TSTP Solution File: HEN010-6 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : HEN010-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n010.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 12:58:00 EDT 2022

% Result   : Unsatisfiable 1.73s 1.93s
% Output   : Refutation 1.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   20 (  16 unt;   0 nHn;   6 RR)
%            Number of literals    :   25 (  10 equ;   7 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   :   30 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( divide(A,B) != zero
    | less_e_qual(A,B) ),
    file('HEN010-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ less_e_qual(A,B)
    | ~ less_e_qual(B,A)
    | A = B ),
    file('HEN010-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ less_e_qual(divide(A,B),C)
    | less_e_qual(divide(A,C),B) ),
    file('HEN010-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ less_e_qual(A,B)
    | less_e_qual(divide(C,B),divide(C,A)) ),
    file('HEN010-6.p',unknown),
    [] ).

cnf(7,axiom,
    divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
    file('HEN010-6.p',unknown),
    [] ).

cnf(8,plain,
    divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
    [iquote('copy,7,flip.1')] ).

cnf(10,axiom,
    less_e_qual(divide(A,B),A),
    file('HEN010-6.p',unknown),
    [] ).

cnf(11,axiom,
    less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)),
    file('HEN010-6.p',unknown),
    [] ).

cnf(12,axiom,
    less_e_qual(zero,A),
    file('HEN010-6.p',unknown),
    [] ).

cnf(19,axiom,
    divide(A,A) = zero,
    file('HEN010-6.p',unknown),
    [] ).

cnf(23,axiom,
    divide(identity,divide(identity,divide(identity,A))) = divide(identity,A),
    file('HEN010-6.p',unknown),
    [] ).

cnf(29,plain,
    less_e_qual(divide(A,B),divide(A,divide(B,C))),
    inference(hyper,[status(thm)],[10,5]),
    [iquote('hyper,10,5')] ).

cnf(52,plain,
    less_e_qual(A,A),
    inference(hyper,[status(thm)],[19,2]),
    [iquote('hyper,18,2')] ).

cnf(56,plain,
    less_e_qual(divide(A,divide(A,B)),B),
    inference(hyper,[status(thm)],[52,4]),
    [iquote('hyper,52,4')] ).

cnf(139,plain,
    divide(A,divide(A,zero)) = zero,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[56,3,12])]),
    [iquote('hyper,56,3,12,flip.1')] ).

cnf(157,plain,
    less_e_qual(A,divide(A,zero)),
    inference(hyper,[status(thm)],[139,2]),
    [iquote('hyper,139,2')] ).

cnf(174,plain,
    divide(A,zero) = A,
    inference(hyper,[status(thm)],[157,3,10]),
    [iquote('hyper,157,3,10')] ).

cnf(212,plain,
    divide(divide(A,B),B) = divide(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[29,3,11]),19,174])]),
    [iquote('hyper,29,3,11,demod,19,174,flip.1')] ).

cnf(805,plain,
    divide(divide(identity,A),divide(identity,divide(identity,A))) = divide(identity,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[212,23]),23]),
    [iquote('para_into,212.1.1.1,22.1.1,demod,23')] ).

