TSTP Solution File: HEN006-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : HEN006-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n006.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 12:57:56 EDT 2022

% Result   : Unsatisfiable 1.94s 2.12s
% Output   : Refutation 1.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   20 (  14 unt;   0 nHn;  17 RR)
%            Number of literals    :   32 (   2 equ;  13 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   25 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ less_e_qual(A,B)
    | quotient(A,B,zero) ),
    file('HEN006-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ quotient(A,B,zero)
    | less_e_qual(A,B) ),
    file('HEN006-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ quotient(A,B,C)
    | less_e_qual(C,A) ),
    file('HEN006-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ quotient(A,B,C)
    | ~ quotient(B,D,E)
    | ~ quotient(A,D,F)
    | ~ quotient(F,E,G)
    | ~ quotient(C,D,H)
    | less_e_qual(G,H) ),
    file('HEN006-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ less_e_qual(A,B)
    | ~ less_e_qual(B,A)
    | A = B ),
    file('HEN006-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ less_e_qual(A,B)
    | ~ less_e_qual(B,C)
    | less_e_qual(A,C) ),
    file('HEN006-2.p',unknown),
    [] ).

cnf(8,axiom,
    ~ less_e_qual(xQz,y),
    file('HEN006-2.p',unknown),
    [] ).

cnf(10,axiom,
    less_e_qual(zero,A),
    file('HEN006-2.p',unknown),
    [] ).

cnf(12,axiom,
    quotient(A,B,divide(A,B)),
    file('HEN006-2.p',unknown),
    [] ).

cnf(17,axiom,
    quotient(x,y,xQy),
    file('HEN006-2.p',unknown),
    [] ).

cnf(18,axiom,
    less_e_qual(xQy,z),
    file('HEN006-2.p',unknown),
    [] ).

cnf(19,axiom,
    quotient(x,z,xQz),
    file('HEN006-2.p',unknown),
    [] ).

cnf(24,plain,
    quotient(xQy,z,zero),
    inference(hyper,[status(thm)],[18,1]),
    [iquote('hyper,18,1')] ).

cnf(38,plain,
    less_e_qual(divide(A,B),A),
    inference(hyper,[status(thm)],[12,3]),
    [iquote('hyper,12,3')] ).

cnf(106,plain,
    less_e_qual(divide(xQz,divide(y,z)),zero),
    inference(hyper,[status(thm)],[24,4,17,12,19,12]),
    [iquote('hyper,24,4,17,12,19,12')] ).

cnf(325,plain,
    divide(xQz,divide(y,z)) = zero,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[106,5,10])]),
    [iquote('hyper,106,5,10,flip.1')] ).

cnf(582,plain,
    quotient(xQz,divide(y,z),zero),
    inference(para_from,[status(thm),theory(equality)],[325,12]),
    [iquote('para_from,325.1.1,12.1.3')] ).

cnf(592,plain,
    less_e_qual(xQz,divide(y,z)),
    inference(hyper,[status(thm)],[582,2]),
    [iquote('hyper,582,2')] ).

cnf(610,plain,
    less_e_qual(xQz,y),
    inference(hyper,[status(thm)],[592,7,38]),
    [iquote('hyper,592,7,38')] ).

