dependent: set(process_input).
% 1.80/2.00     dependent: clear(print_kept).
% 1.80/2.00     dependent: clear(print_new_demod).
% 1.80/2.00     dependent: clear(print_back_demod).
% 1.80/2.00     dependent: clear(print_back_sub).
% 1.80/2.00     dependent: set(control_memory).
% 1.80/2.00     dependent: assign(max_mem, 12000).
% 1.80/2.00     dependent: assign(pick_given_ratio, 4).
% 1.80/2.00     dependent: assign(stats_level, 1).
% 1.80/2.00     dependent: assign(max_seconds, 10800).
% 1.80/2.00  clear(print_given).
% 1.80/2.00  
% 1.80/2.00  list(usable).
% 1.80/2.00  0 [] A=A.
% 1.80/2.00  0 [] apply(apply(apply(b,X),Y),Z)=apply(X,apply(Y,Z)).
% 1.80/2.00  0 [] apply(apply(w1,X),Y)=apply(apply(Y,X),X).
% 1.80/2.00  0 [] strong_fixed_point=apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b).
% 1.80/2.00  0 [] apply(strong_fixed_point,fixed_pt)!=apply(fixed_pt,apply(strong_fixed_point,fixed_pt)).
% 1.80/2.00  end_of_list.
% 1.80/2.00  
% 1.80/2.00  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.80/2.00  
% 1.80/2.00  All clauses are units, and equality is present; the
% 1.80/2.00  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.80/2.00  
% 1.80/2.00     dependent: set(knuth_bendix).
% 1.80/2.00     dependent: set(anl_eq).
% 1.80/2.00     dependent: set(para_from).
% 1.80/2.00     dependent: set(para_into).
% 1.80/2.00     dependent: clear(para_from_right).
% 1.80/2.00     dependent: clear(para_into_right).
% 1.80/2.00     dependent: set(para_from_vars).
% 1.80/2.00     dependent: set(eq_units_both_ways).
% 1.80/2.00     dependent: set(dynamic_demod_all).
% 1.80/2.00     dependent: set(dynamic_demod).
% 1.80/2.00     dependent: set(order_eq).
% 1.80/2.00     dependent: set(back_demod).
% 1.80/2.00     dependent: set(lrpo).
% 1.80/2.00  
% 1.80/2.00  ------------> process usable:
% 1.80/2.00  ** KEPT (pick-wt=9): 2 [copy,1,flip.1] apply(fixed_pt,apply(strong_fixed_point,fixed_pt))!=apply(strong_fixed_point,fixed_pt).
% 1.80/2.00  
% 1.80/2.00  ------------> process sos:
% 1.80/2.00  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.80/2.00  ** KEPT (pick-wt=13): 4 [] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.80/2.00  ---> New Demodulator: 5 [new_demod,4] apply(apply(apply(b,A),B),C)=apply(A,apply(B,C)).
% 1.80/2.00  ** KEPT (pick-wt=11): 6 [] apply(apply(w1,A),B)=apply(apply(B,A),A).
% 1.80/2.00  ** KEPT (pick-wt=19): 8 [copy,7,flip.1] apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b)=strong_fixed_point.
% 1.80/2.00  ---> New Demodulator: 9 [new_demod,8] apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b)=strong_fixed_point.
% 1.80/2.00    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.80/2.00  >>>> Starting back demodulation with 5.
% 1.80/2.00  ** KEPT (pick-wt=11): 10 [copy,6,flip.1] apply(apply(A,B),B)=apply(apply(w1,B),A).
% 1.80/2.00  >>>> Starting back demodulation with 9.
% 1.80/2.00    Following clause subsumed by 6 during input processing: 0 [copy,10,flip.1] apply(apply(w1,A),B)=apply(apply(B,A),A).
% 1.80/2.00  
% 1.80/2.00  ======= end of input processing =======
% 1.80/2.00  
% 1.80/2.00  =========== start of search ===========
% 1.80/2.00  
% 1.80/2.00  
% 1.80/2.00  Resetting weight limit to 19.
% 1.80/2.00  
% 1.80/2.00  
% 1.80/2.00  Resetting weight limit to 19.
% 1.80/2.00  
% 1.80/2.00  sos_size=884
% 1.80/2.00  
% 1.80/2.00  -------- PROOF -------- 
% 1.80/2.00  
% 1.80/2.00  ----> UNIT CONFLICT at   0.19 sec ----> 1540 [binary,1538.1,2.1] $F.
% 1.80/2.00  
% 1.80/2.00  Length of proof is 12.  Level of proof is 6.
% 1.80/2.00  
% 1.80/2.00  ---------------- PROOF ----------------
% 1.80/2.00  % SZS status Unsatisfiable
% 1.80/2.00  % SZS output start Refutation
% See solution above
% 1.80/2.00  ------------ end of proof -------------
% 1.80/2.00  
% 1.80/2.00  
% 1.80/2.00  Search stopped by max_proofs option.
% 1.80/2.00  
% 1.80/2.00  
% 1.80/2.00  Search stopped by max_proofs option.
% 1.80/2.00  
% 1.80/2.00  ============ end of search ============
% 1.80/2.00  
% 1.80/2.00  -------------- statistics -------------
% 1.80/2.00  clauses given                130
% 1.80/2.00  clauses generated           8323
% 1.80/2.00  clauses kept                1106
% 1.80/2.00  clauses forward subsumed    1799
% 1.80/2.00  clauses back subsumed         12
% 1.80/2.00  Kbytes malloced             4882
% 1.80/2.00  
% 1.80/2.00  ----------- times (seconds) -----------
% 1.80/2.00  user CPU time          0.19          (0 hr, 0 min, 0 sec)
% 1.80/2.00  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.80/2.00  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.80/2.00  
% 1.80/2.00  That finishes the proof of the theorem.
% 1.80/2.00  
% 1.80/2.00  Process 11479 finished Wed Jul 27 02:32:20 2022
% 1.80/2.00  Otter interrupted
% 1.80/2.00  PROOF FOUND
%------------------------------------------------------------------------------