cnf(807,plain,
    $false,
    inference(binary,[status(thm)],[805,8]),
    [iquote('binary,805.1,8.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : HEN010-6 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n010.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 08:51:10 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.73/1.93  ----- Otter 3.3f, August 2004 -----
% 1.73/1.93  The process was started by sandbox2 on n010.cluster.edu,
% 1.73/1.93  Wed Jul 27 08:51:10 2022
% 1.73/1.93  The command was "./otter".  The process ID is 15384.
% 1.73/1.93  
% 1.73/1.93  set(prolog_style_variables).
% 1.73/1.93  set(auto).
% 1.73/1.93     dependent: set(auto1).
% 1.73/1.93     dependent: set(process_input).
% 1.73/1.93     dependent: clear(print_kept).
% 1.73/1.93     dependent: clear(print_new_demod).
% 1.73/1.93     dependent: clear(print_back_demod).
% 1.73/1.93     dependent: clear(print_back_sub).
% 1.73/1.93     dependent: set(control_memory).
% 1.73/1.93     dependent: assign(max_mem, 12000).
% 1.73/1.93     dependent: assign(pick_given_ratio, 4).
% 1.73/1.93     dependent: assign(stats_level, 1).
% 1.73/1.93     dependent: assign(max_seconds, 10800).
% 1.73/1.93  clear(print_given).
% 1.73/1.93  
% 1.73/1.93  list(usable).
% 1.73/1.93  0 [] A=A.
% 1.73/1.93  0 [] -less_e_qual(X,Y)|divide(X,Y)=zero.
% 1.73/1.93  0 [] divide(X,Y)!=zero|less_e_qual(X,Y).
% 1.73/1.93  0 [] less_e_qual(divide(X,Y),X).
% 1.73/1.93  0 [] less_e_qual(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)).
% 1.73/1.93  0 [] less_e_qual(zero,X).
% 1.73/1.93  0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.73/1.93  0 [] less_e_qual(X,identity).
% 1.73/1.93  0 [] divide(X,identity)=zero.
% 1.73/1.93  0 [] divide(zero,X)=zero.
% 1.73/1.93  0 [] divide(X,X)=zero.
% 1.73/1.93  0 [] divide(a,zero)=a.
% 1.73/1.93  0 [] -less_e_qual(divide(X,Y),Z)|less_e_qual(divide(X,Z),Y).
% 1.73/1.93  0 [] -less_e_qual(X,Y)|less_e_qual(divide(Z,Y),divide(Z,X)).
% 1.73/1.93  0 [] -less_e_qual(X,Y)|less_e_qual(divide(X,Z),divide(Y,Z)).
% 1.73/1.93  0 [] divide(identity,divide(identity,divide(identity,X)))=divide(identity,X).
% 1.73/1.93  0 [] divide(identity,a)!=divide(divide(identity,a),divide(identity,divide(identity,a))).
% 1.73/1.93  end_of_list.
% 1.73/1.93  
% 1.73/1.93  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.73/1.93  
% 1.73/1.93  This is a Horn set with equality.  The strategy will be
% 1.73/1.93  Knuth-Bendix and hyper_res, with positive clauses in
% 1.73/1.93  sos and nonpositive clauses in usable.
% 1.73/1.93  
% 1.73/1.93     dependent: set(knuth_bendix).
% 1.73/1.93     dependent: set(anl_eq).
% 1.73/1.93     dependent: set(para_from).
% 1.73/1.93     dependent: set(para_into).
% 1.73/1.93     dependent: clear(para_from_right).
% 1.73/1.93     dependent: clear(para_into_right).
% 1.73/1.93     dependent: set(para_from_vars).
% 1.73/1.93     dependent: set(eq_units_both_ways).
% 1.73/1.93     dependent: set(dynamic_demod_all).
% 1.73/1.93     dependent: set(dynamic_demod).
% 1.73/1.93     dependent: set(order_eq).
% 1.73/1.93     dependent: set(back_demod).
% 1.73/1.93     dependent: set(lrpo).
% 1.73/1.93     dependent: set(hyper_res).
% 1.73/1.93     dependent: clear(order_hyper).
% 1.73/1.93  
% 1.73/1.93  ------------> process usable:
% 1.73/1.93  ** KEPT (pick-wt=8): 1 [] -less_e_qual(A,B)|divide(A,B)=zero.
% 1.73/1.93  ** KEPT (pick-wt=8): 2 [] divide(A,B)!=zero|less_e_qual(A,B).
% 1.73/1.93  ** KEPT (pick-wt=9): 3 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.73/1.93  ** KEPT (pick-wt=10): 4 [] -less_e_qual(divide(A,B),C)|less_e_qual(divide(A,C),B).
