TSTP Solution File: GRP548-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP548-1 : 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 12:57:13 EDT 2022

% Result   : Unsatisfiable 1.91s 2.09s
% Output   : Refutation 1.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   22 (  22 unt;   0 nHn;   5 RR)
%            Number of literals    :   22 (  21 equ;   4 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;   3 con; 0-2 aty)
%            Number of variables   :   34 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(a,b) != multiply(b,a),
    file('GRP548-1.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(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C,
    file('GRP548-1.p',unknown),
    [] ).

cnf(7,axiom,
    multiply(A,B) = divide(A,divide(identity,B)),
    file('GRP548-1.p',unknown),
    [] ).

cnf(10,axiom,
    identity = divide(A,A),
    file('GRP548-1.p',unknown),
    [] ).

cnf(12,plain,
    divide(A,A) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
    [iquote('copy,10,flip.1')] ).

cnf(13,plain,
    divide(a,divide(identity,b)) != divide(b,divide(identity,a)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),7,7])]),
    [iquote('back_demod,2,demod,7,7,flip.1')] ).

cnf(15,plain,
    divide(identity,divide(divide(A,B),A)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),12]),
    [iquote('para_into,4.1.1.1.2,11.1.1,demod,12')] ).

cnf(22,plain,
    divide(A,identity) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),15]),
    [iquote('para_into,4.1.1.2,11.1.1,demod,15')] ).

cnf(23,plain,
    divide(divide(identity,divide(divide(A,B),C)),B) = divide(C,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4]),22]),
    [iquote('para_into,4.1.1.2,4.1.1,demod,22')] ).

cnf(26,plain,
    divide(divide(identity,divide(identity,A)),divide(A,B)) = B,
    inference(para_from,[status(thm),theory(equality)],[22,4]),
    [iquote('para_from,21.1.1,4.1.1.2')] ).

cnf(32,plain,
    divide(divide(A,B),A) = divide(identity,B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,15]),22])]),
    [iquote('para_into,14.1.1.2.1,14.1.1,demod,22,flip.1')] ).

cnf(35,plain,
    divide(identity,divide(identity,A)) = A,
    inference(para_into,[status(thm),theory(equality)],[15,12]),
    [iquote('para_into,14.1.1.2.1,11.1.1')] ).

cnf(37,plain,
    divide(A,divide(A,B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),35]),
    [iquote('back_demod,26,demod,35')] ).

cnf(46,plain,
    divide(A,B) = divide(identity,divide(B,A)),
    inference(para_into,[status(thm),theory(equality)],[32,37]),
    [iquote('para_into,32.1.1.1,37.1.1')] ).

cnf(47,plain,
    divide(divide(identity,A),divide(B,A)) = divide(identity,B),
    inference(para_into,[status(thm),theory(equality)],[32,32]),
    [iquote('para_into,32.1.1.1,32.1.1')] ).

cnf(50,plain,
    divide(divide(A,B),divide(identity,B)) = A,
    inference(para_from,[status(thm),theory(equality)],[32,37]),
    [iquote('para_from,32.1.1,37.1.1.2')] ).

cnf(88,plain,
    divide(identity,divide(divide(identity,b),a)) != divide(b,divide(identity,a)),
    inference(para_from,[status(thm),theory(equality)],[46,13]),
    [iquote('para_from,46.1.1,13.1.1')] ).

cnf(103,plain,
    divide(divide(identity,divide(A,B)),divide(identity,C)) = divide(B,divide(A,C)),
    inference(para_into,[status(thm),theory(equality)],[23,50]),
    [iquote('para_into,23.1.1.1.2.1,50.1.1')] ).

cnf(140,plain,
    divide(divide(identity,A),divide(identity,B)) = divide(identity,divide(A,B)),
    inference(para_into,[status(thm),theory(equality)],[47,32]),
    [iquote('para_into,47.1.1.2,32.1.1')] ).

cnf(142,plain,
    divide(identity,divide(divide(A,B),C)) = divide(B,divide(A,C)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[103]),140]),
    [iquote('back_demod,103,demod,140')] ).

