TSTP Solution File: GRP528-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n009.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 12:57:11 EDT 2022

% Result   : Unsatisfiable 1.57s 1.77s
% Output   : Refutation 1.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   25 (  25 unt;   0 nHn;   3 RR)
%            Number of literals    :   25 (  24 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   49 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(a,b) != multiply(b,a),
    file('GRP528-1.p',unknown),
    [] ).

cnf(2,plain,
    multiply(b,a) != multiply(a,b),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
    [iquote('copy,1,flip.1')] ).

cnf(4,axiom,
    divide(A,divide(divide(A,B),divide(C,B))) = C,
    file('GRP528-1.p',unknown),
    [] ).

cnf(6,axiom,
    multiply(A,B) = divide(A,divide(divide(C,C),B)),
    file('GRP528-1.p',unknown),
    [] ).

cnf(7,axiom,
    inverse(A) = divide(divide(B,B),A),
    file('GRP528-1.p',unknown),
    [] ).

cnf(8,plain,
    divide(A,divide(divide(B,B),C)) = multiply(A,C),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
    [iquote('copy,6,flip.1')] ).

cnf(9,plain,
    divide(divide(A,A),B) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
    [iquote('copy,7,flip.1')] ).

cnf(11,plain,
    divide(inverse(divide(A,A)),B) = inverse(B),
    inference(para_into,[status(thm),theory(equality)],[9,9]),
    [iquote('para_into,9.1.1.1,9.1.1')] ).

cnf(34,plain,
    divide(A,inverse(divide(B,A))) = B,
    inference(para_into,[status(thm),theory(equality)],[4,9]),
    [iquote('para_into,4.1.1.2,9.1.1')] ).

cnf(44,plain,
    divide(inverse(divide(A,B)),inverse(A)) = B,
    inference(para_into,[status(thm),theory(equality)],[34,34]),
    [iquote('para_into,34.1.1.2.1,34.1.1')] ).

cnf(48,plain,
    divide(divide(divide(A,B),divide(C,B)),inverse(C)) = A,
    inference(para_into,[status(thm),theory(equality)],[34,4]),
    [iquote('para_into,34.1.1.2.1,4.1.1')] ).

cnf(56,plain,
    inverse(inverse(divide(A,divide(B,B)))) = A,
    inference(para_into,[status(thm),theory(equality)],[34,9]),
    [iquote('para_into,34.1.1,9.1.1')] ).

cnf(67,plain,
    inverse(divide(A,B)) = divide(inverse(A),inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[44,34])]),
    [iquote('para_into,44.1.1.1.1,34.1.1,flip.1')] ).

cnf(82,plain,
    inverse(inverse(A)) = A,
    inference(para_into,[status(thm),theory(equality)],[44,11]),
    [iquote('para_into,44.1.1,11.1.1')] ).

cnf(89,plain,
    divide(A,divide(B,B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),67,67,67,82,67,82,82]),
    [iquote('back_demod,56,demod,67,67,67,82,67,82,82')] ).

cnf(106,plain,
    divide(divide(A,A),inverse(B)) = B,
    inference(para_into,[status(thm),theory(equality)],[82,7]),
    [iquote('para_into,81.1.1,7.1.1')] ).

cnf(107,plain,
    divide(A,divide(A,B)) = B,
    inference(para_from,[status(thm),theory(equality)],[89,4]),
    [iquote('para_from,89.1.1,4.1.1.2')] ).

cnf(113,plain,
    divide(divide(A,B),divide(C,B)) = divide(A,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[107,4])]),
    [iquote('para_into,107.1.1.2,4.1.1,flip.1')] ).

cnf(116,plain,
    divide(divide(A,B),inverse(B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),113]),
    [iquote('back_demod,48,demod,113')] ).

cnf(130,plain,
    multiply(A,divide(divide(B,B),C)) = divide(A,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,107])]),
    [iquote('para_into,8.1.1.2,107.1.1,flip.1')] ).

cnf(147,plain,
    divide(multiply(A,B),B) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,116]),67,67,106]),
    [iquote('para_from,8.1.1,116.1.1.1,demod,67,67,106')] ).

cnf(156,plain,
    multiply(divide(A,B),B) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[147,8]),130]),
    [iquote('para_into,147.1.1,8.1.1,demod,130')] ).

cnf(158,plain,
    divide(multiply(A,B),A) = B,
    inference(para_from,[status(thm),theory(equality)],[147,107]),
    [iquote('para_from,147.1.1,107.1.1.2')] ).

cnf(168,plain,
    multiply(A,B) = multiply(B,A),
    inference(para_from,[status(thm),theory(equality)],[158,156]),
    [iquote('para_from,158.1.1,156.1.1.1')] ).