cnf(611,plain,
    $false,
    inference(binary,[status(thm)],[610,8]),
    [iquote('binary,610.1,8.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : HEN006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.32  % Computer : n006.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Wed Jul 27 08:56:46 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.94/2.12  ----- Otter 3.3f, August 2004 -----
% 1.94/2.12  The process was started by sandbox2 on n006.cluster.edu,
% 1.94/2.12  Wed Jul 27 08:56:47 2022
% 1.94/2.12  The command was "./otter".  The process ID is 30104.
% 1.94/2.12  
% 1.94/2.12  set(prolog_style_variables).
% 1.94/2.12  set(auto).
% 1.94/2.12     dependent: set(auto1).
% 1.94/2.12     dependent: set(process_input).
% 1.94/2.12     dependent: clear(print_kept).
% 1.94/2.12     dependent: clear(print_new_demod).
% 1.94/2.12     dependent: clear(print_back_demod).
% 1.94/2.12     dependent: clear(print_back_sub).
% 1.94/2.12     dependent: set(control_memory).
% 1.94/2.12     dependent: assign(max_mem, 12000).
% 1.94/2.12     dependent: assign(pick_given_ratio, 4).
% 1.94/2.12     dependent: assign(stats_level, 1).
% 1.94/2.12     dependent: assign(max_seconds, 10800).
% 1.94/2.12  clear(print_given).
% 1.94/2.12  
% 1.94/2.12  list(usable).
% 1.94/2.12  0 [] A=A.
% 1.94/2.12  0 [] -less_e_qual(X,Y)|quotient(X,Y,zero).
% 1.94/2.12  0 [] -quotient(X,Y,zero)|less_e_qual(X,Y).
% 1.94/2.12  0 [] -quotient(X,Y,Z)|less_e_qual(Z,X).
% 1.94/2.12  0 [] -quotient(X,Y,V1)| -quotient(Y,Z,V2)| -quotient(X,Z,V3)| -quotient(V3,V2,V4)| -quotient(V1,Z,V5)|less_e_qual(V4,V5).
% 1.94/2.12  0 [] less_e_qual(zero,X).
% 1.94/2.12  0 [] -less_e_qual(X,Y)| -less_e_qual(Y,X)|X=Y.
% 1.94/2.12  0 [] less_e_qual(X,identity).
% 1.94/2.12  0 [] quotient(X,Y,divide(X,Y)).
% 1.94/2.12  0 [] -quotient(X,Y,Z)| -quotient(X,Y,W)|Z=W.
% 1.94/2.12  0 [] quotient(X,identity,zero).
% 1.94/2.12  0 [] quotient(zero,X,zero).
% 1.94/2.12  0 [] quotient(X,X,zero).
% 1.94/2.12  0 [] quotient(X,zero,X).
% 1.94/2.12  0 [] -less_e_qual(X,Y)| -less_e_qual(Y,Z)|less_e_qual(X,Z).
% 1.94/2.12  0 [] quotient(x,y,xQy).
% 1.94/2.12  0 [] less_e_qual(xQy,z).
% 1.94/2.12  0 [] quotient(x,z,xQz).
% 1.94/2.12  0 [] -less_e_qual(xQz,y).
% 1.94/2.12  end_of_list.
% 1.94/2.12  
% 1.94/2.12  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=6.
% 1.94/2.12  
% 1.94/2.12  This is a Horn set with equality.  The strategy will be
% 1.94/2.12  Knuth-Bendix and hyper_res, with positive clauses in
% 1.94/2.12  sos and nonpositive clauses in usable.
% 1.94/2.12  
% 1.94/2.12     dependent: set(knuth_bendix).
% 1.94/2.12     dependent: set(anl_eq).
% 1.94/2.12     dependent: set(para_from).
% 1.94/2.12     dependent: set(para_into).
% 1.94/2.12     dependent: clear(para_from_right).
% 1.94/2.12     dependent: clear(para_into_right).
% 1.94/2.12     dependent: set(para_from_vars).
% 1.94/2.12     dependent: set(eq_units_both_ways).
% 1.94/2.12     dependent: set(dynamic_demod_all).
% 1.94/2.12     dependent: set(dynamic_demod).
% 1.94/2.12     dependent: set(order_eq).
% 1.94/2.12     dependent: set(back_demod).
% 1.94/2.12     dependent: set(lrpo).
% 1.94/2.12     dependent: set(hyper_res).
% 1.94/2.12     dependent: clear(order_hyper).
