TSTP Solution File: GRP600-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP600-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 12:57:20 EDT 2022

% Result   : Unsatisfiable 1.96s 2.14s
% Output   : Refutation 1.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    3
% 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    :    7 (   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   :   53 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(a,b) != multiply(b,a),
    file('GRP600-1.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,
    double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B))))) = C,
    file('GRP600-1.p',unknown),
    [] ).

cnf(6,axiom,
    multiply(A,B) = inverse(double_divide(B,A)),
    file('GRP600-1.p',unknown),
    [] ).

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

cnf(10,plain,
    double_divide(double_divide(A,B),multiply(multiply(B,inverse(C)),A)) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8]),
    [iquote('back_demod,4,demod,8,8')] ).

cnf(11,plain,
    double_divide(A,multiply(multiply(multiply(multiply(B,inverse(A)),C),inverse(D)),double_divide(C,B))) = D,
    inference(para_into,[status(thm),theory(equality)],[10,10]),
    [iquote('para_into,9.1.1.1,9.1.1')] ).

cnf(15,plain,
    multiply(multiply(multiply(A,inverse(B)),C),double_divide(C,A)) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[10,8])]),
    [iquote('para_from,9.1.1,7.1.1.1,flip.1')] ).

cnf(21,plain,
    multiply(multiply(multiply(multiply(multiply(A,inverse(B)),C),inverse(D)),double_divide(C,A)),B) = inverse(D),
    inference(para_into,[status(thm),theory(equality)],[15,10]),
    [iquote('para_into,15.1.1.2,9.1.1')] ).

cnf(89,plain,
    multiply(multiply(inverse(A),inverse(B)),A) = inverse(B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,21]),10]),
    [iquote('para_into,21.1.1.1.1,21.1.1,demod,10')] ).

cnf(109,plain,
    double_divide(A,multiply(inverse(A),inverse(B))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[21,11]),10]),
    [iquote('para_from,21.1.1,11.1.1.2.1,demod,10')] ).

cnf(117,plain,
    double_divide(double_divide(A,B),multiply(multiply(B,A),inverse(C))) = C,
    inference(para_into,[status(thm),theory(equality)],[109,8]),
    [iquote('para_into,109.1.1.2.1,7.1.1')] ).

cnf(163,plain,
    double_divide(double_divide(A,inverse(A)),inverse(B)) = B,
    inference(para_from,[status(thm),theory(equality)],[89,10]),
    [iquote('para_from,89.1.1,9.1.1.2')] ).

cnf(171,plain,
    double_divide(double_divide(A,inverse(A)),multiply(B,C)) = double_divide(C,B),
    inference(para_into,[status(thm),theory(equality)],[163,8]),
    [iquote('para_into,163.1.1.2,7.1.1')] ).

cnf(337,plain,
    double_divide(inverse(A),multiply(inverse(B),B)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[171,117])]),
    [iquote('para_into,171.1.1,117.1.1,flip.1')] ).

cnf(364,plain,
    double_divide(A,multiply(multiply(multiply(inverse(B),B),inverse(C)),inverse(A))) = C,
    inference(para_from,[status(thm),theory(equality)],[337,10]),
    [iquote('para_from,337.1.1,9.1.1.1')] ).

cnf(367,plain,
    multiply(multiply(inverse(A),A),inverse(B)) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[337,8])]),
    [iquote('para_from,337.1.1,7.1.1.1,flip.1')] ).

cnf(369,plain,
    double_divide(A,multiply(inverse(B),inverse(A))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[364]),367]),
    [iquote('back_demod,364,demod,367')] ).

cnf(387,plain,
    inverse(inverse(A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[369,337])]),
    [iquote('para_into,369.1.1,337.1.1,flip.1')] ).

cnf(585,plain,
    multiply(multiply(inverse(A),B),A) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[387,89]),387]),
    [iquote('para_from,386.1.1,89.1.1.1.2,demod,387')] ).

cnf(682,plain,
    double_divide(double_divide(A,B),A) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[585,117]),387]),
    [iquote('para_from,585.1.1,117.1.1.2,demod,387')] ).

cnf(702,plain,
    multiply(inverse(A),inverse(B)) = double_divide(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[682,369])]),
    [iquote('para_into,682.1.1.1,369.1.1,flip.1')] ).

cnf(711,plain,
    double_divide(A,B) = double_divide(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[682,109]),702]),
    [iquote('para_into,682.1.1.1,109.1.1,demod,702')] ).

cnf(931,plain,
    multiply(A,B) = multiply(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[711,8]),8]),
    [iquote('para_from,711.1.1,7.1.1.1,demod,8')] ).

