TSTP Solution File: LAT035-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n026.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 13:01:50 EDT 2022

% Result   : Unsatisfiable 1.85s 2.07s
% Output   : Refutation 1.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    6
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   5 RR)
%            Number of literals    :   10 (   9 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :    5 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb)))
    | f(k(n0)) != n0 ),
    file('LAT035-1.p',unknown),
    [] ).

cnf(3,axiom,
    A = A,
    file('LAT035-1.p',unknown),
    [] ).

cnf(27,axiom,
    k(join(A,B)) = meet(k(A),k(B)),
    file('LAT035-1.p',unknown),
    [] ).

cnf(31,axiom,
    k(n0) = n1,
    file('LAT035-1.p',unknown),
    [] ).

cnf(35,axiom,
    f(meet(A,B)) = join(f(A),f(B)),
    file('LAT035-1.p',unknown),
    [] ).

cnf(37,axiom,
    f(n1) = n0,
    file('LAT035-1.p',unknown),
    [] ).

cnf(38,plain,
    ( join(f(k(aa)),f(k(bb))) != join(f(k(aa)),f(k(bb)))
    | n0 != n0 ),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),27,35,31,37]),
    [iquote('back_demod,2,demod,27,35,31,37')] ).

cnf(274,plain,
    $false,
    inference(hyper,[status(thm)],[38,3,3]),
    [iquote('hyper,38,3,3')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n026.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 08:40:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.85/2.06  ----- Otter 3.3f, August 2004 -----
% 1.85/2.06  The process was started by sandbox2 on n026.cluster.edu,
% 1.85/2.06  Wed Jul 27 08:40:09 2022
% 1.85/2.06  The command was "./otter".  The process ID is 14197.
% 1.85/2.06  
% 1.85/2.06  set(prolog_style_variables).
% 1.85/2.06  set(auto).
% 1.85/2.06     dependent: set(auto1).
% 1.85/2.06     dependent: set(process_input).
% 1.85/2.06     dependent: clear(print_kept).
% 1.85/2.06     dependent: clear(print_new_demod).
% 1.85/2.06     dependent: clear(print_back_demod).
% 1.85/2.06     dependent: clear(print_back_sub).
% 1.85/2.06     dependent: set(control_memory).
% 1.85/2.06     dependent: assign(max_mem, 12000).
% 1.85/2.06     dependent: assign(pick_given_ratio, 4).
% 1.85/2.06     dependent: assign(stats_level, 1).
% 1.85/2.06     dependent: assign(max_seconds, 10800).
% 1.85/2.06  clear(print_given).
% 1.85/2.06  
% 1.85/2.06  list(usable).
% 1.85/2.06  0 [] A=A.
% 1.85/2.06  0 [] meet(X,X)=X.
% 1.85/2.06  0 [] join(X,X)=X.
% 1.85/2.06  0 [] meet(X,join(X,Y))=X.
% 1.85/2.06  0 [] join(X,meet(X,Y))=X.
% 1.85/2.06  0 [] meet(X,Y)=meet(Y,X).
% 1.85/2.06  0 [] join(X,Y)=join(Y,X).
% 1.85/2.06  0 [] meet(meet(X,Y),Z)=meet(X,meet(Y,Z)).
% 1.85/2.06  0 [] join(join(X,Y),Z)=join(X,join(Y,Z)).
% 1.85/2.06  0 [] meet(X,n0)=n0.
% 1.85/2.06  0 [] join(X,n0)=X.
% 1.85/2.06  0 [] meet(X,n1)=X.
% 1.85/2.06  0 [] join(X,n1)=n1.
% 1.85/2.06  0 [] meet(X,Z)!=X|meet(Z,join(X,Y))=join(X,meet(Y,Z)).
% 1.85/2.06  0 [] k(join(U,V))=meet(k(U),k(V)).
% 1.85/2.06  0 [] k(meet(U,V))=join(k(U),k(V)).
% 1.85/2.06  0 [] k(n0)=n1.
% 1.85/2.06  0 [] k(n1)=n0.
% 1.85/2.06  0 [] f(meet(U,V))=join(f(U),f(V)).
% 1.85/2.06  0 [] f(n1)=n0.
% 1.85/2.06  0 [] f(k(join(aa,bb)))!=join(f(k(aa)),f(k(bb)))|f(k(n0))!=n0.
