TSTP Solution File: HEN009-4 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : HEN009-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n011.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 12:57:59 EDT 2022

% Result   : Unsatisfiable 2.36s 2.54s
% Output   : Refutation 2.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   16 (  11 unt;   0 nHn;   6 RR)
%            Number of literals    :   22 (   6 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   26 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( divide(A,B) != zero
    | less_e_qual(A,B) ),
    file('HEN009-4.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ less_e_qual(A,B)
    | ~ less_e_qual(B,A)
    | A = B ),
    file('HEN009-4.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ less_e_qual(divide(A,B),C)
    | less_e_qual(divide(A,C),B) ),
    file('HEN009-4.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ less_e_qual(A,B)
    | less_e_qual(divide(C,B),divide(C,A)) ),
    file('HEN009-4.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ less_e_qual(A,B)
    | less_e_qual(divide(A,C),divide(B,C)) ),
    file('HEN009-4.p',unknown),
    [] ).

cnf(8,axiom,
    divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
    file('HEN009-4.p',unknown),
    [] ).

cnf(9,plain,
    divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
    [iquote('copy,8,flip.1')] ).

cnf(14,axiom,
    less_e_qual(A,identity),
    file('HEN009-4.p',unknown),
    [] ).

cnf(19,axiom,
    divide(A,A) = zero,
    file('HEN009-4.p',unknown),
    [] ).

cnf(25,plain,
    less_e_qual(divide(A,B),divide(identity,B)),
    inference(hyper,[status(thm)],[14,7]),
    [iquote('hyper,14,7')] ).

cnf(55,plain,
    less_e_qual(A,A),
    inference(hyper,[status(thm)],[19,2]),
    [iquote('hyper,19,2')] ).

cnf(59,plain,
    less_e_qual(divide(A,divide(A,B)),B),
    inference(hyper,[status(thm)],[55,5]),
    [iquote('hyper,55,5')] ).

cnf(94,plain,
    less_e_qual(divide(A,divide(identity,B)),B),
    inference(hyper,[status(thm)],[25,5]),
    [iquote('hyper,25,5')] ).

cnf(140,plain,
    less_e_qual(divide(A,B),divide(A,divide(C,divide(C,B)))),
    inference(hyper,[status(thm)],[59,6]),
    [iquote('hyper,59,6')] ).

cnf(2249,plain,
    divide(identity,divide(identity,divide(identity,A))) = divide(identity,A),
    inference(hyper,[status(thm)],[140,3,94]),
    [iquote('hyper,140,3,94')] ).