% 1.94/2.12  
% 1.94/2.12  ------------> process usable:
% 1.94/2.12  ** KEPT (pick-wt=7): 1 [] -less_e_qual(A,B)|quotient(A,B,zero).
% 1.94/2.12  ** KEPT (pick-wt=7): 2 [] -quotient(A,B,zero)|less_e_qual(A,B).
% 1.94/2.12  ** KEPT (pick-wt=7): 3 [] -quotient(A,B,C)|less_e_qual(C,A).
% 1.94/2.12  ** KEPT (pick-wt=23): 4 [] -quotient(A,B,C)| -quotient(B,D,E)| -quotient(A,D,F)| -quotient(F,E,G)| -quotient(C,D,H)|less_e_qual(G,H).
% 1.94/2.12  ** KEPT (pick-wt=9): 5 [] -less_e_qual(A,B)| -less_e_qual(B,A)|A=B.
% 1.94/2.12  ** KEPT (pick-wt=11): 6 [] -quotient(A,B,C)| -quotient(A,B,D)|C=D.
% 1.94/2.12  ** KEPT (pick-wt=9): 7 [] -less_e_qual(A,B)| -less_e_qual(B,C)|less_e_qual(A,C).
% 1.94/2.12  ** KEPT (pick-wt=3): 8 [] -less_e_qual(xQz,y).
% 1.94/2.12  
% 1.94/2.12  ------------> process sos:
% 1.94/2.12  ** KEPT (pick-wt=3): 9 [] A=A.
% 1.94/2.12  ** KEPT (pick-wt=3): 10 [] less_e_qual(zero,A).
% 1.94/2.12  ** KEPT (pick-wt=3): 11 [] less_e_qual(A,identity).
% 1.94/2.12  ** KEPT (pick-wt=6): 12 [] quotient(A,B,divide(A,B)).
% 1.94/2.12  ** KEPT (pick-wt=4): 13 [] quotient(A,identity,zero).
% 1.94/2.12  ** KEPT (pick-wt=4): 14 [] quotient(zero,A,zero).
% 1.94/2.12  ** KEPT (pick-wt=4): 15 [] quotient(A,A,zero).
% 1.94/2.12  ** KEPT (pick-wt=4): 16 [] quotient(A,zero,A).
% 1.94/2.12  ** KEPT (pick-wt=4): 17 [] quotient(x,y,xQy).
% 1.94/2.12  ** KEPT (pick-wt=3): 18 [] less_e_qual(xQy,z).
% 1.94/2.12  ** KEPT (pick-wt=4): 19 [] quotient(x,z,xQz).
% 1.94/2.12    Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.94/2.12  
% 1.94/2.12  ======= end of input processing =======
% 1.94/2.12  
% 1.94/2.12  =========== start of search ===========
% 1.94/2.12  
% 1.94/2.12  -------- PROOF -------- 
% 1.94/2.12  
% 1.94/2.12  ----> UNIT CONFLICT at   0.04 sec ----> 611 [binary,610.1,8.1] $F.
% 1.94/2.12  
% 1.94/2.12  Length of proof is 7.  Level of proof is 6.
% 1.94/2.12  
% 1.94/2.12  ---------------- PROOF ----------------
% 1.94/2.12  % SZS status Unsatisfiable
% 1.94/2.12  % SZS output start Refutation
% See solution above
% 1.94/2.12  ------------ end of proof -------------
% 1.94/2.12  
% 1.94/2.12  
% 1.94/2.12  Search stopped by max_proofs option.
% 1.94/2.12  
% 1.94/2.12  
% 1.94/2.12  Search stopped by max_proofs option.
% 1.94/2.12  
% 1.94/2.12  ============ end of search ============
% 1.94/2.12  
% 1.94/2.12  -------------- statistics -------------
% 1.94/2.12  clauses given                 84
% 1.94/2.12  clauses generated           7517
% 1.94/2.12  clauses kept                 586
% 1.94/2.12  clauses forward subsumed    6989
% 1.94/2.12  clauses back subsumed         15
% 1.94/2.12  Kbytes malloced             1953
% 1.94/2.12  
% 1.94/2.12  ----------- times (seconds) -----------
% 1.94/2.12  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.94/2.12  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.94/2.12  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.94/2.12  
% 1.94/2.12  That finishes the proof of the theorem.
% 1.94/2.12  
% 1.94/2.12  Process 30104 finished Wed Jul 27 08:56:48 2022
% 1.94/2.12  Otter interrupted
% 1.94/2.12  PROOF FOUND
%------------------------------------------------------------------------------