% 1.85/2.06  end_of_list.
% 1.85/2.06  
% 1.85/2.06  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.85/2.06  
% 1.85/2.06  This is a Horn set with equality.  The strategy will be
% 1.85/2.06  Knuth-Bendix and hyper_res, with positive clauses in
% 1.85/2.06  sos and nonpositive clauses in usable.
% 1.85/2.06  
% 1.85/2.06     dependent: set(knuth_bendix).
% 1.85/2.06     dependent: set(anl_eq).
% 1.85/2.06     dependent: set(para_from).
% 1.85/2.06     dependent: set(para_into).
% 1.85/2.06     dependent: clear(para_from_right).
% 1.85/2.06     dependent: clear(para_into_right).
% 1.85/2.06     dependent: set(para_from_vars).
% 1.85/2.06     dependent: set(eq_units_both_ways).
% 1.85/2.06     dependent: set(dynamic_demod_all).
% 1.85/2.06     dependent: set(dynamic_demod).
% 1.85/2.06     dependent: set(order_eq).
% 1.85/2.06     dependent: set(back_demod).
% 1.85/2.06     dependent: set(lrpo).
% 1.85/2.06     dependent: set(hyper_res).
% 1.85/2.06     dependent: clear(order_hyper).
% 1.85/2.06  
% 1.85/2.06  ------------> process usable:
% 1.85/2.06  ** KEPT (pick-wt=16): 1 [] meet(A,B)!=A|meet(B,join(A,C))=join(A,meet(C,B)).
% 1.85/2.06  ** KEPT (pick-wt=18): 2 [] f(k(join(aa,bb)))!=join(f(k(aa)),f(k(bb)))|f(k(n0))!=n0.
% 1.85/2.06  
% 1.85/2.06  ------------> process sos:
% 1.85/2.06  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.85/2.06  ** KEPT (pick-wt=5): 4 [] meet(A,A)=A.
% 1.85/2.06  ---> New Demodulator: 5 [new_demod,4] meet(A,A)=A.
% 1.85/2.06  ** KEPT (pick-wt=5): 6 [] join(A,A)=A.
% 1.85/2.06  ---> New Demodulator: 7 [new_demod,6] join(A,A)=A.
% 1.85/2.06  ** KEPT (pick-wt=7): 8 [] meet(A,join(A,B))=A.
% 1.85/2.06  ---> New Demodulator: 9 [new_demod,8] meet(A,join(A,B))=A.
% 1.85/2.06  ** KEPT (pick-wt=7): 10 [] join(A,meet(A,B))=A.
% 1.85/2.06  ---> New Demodulator: 11 [new_demod,10] join(A,meet(A,B))=A.
% 1.85/2.06  ** KEPT (pick-wt=7): 12 [] meet(A,B)=meet(B,A).
% 1.85/2.06  ** KEPT (pick-wt=7): 13 [] join(A,B)=join(B,A).
% 1.85/2.06  ** KEPT (pick-wt=11): 14 [] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.85/2.06  ---> New Demodulator: 15 [new_demod,14] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.85/2.06  ** KEPT (pick-wt=11): 16 [] join(join(A,B),C)=join(A,join(B,C)).
% 1.85/2.06  ---> New Demodulator: 17 [new_demod,16] join(join(A,B),C)=join(A,join(B,C)).
% 1.85/2.06  ** KEPT (pick-wt=5): 18 [] meet(A,n0)=n0.
% 1.85/2.06  ---> New Demodulator: 19 [new_demod,18] meet(A,n0)=n0.
% 1.85/2.06  ** KEPT (pick-wt=5): 20 [] join(A,n0)=A.
% 1.85/2.06  ---> New Demodulator: 21 [new_demod,20] join(A,n0)=A.
% 1.85/2.06  ** KEPT (pick-wt=5): 22 [] meet(A,n1)=A.
% 1.85/2.06  ---> New Demodulator: 23 [new_demod,22] meet(A,n1)=A.
% 1.85/2.06  ** KEPT (pick-wt=5): 24 [] join(A,n1)=n1.
% 1.85/2.06  ---> New Demodulator: 25 [new_demod,24] join(A,n1)=n1.
% 1.85/2.06  ** KEPT (pick-wt=10): 26 [] k(join(A,B))=meet(k(A),k(B)).
% 1.85/2.06  ---> New Demodulator: 27 [new_demod,26] k(join(A,B))=meet(k(A),k(B)).
% 1.85/2.06  ** KEPT (pick-wt=10): 28 [] k(meet(A,B))=join(k(A),k(B)).
% 1.85/2.06  ---> New Demodulator: 29 [new_demod,28] k(meet(A,B))=join(k(A),k(B)).
% 1.85/2.06  ** KEPT (pick-wt=4): 30 [] k(n0)=n1.
% 1.85/2.06  ---> New Demodulator: 31 [new_demod,30] k(n0)=n1.