cnf(932,plain,
    $false,
    inference(binary,[status(thm)],[931,2]),
    [iquote('binary,931.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP600-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12  % 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 05:17:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.96/2.14  ----- Otter 3.3f, August 2004 -----
% 1.96/2.14  The process was started by sandbox on n026.cluster.edu,
% 1.96/2.14  Wed Jul 27 05:17:24 2022
% 1.96/2.14  The command was "./otter".  The process ID is 21620.
% 1.96/2.14  
% 1.96/2.14  set(prolog_style_variables).
% 1.96/2.14  set(auto).
% 1.96/2.14     dependent: set(auto1).
% 1.96/2.14     dependent: set(process_input).
% 1.96/2.14     dependent: clear(print_kept).
% 1.96/2.14     dependent: clear(print_new_demod).
% 1.96/2.14     dependent: clear(print_back_demod).
% 1.96/2.14     dependent: clear(print_back_sub).
% 1.96/2.14     dependent: set(control_memory).
% 1.96/2.14     dependent: assign(max_mem, 12000).
% 1.96/2.14     dependent: assign(pick_given_ratio, 4).
% 1.96/2.14     dependent: assign(stats_level, 1).
% 1.96/2.14     dependent: assign(max_seconds, 10800).
% 1.96/2.14  clear(print_given).
% 1.96/2.14  
% 1.96/2.14  list(usable).
% 1.96/2.14  0 [] A=A.
% 1.96/2.14  0 [] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.96/2.14  0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.96/2.14  0 [] multiply(a,b)!=multiply(b,a).
% 1.96/2.14  end_of_list.
% 1.96/2.14  
% 1.96/2.14  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.96/2.14  
% 1.96/2.14  All clauses are units, and equality is present; the
% 1.96/2.14  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.96/2.14  
% 1.96/2.14     dependent: set(knuth_bendix).
% 1.96/2.14     dependent: set(anl_eq).
% 1.96/2.14     dependent: set(para_from).
% 1.96/2.14     dependent: set(para_into).
% 1.96/2.14     dependent: clear(para_from_right).
% 1.96/2.14     dependent: clear(para_into_right).
% 1.96/2.14     dependent: set(para_from_vars).
% 1.96/2.14     dependent: set(eq_units_both_ways).
% 1.96/2.14     dependent: set(dynamic_demod_all).
% 1.96/2.14     dependent: set(dynamic_demod).
% 1.96/2.14     dependent: set(order_eq).
% 1.96/2.14     dependent: set(back_demod).
% 1.96/2.14     dependent: set(lrpo).
% 1.96/2.14  
% 1.96/2.14  ------------> process usable:
% 1.96/2.14  ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.96/2.14  
% 1.96/2.14  ------------> process sos:
% 1.96/2.14  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.96/2.14  ** KEPT (pick-wt=14): 4 [] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.96/2.14  ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.96/2.14  ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.96/2.14  ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.96/2.14    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.96/2.14  >>>> Starting back demodulation with 5.
% 1.96/2.14  >>>> Starting back demodulation with 8.
% 1.96/2.14      >> back demodulating 4 with 8.
% 1.96/2.14  >>>> Starting back demodulation with 10.
% 1.96/2.14  
% 1.96/2.14  ======= end of input processing =======
% 1.96/2.14  
% 1.96/2.14  =========== start of search ===========
% 1.96/2.14  
% 1.96/2.14  
% 1.96/2.14  Resetting weight limit to 9.
% 1.96/2.14  
% 1.96/2.14  
% 1.96/2.14  Resetting weight limit to 9.
% 1.96/2.14  
% 1.96/2.14  sos_size=237
% 1.96/2.14  
% 1.96/2.14  -------- PROOF -------- 
% 1.96/2.14  
% 1.96/2.14  ----> UNIT CONFLICT at   0.04 sec ----> 932 [binary,931.1,2.1] $F.
% 1.96/2.14  
% 1.96/2.14  Length of proof is 21.  Level of proof is 16.
% 1.96/2.14  
% 1.96/2.14  ---------------- PROOF ----------------
% 1.96/2.14  % SZS status Unsatisfiable
% 1.96/2.14  % SZS output start Refutation
% See solution above
% 1.96/2.14  ------------ end of proof -------------
% 1.96/2.14  
% 1.96/2.14  
% 1.96/2.14  Search stopped by max_proofs option.
% 1.96/2.14  
% 1.96/2.14  
% 1.96/2.14  Search stopped by max_proofs option.
% 1.96/2.14  
% 1.96/2.14  ============ end of search ============
% 1.96/2.14  
% 1.96/2.14  -------------- statistics -------------
% 1.96/2.14  clauses given                 33
% 1.96/2.14  clauses generated            642
% 1.96/2.14  clauses kept                 540
% 1.96/2.14  clauses forward subsumed     521
% 1.96/2.14  clauses back subsumed          2
% 1.96/2.14  Kbytes malloced             4882
% 1.96/2.14  
% 1.96/2.14  ----------- times (seconds) -----------
% 1.96/2.14  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.96/2.14  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.96/2.14  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.96/2.14  
% 1.96/2.14  That finishes the proof of the theorem.
% 1.96/2.14  
% 1.96/2.14  Process 21620 finished Wed Jul 27 05:17:25 2022
% 1.96/2.14  Otter interrupted
% 1.96/2.14  PROOF FOUND
%------------------------------------------------------------------------------