% 1.73/1.93  ** KEPT (pick-wt=10): 5 [] -less_e_qual(A,B)|less_e_qual(divide(C,B),divide(C,A)).
% 1.73/1.93  ** KEPT (pick-wt=10): 6 [] -less_e_qual(A,B)|less_e_qual(divide(A,C),divide(B,C)).
% 1.73/1.93  ** KEPT (pick-wt=13): 8 [copy,7,flip.1] divide(divide(identity,a),divide(identity,divide(identity,a)))!=divide(identity,a).
% 1.73/1.93  
% 1.73/1.93  ------------> process sos:
% 1.73/1.93  ** KEPT (pick-wt=3): 9 [] A=A.
% 1.73/1.93  ** KEPT (pick-wt=5): 10 [] less_e_qual(divide(A,B),A).
% 1.73/1.93  ** KEPT (pick-wt=13): 11 [] less_e_qual(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)).
% 1.73/1.93  ** KEPT (pick-wt=3): 12 [] less_e_qual(zero,A).
% 1.73/1.93  ** KEPT (pick-wt=3): 13 [] less_e_qual(A,identity).
% 1.73/1.93  ** KEPT (pick-wt=5): 14 [] divide(A,identity)=zero.
% 1.73/1.93  ---> New Demodulator: 15 [new_demod,14] divide(A,identity)=zero.
% 1.73/1.93  ** KEPT (pick-wt=5): 16 [] divide(zero,A)=zero.
% 1.73/1.93  ---> New Demodulator: 17 [new_demod,16] divide(zero,A)=zero.
% 1.73/1.93  ** KEPT (pick-wt=5): 18 [] divide(A,A)=zero.
% 1.73/1.93  ---> New Demodulator: 19 [new_demod,18] divide(A,A)=zero.
% 1.73/1.93  ** KEPT (pick-wt=5): 20 [] divide(a,zero)=a.
% 1.73/1.93  ---> New Demodulator: 21 [new_demod,20] divide(a,zero)=a.
% 1.73/1.93  ** KEPT (pick-wt=11): 22 [] divide(identity,divide(identity,divide(identity,A)))=divide(identity,A).
% 1.73/1.93  ---> New Demodulator: 23 [new_demod,22] divide(identity,divide(identity,divide(identity,A)))=divide(identity,A).
% 1.73/1.93    Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.73/1.93  >>>> Starting back demodulation with 15.
% 1.73/1.93  >>>> Starting back demodulation with 17.
% 1.73/1.93  >>>> Starting back demodulation with 19.
% 1.73/1.93  >>>> Starting back demodulation with 21.
% 1.73/1.93  >>>> Starting back demodulation with 23.
% 1.73/1.93  
% 1.73/1.93  ======= end of input processing =======
% 1.73/1.93  
% 1.73/1.93  =========== start of search ===========
% 1.73/1.93  
% 1.73/1.93  -------- PROOF -------- 
% 1.73/1.93  
% 1.73/1.93  ----> UNIT CONFLICT at   0.09 sec ----> 807 [binary,805.1,8.1] $F.
% 1.73/1.93  
% 1.73/1.93  Length of proof is 9.  Level of proof is 7.
% 1.73/1.93  
% 1.73/1.93  ---------------- PROOF ----------------
% 1.73/1.93  % SZS status Unsatisfiable
% 1.73/1.93  % SZS output start Refutation
% See solution above
% 1.73/1.93  ------------ end of proof -------------
% 1.73/1.93  
% 1.73/1.93  
% 1.73/1.93  Search stopped by max_proofs option.
% 1.73/1.93  
% 1.73/1.93  
% 1.73/1.93  Search stopped by max_proofs option.
% 1.73/1.93  
% 1.73/1.93  ============ end of search ============
% 1.73/1.93  
% 1.73/1.93  -------------- statistics -------------
% 1.73/1.93  clauses given                 77
% 1.73/1.93  clauses generated           3100
% 1.73/1.93  clauses kept                 764
% 1.73/1.93  clauses forward subsumed    2346
% 1.73/1.93  clauses back subsumed        120
% 1.73/1.93  Kbytes malloced             1953
% 1.73/1.93  
% 1.73/1.93  ----------- times (seconds) -----------
% 1.73/1.93  user CPU time          0.09          (0 hr, 0 min, 0 sec)
% 1.73/1.93  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.73/1.93  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.73/1.93  
% 1.73/1.93  That finishes the proof of the theorem.
% 1.73/1.93  
% 1.73/1.93  Process 15384 finished Wed Jul 27 08:51:11 2022
% 1.73/1.93  Otter interrupted
% 1.73/1.93  PROOF FOUND
%------------------------------------------------------------------------------