cnf(2251,plain,
    $false,
    inference(binary,[status(thm)],[2249,9]),
    [iquote('binary,2249.1,9.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : HEN009-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n011.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 08:55:40 EDT 2022
% 0.18/0.33  % CPUTime  : 
% 2.36/2.54  ----- Otter 3.3f, August 2004 -----
% 2.36/2.54  The process was started by sandbox2 on n011.cluster.edu,
% 2.36/2.54  Wed Jul 27 08:55:40 2022
% 2.36/2.54  The command was "./otter".  The process ID is 5082.
% 2.36/2.54  
% 2.36/2.54  set(prolog_style_variables).
% 2.36/2.54  set(auto).
% 2.36/2.54     dependent: set(auto1).
% 2.36/2.54     dependent: set(process_input).
% 2.36/2.54     dependent: clear(print_kept).
% 2.36/2.54     dependent: clear(print_new_demod).
% 2.36/2.54     dependent: clear(print_back_demod).
% 2.36/2.54     dependent: clear(print_back_sub).
% 2.36/2.54     dependent: set(control_memory).
% 2.36/2.54     dependent: assign(max_mem, 12000).
% 2.36/2.54     dependent: assign(pick_given_ratio, 4).
% 2.36/2.54     dependent: assign(stats_level, 1).
% 2.36/2.54     dependent: assign(max_seconds, 10800).
% 2.36/2.54  clear(print_given).
% 2.36/2.54  
% 2.36/2.54  list(usable).
% 2.36/2.54  0 [] A=A.
% 2.36/2.54  0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 2.36/2.54  0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 2.36/2.54  0 [] less_e_qual(divide(X,Y),X).
% 2.36/2.54  0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 2.36/2.54  0 [] less_e_qual(zero,X).
% 2.36/2.54  0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 2.36/2.54  0 [] less_e_qual(X,identity).
% 2.36/2.54  0 [] divide(X,identity)=zero.
% 2.36/2.54  0 [] divide(zero,X)=zero.
% 2.36/2.54  0 [] divide(X,X)=zero.
% 2.36/2.54  0 [] divide(a,zero)=a.
% 2.36/2.54  0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 2.36/2.54  0 [] -less_e_qual(divide(X,Y),Z)|less_e_qual(divide(X,Z),Y).
% 2.36/2.54  0 [] -less_e_qual(X,Y)|less_e_qual(divide(Z,Y),divide(Z,X)).
% 2.36/2.54  0 [] -less_e_qual(X,Y)|less_e_qual(divide(X,Z),divide(Y,Z)).
% 2.36/2.54  0 [] divide(identity,a)!=divide(identity,divide(identity,divide(identity,a))).
% 2.36/2.54  end_of_list.
% 2.36/2.54  
% 2.36/2.54  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.36/2.54  
% 2.36/2.54  This is a Horn set with equality.  The strategy will be
% 2.36/2.54  Knuth-Bendix and hyper_res, with positive clauses in
% 2.36/2.54  sos and nonpositive clauses in usable.
% 2.36/2.54  
% 2.36/2.54     dependent: set(knuth_bendix).
% 2.36/2.54     dependent: set(anl_eq).
% 2.36/2.54     dependent: set(para_from).
% 2.36/2.54     dependent: set(para_into).
% 2.36/2.54     dependent: clear(para_from_right).
% 2.36/2.54     dependent: clear(para_into_right).
% 2.36/2.54     dependent: set(para_from_vars).
% 2.36/2.54     dependent: set(eq_units_both_ways).
% 2.36/2.54     dependent: set(dynamic_demod_all).
% 2.36/2.54     dependent: set(dynamic_demod).
% 2.36/2.54     dependent: set(order_eq).
% 2.36/2.54     dependent: set(back_demod).
% 2.36/2.54     dependent: set(lrpo).
% 2.36/2.54     dependent: set(hyper_res).
% 2.36/2.54     dependent: clear(order_hyper).
% 2.36/2.54  
% 2.36/2.54  ------------> process usable:
% 2.36/2.54  ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 2.36/2.54  ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 2.36/2.54  ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 2.36/2.54  ** KEPT (pick-wt=9): 4 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 2.36/2.54  ** KEPT (pick-wt=10): 5 [] -less_e_qual(divide(A,B),C)|less_e_qual(divide(A,C),B).
% 2.36/2.54  ** KEPT (pick-wt=10): 6 [] -less_e_qual(A,B)|less_e_qual(divide(C,B),divide(C,A)).
% 2.36/2.54  ** KEPT (pick-wt=10): 7 [] -less_e_qual(A,B)|less_e_qual(divide(A,C),divide(B,C)).
% 2.36/2.54  ** KEPT (pick-wt=11): 9 [copy,8,flip.1] divide(identity,divide(identity,divide(identity,a)))!=divide(identity,a).
% 2.36/2.54  
% 2.36/2.54  ------------> process sos:
% 2.36/2.54  ** KEPT (pick-wt=3): 10 [] A=A.
% 2.36/2.54  ** KEPT (pick-wt=5): 11 [] less_e_qual(divide(A,B),A).
% 2.36/2.54  ** KEPT (pick-wt=13): 12 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 2.36/2.54  ** KEPT (pick-wt=3): 13 [] less_e_qual(zero,A).
% 2.36/2.54  ** KEPT (pick-wt=3): 14 [] less_e_qual(A,identity).
% 2.36/2.54  ** KEPT (pick-wt=5): 15 [] divide(A,identity)=zero.
% 2.36/2.54  ---> New Demodulator: 16 [new_demod,15] divide(A,identity)=zero.
% 2.36/2.54  ** KEPT (pick-wt=5): 17 [] divide(zero,A)=zero.
% 2.36/2.54  ---> New Demodulator: 18 [new_demod,17] divide(zero,A)=zero.
% 2.36/2.54  ** KEPT (pick-wt=5): 19 [] divide(A,A)=zero.
% 2.36/2.54  ---> New Demodulator: 20 [new_demod,19] divide(A,A)=zero.
% 2.36/2.54  ** KEPT (pick-wt=5): 21 [] divide(a,zero)=a.
% 2.36/2.54  ---> New Demodulator: 22 [new_demod,21] divide(a,zero)=a.
% 2.36/2.54    Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 2.36/2.54  >>>> Starting back demodulation with 16.
% 2.36/2.54  >>>> Starting back demodulation with 18.
% 2.36/2.54  >>>> Starting back demodulation with 20.
% 2.36/2.54  >>>> Starting back demodulation with 22.
% 2.36/2.54  
% 2.36/2.54  ======= end of input processing =======
% 2.36/2.54  
% 2.36/2.54  =========== start of search ===========
% 2.36/2.54  
% 2.36/2.54  -------- PROOF -------- 
% 2.36/2.54  
% 2.36/2.54  ----> UNIT CONFLICT at   0.43 sec ----> 2251 [binary,2249.1,9.1] $F.
% 2.36/2.54  
% 2.36/2.54  Length of proof is 7.  Level of proof is 4.
% 2.36/2.54  
% 2.36/2.54  ---------------- PROOF ----------------
% 2.36/2.54  % SZS status Unsatisfiable
% 2.36/2.54  % SZS output start Refutation
% See solution above
% 2.36/2.54  ------------ end of proof -------------
% 2.36/2.54  
% 2.36/2.54  
% 2.36/2.54  Search stopped by max_proofs option.
% 2.36/2.54  
% 2.36/2.54  
% 2.36/2.54  Search stopped by max_proofs option.
% 2.36/2.54  
% 2.36/2.54  ============ end of search ============
% 2.36/2.54  
% 2.36/2.54  -------------- statistics -------------
% 2.36/2.54  clauses given                149
% 2.36/2.54  clauses generated          11730
% 2.36/2.54  clauses kept                2193
% 2.36/2.54  clauses forward subsumed    9437
% 2.36/2.54  clauses back subsumed        204
% 2.36/2.54  Kbytes malloced             2929
% 2.36/2.54  
% 2.36/2.54  ----------- times (seconds) -----------
% 2.36/2.54  user CPU time          0.43          (0 hr, 0 min, 0 sec)
% 2.36/2.54  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.36/2.54  wall-clock time        3             (0 hr, 0 min, 3 sec)
% 2.36/2.54  
% 2.36/2.54  That finishes the proof of the theorem.
% 2.36/2.54  
% 2.36/2.54  Process 5082 finished Wed Jul 27 08:55:43 2022
% 2.36/2.54  Otter interrupted
% 2.36/2.54  PROOF FOUND
%------------------------------------------------------------------------------