cnf(169,plain,
    $false,
    inference(binary,[status(thm)],[168,2]),
    [iquote('binary,168.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP528-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Jul 27 05:21:51 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 1.57/1.77  ----- Otter 3.3f, August 2004 -----
% 1.57/1.77  The process was started by sandbox2 on n009.cluster.edu,
% 1.57/1.77  Wed Jul 27 05:21:51 2022
% 1.57/1.77  The command was "./otter".  The process ID is 21254.
% 1.57/1.77  
% 1.57/1.77  set(prolog_style_variables).
% 1.57/1.77  set(auto).
% 1.57/1.77     dependent: set(auto1).
% 1.57/1.77     dependent: set(process_input).
% 1.57/1.77     dependent: clear(print_kept).
% 1.57/1.77     dependent: clear(print_new_demod).
% 1.57/1.77     dependent: clear(print_back_demod).
% 1.57/1.77     dependent: clear(print_back_sub).
% 1.57/1.77     dependent: set(control_memory).
% 1.57/1.77     dependent: assign(max_mem, 12000).
% 1.57/1.77     dependent: assign(pick_given_ratio, 4).
% 1.57/1.77     dependent: assign(stats_level, 1).
% 1.57/1.77     dependent: assign(max_seconds, 10800).
% 1.57/1.77  clear(print_given).
% 1.57/1.77  
% 1.57/1.77  list(usable).
% 1.57/1.77  0 [] A=A.
% 1.57/1.77  0 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.57/1.77  0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.57/1.77  0 [] inverse(A)=divide(divide(B,B),A).
% 1.57/1.77  0 [] multiply(a,b)!=multiply(b,a).
% 1.57/1.77  end_of_list.
% 1.57/1.77  
% 1.57/1.77  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.57/1.77  
% 1.57/1.77  All clauses are units, and equality is present; the
% 1.57/1.77  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.57/1.77  
% 1.57/1.77     dependent: set(knuth_bendix).
% 1.57/1.77     dependent: set(anl_eq).
% 1.57/1.77     dependent: set(para_from).
% 1.57/1.77     dependent: set(para_into).
% 1.57/1.77     dependent: clear(para_from_right).
% 1.57/1.77     dependent: clear(para_into_right).
% 1.57/1.77     dependent: set(para_from_vars).
% 1.57/1.77     dependent: set(eq_units_both_ways).
% 1.57/1.77     dependent: set(dynamic_demod_all).
% 1.57/1.77     dependent: set(dynamic_demod).
% 1.57/1.77     dependent: set(order_eq).
% 1.57/1.77     dependent: set(back_demod).
% 1.57/1.77     dependent: set(lrpo).
% 1.57/1.77  
% 1.57/1.77  ------------> process usable:
% 1.57/1.77  ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.57/1.77  
% 1.57/1.77  ------------> process sos:
% 1.57/1.77  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.57/1.77  ** KEPT (pick-wt=11): 4 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.57/1.77  ---> New Demodulator: 5 [new_demod,4] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.57/1.77  ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.57/1.77  ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.57/1.77    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.57/1.77  >>>> Starting back demodulation with 5.
% 1.57/1.77  ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.57/1.77  ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.57/1.77    Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.57/1.77    Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.57/1.77  
% 1.57/1.77  ======= end of input processing =======
% 1.57/1.77  
% 1.57/1.77  =========== start of search ===========
% 1.57/1.77  
% 1.57/1.77  -------- PROOF -------- 
% 1.57/1.77  
% 1.57/1.77  ----> UNIT CONFLICT at   0.00 sec ----> 169 [binary,168.1,2.1] $F.
% 1.57/1.77  
% 1.57/1.77  Length of proof is 20.  Level of proof is 11.
% 1.57/1.77  
% 1.57/1.77  ---------------- PROOF ----------------
% 1.57/1.77  % SZS status Unsatisfiable
% 1.57/1.77  % SZS output start Refutation
% See solution above
% 1.57/1.77  ------------ end of proof -------------
% 1.57/1.77  
% 1.57/1.77  
% 1.57/1.77  Search stopped by max_proofs option.
% 1.57/1.77  
% 1.57/1.77  
% 1.57/1.77  Search stopped by max_proofs option.
% 1.57/1.77  
% 1.57/1.77  ============ end of search ============
% 1.57/1.77  
% 1.57/1.77  -------------- statistics -------------
% 1.57/1.77  clauses given                 22
% 1.57/1.77  clauses generated            252
% 1.57/1.77  clauses kept                 111
% 1.57/1.77  clauses forward subsumed     255
% 1.57/1.77  clauses back subsumed          2
% 1.57/1.77  Kbytes malloced             1953
% 1.57/1.77  
% 1.57/1.77  ----------- times (seconds) -----------
% 1.57/1.77  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.57/1.77  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.57/1.77  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.57/1.77  
% 1.57/1.77  That finishes the proof of the theorem.
% 1.57/1.77  
% 1.57/1.77  Process 21254 finished Wed Jul 27 05:21:52 2022
% 1.57/1.77  Otter interrupted
% 1.57/1.77  PROOF FOUND
%------------------------------------------------------------------------------