% 1.85/2.06  ** KEPT (pick-wt=4): 32 [] k(n1)=n0.
% 1.85/2.06  ---> New Demodulator: 33 [new_demod,32] k(n1)=n0.
% 1.85/2.06  ** KEPT (pick-wt=10): 34 [] f(meet(A,B))=join(f(A),f(B)).
% 1.85/2.06  ---> New Demodulator: 35 [new_demod,34] f(meet(A,B))=join(f(A),f(B)).
% 1.85/2.06  ** KEPT (pick-wt=4): 36 [] f(n1)=n0.
% 1.85/2.06  ---> New Demodulator: 37 [new_demod,36] f(n1)=n0.
% 1.85/2.06    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.85/2.06  >>>> Starting back demodulation with 5.
% 1.85/2.07  >>>> Starting back demodulation with 7.
% 1.85/2.07  >>>> Starting back demodulation with 9.
% 1.85/2.07  >>>> Starting back demodulation with 11.
% 1.85/2.07    Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] meet(A,B)=meet(B,A).
% 1.85/2.07    Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] join(A,B)=join(B,A).
% 1.85/2.07  >>>> Starting back demodulation with 15.
% 1.85/2.07  >>>> Starting back demodulation with 17.
% 1.85/2.07  >>>> Starting back demodulation with 19.
% 1.85/2.07  >>>> Starting back demodulation with 21.
% 1.85/2.07  >>>> Starting back demodulation with 23.
% 1.85/2.07  >>>> Starting back demodulation with 25.
% 1.85/2.07  >>>> Starting back demodulation with 27.
% 1.85/2.07      >> back demodulating 2 with 27.
% 1.85/2.07  >>>> Starting back demodulation with 29.
% 1.85/2.07  >>>> Starting back demodulation with 31.
% 1.85/2.07  >>>> Starting back demodulation with 33.
% 1.85/2.07  >>>> Starting back demodulation with 35.
% 1.85/2.07  >>>> Starting back demodulation with 37.
% 1.85/2.07  
% 1.85/2.07  ======= end of input processing =======
% 1.85/2.07  
% 1.85/2.07  =========== start of search ===========
% 1.85/2.07  
% 1.85/2.07  -------- PROOF -------- 
% 1.85/2.07  
% 1.85/2.07  -----> EMPTY CLAUSE at   0.01 sec ----> 274 [hyper,38,3,3] $F.
% 1.85/2.07  
% 1.85/2.07  Length of proof is 1.  Level of proof is 1.
% 1.85/2.07  
% 1.85/2.07  ---------------- PROOF ----------------
% 1.85/2.07  % SZS status Unsatisfiable
% 1.85/2.07  % SZS output start Refutation
% See solution above
% 1.85/2.07  ------------ end of proof -------------
% 1.85/2.07  
% 1.85/2.07  
% 1.85/2.07  Search stopped by max_proofs option.
% 1.85/2.07  
% 1.85/2.07  
% 1.85/2.07  Search stopped by max_proofs option.
% 1.85/2.07  
% 1.85/2.07  ============ end of search ============
% 1.85/2.07  
% 1.85/2.07  -------------- statistics -------------
% 1.85/2.07  clauses given                 46
% 1.85/2.07  clauses generated           1205
% 1.85/2.07  clauses kept                 215
% 1.85/2.07  clauses forward subsumed     943
% 1.85/2.07  clauses back subsumed         12
% 1.85/2.07  Kbytes malloced             1953
% 1.85/2.07  
% 1.85/2.07  ----------- times (seconds) -----------
% 1.85/2.07  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.85/2.07  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.85/2.07  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.85/2.07  
% 1.85/2.07  That finishes the proof of the theorem.
% 1.85/2.07  
% 1.85/2.07  Process 14197 finished Wed Jul 27 08:40:11 2022
% 1.85/2.07  Otter interrupted
% 1.85/2.07  PROOF FOUND
%------------------------------------------------------------------------------