cnf(144,plain,
    $false,
    inference(binary,[status(thm)],[142,88]),
    [iquote('binary,142.1,88.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.14/0.33  % Computer : n026.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Wed Jul 27 05:42:39 EDT 2022
% 0.14/0.33  % CPUTime  : 
% 1.91/2.09  ----- Otter 3.3f, August 2004 -----
% 1.91/2.09  The process was started by sandbox on n026.cluster.edu,
% 1.91/2.09  Wed Jul 27 05:42:39 2022
% 1.91/2.09  The command was "./otter".  The process ID is 30629.
% 1.91/2.09  
% 1.91/2.09  set(prolog_style_variables).
% 1.91/2.09  set(auto).
% 1.91/2.09     dependent: set(auto1).
% 1.91/2.09     dependent: set(process_input).
% 1.91/2.09     dependent: clear(print_kept).
% 1.91/2.09     dependent: clear(print_new_demod).
% 1.91/2.09     dependent: clear(print_back_demod).
% 1.91/2.09     dependent: clear(print_back_sub).
% 1.91/2.09     dependent: set(control_memory).
% 1.91/2.09     dependent: assign(max_mem, 12000).
% 1.91/2.09     dependent: assign(pick_given_ratio, 4).
% 1.91/2.09     dependent: assign(stats_level, 1).
% 1.91/2.09     dependent: assign(max_seconds, 10800).
% 1.91/2.09  clear(print_given).
% 1.91/2.09  
% 1.91/2.09  list(usable).
% 1.91/2.09  0 [] A=A.
% 1.91/2.09  0 [] divide(divide(identity,divide(A,B)),divide(divide(B,C),A))=C.
% 1.91/2.09  0 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.91/2.09  0 [] inverse(A)=divide(identity,A).
% 1.91/2.09  0 [] identity=divide(A,A).
% 1.91/2.09  0 [] multiply(a,b)!=multiply(b,a).
% 1.91/2.09  end_of_list.
% 1.91/2.09  
% 1.91/2.09  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.91/2.09  
% 1.91/2.09  All clauses are units, and equality is present; the
% 1.91/2.09  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.91/2.09  
% 1.91/2.09     dependent: set(knuth_bendix).
% 1.91/2.09     dependent: set(anl_eq).
% 1.91/2.09     dependent: set(para_from).
% 1.91/2.09     dependent: set(para_into).
% 1.91/2.09     dependent: clear(para_from_right).
% 1.91/2.09     dependent: clear(para_into_right).
% 1.91/2.09     dependent: set(para_from_vars).
% 1.91/2.09     dependent: set(eq_units_both_ways).
% 1.91/2.09     dependent: set(dynamic_demod_all).
% 1.91/2.09     dependent: set(dynamic_demod).
% 1.91/2.09     dependent: set(order_eq).
% 1.91/2.09     dependent: set(back_demod).
% 1.91/2.09     dependent: set(lrpo).
% 1.91/2.09  
% 1.91/2.09  ------------> process usable:
% 1.91/2.09  ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.91/2.09  
% 1.91/2.09  ------------> process sos:
% 1.91/2.09  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.91/2.09  ** KEPT (pick-wt=13): 4 [] divide(divide(identity,divide(A,B)),divide(divide(B,C),A))=C.
% 1.91/2.09  ---> New Demodulator: 5 [new_demod,4] divide(divide(identity,divide(A,B)),divide(divide(B,C),A))=C.
% 1.91/2.09  ** KEPT (pick-wt=9): 6 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.91/2.09  ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=divide(A,divide(identity,B)).
% 1.91/2.09  ** KEPT (pick-wt=6): 8 [] inverse(A)=divide(identity,A).
% 1.91/2.09  ---> New Demodulator: 9 [new_demod,8] inverse(A)=divide(identity,A).
% 1.91/2.09  ** KEPT (pick-wt=5): 11 [copy,10,flip.1] divide(A,A)=identity.
% 1.91/2.09  ---> New Demodulator: 12 [new_demod,11] divide(A,A)=identity.
% 1.91/2.09    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.91/2.09  >>>> Starting back demodulation with 5.
% 1.91/2.09  >>>> Starting back demodulation with 7.
% 1.91/2.09      >> back demodulating 2 with 7.
% 1.91/2.09  >>>> Starting back demodulation with 9.
% 1.91/2.09  >>>> Starting back demodulation with 12.
% 1.91/2.09  
% 1.91/2.09  ======= end of input processing =======
% 1.91/2.09  
% 1.91/2.09  =========== start of search ===========
% 1.91/2.09  
% 1.91/2.09  -------- PROOF -------- 
% 1.91/2.09  
% 1.91/2.09  ----> UNIT CONFLICT at   0.01 sec ----> 144 [binary,142.1,88.1] $F.
% 1.91/2.09  
% 1.91/2.09  Length of proof is 17.  Level of proof is 8.
% 1.91/2.09  
% 1.91/2.09  ---------------- PROOF ----------------
% 1.91/2.09  % SZS status Unsatisfiable
% 1.91/2.09  % SZS output start Refutation
% See solution above
% 1.91/2.09  ------------ end of proof -------------
% 1.91/2.09  
% 1.91/2.09  
% 1.91/2.09  Search stopped by max_proofs option.
% 1.91/2.09  
% 1.91/2.09  
% 1.91/2.09  Search stopped by max_proofs option.
% 1.91/2.09  
% 1.91/2.09  ============ end of search ============
% 1.91/2.09  
% 1.91/2.09  -------------- statistics -------------
% 1.91/2.09  clauses given                 17
% 1.91/2.09  clauses generated            218
% 1.91/2.09  clauses kept                  88
% 1.91/2.09  clauses forward subsumed     193
% 1.91/2.09  clauses back subsumed          0
% 1.91/2.09  Kbytes malloced              976
% 1.91/2.09  
% 1.91/2.09  ----------- times (seconds) -----------
% 1.91/2.09  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.91/2.09  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.91/2.09  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.91/2.09  
% 1.91/2.09  That finishes the proof of the theorem.
% 1.91/2.09  
% 1.91/2.09  Process 30629 finished Wed Jul 27 05:42:40 2022
% 1.91/2.09  Otter interrupted
% 1.91/2.09  PROOF FOUND
%------------------------------------------------------------------------------