TSTP Solution File: GRP448-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP448-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n018.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 12:57:02 EDT 2022

% Result   : Unsatisfiable 1.79s 1.98s
% Output   : Refutation 1.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   28 (  28 unt;   0 nHn;   6 RR)
%            Number of literals    :   28 (  27 equ;   5 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(inverse(a1),a1) != multiply(inverse(b1),b1),
    file('GRP448-1.p',unknown),
    [] ).

cnf(2,plain,
    multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
    [iquote('copy,1,flip.1')] ).

cnf(4,axiom,
    divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C))) = B,
    file('GRP448-1.p',unknown),
    [] ).

cnf(6,axiom,
    multiply(A,B) = divide(A,divide(divide(C,C),B)),
    file('GRP448-1.p',unknown),
    [] ).

cnf(7,axiom,
    inverse(A) = divide(divide(B,B),A),
    file('GRP448-1.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,
    multiply(divide(divide(A,A),b1),b1) != multiply(inverse(a1),a1),
    inference(para_from,[status(thm),theory(equality)],[7,2]),
    [iquote('para_from,7.1.1,2.1.1.1')] ).

cnf(13,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(14,plain,
    inverse(A) = divide(inverse(divide(B,B)),A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
    [iquote('copy,13,flip.1')] ).

cnf(16,plain,
    divide(inverse(inverse(divide(A,A))),B) = inverse(B),
    inference(para_into,[status(thm),theory(equality)],[13,9]),
    [iquote('para_into,13.1.1.1.1,9.1.1')] ).

cnf(21,plain,
    divide(inverse(divide(A,A)),B) = divide(inverse(divide(C,C)),B),
    inference(para_into,[status(thm),theory(equality)],[14,14]),
    [iquote('para_into,14.1.1,14.1.1')] ).

cnf(31,plain,
    divide(A,divide(divide(inverse(B),C),divide(divide(divide(B,B),A),C))) = B,
    inference(para_into,[status(thm),theory(equality)],[4,9]),
    [iquote('para_into,4.1.1.2.1.1,9.1.1')] ).

cnf(89,plain,
    divide(A,inverse(B)) = multiply(A,B),
    inference(para_into,[status(thm),theory(equality)],[8,9]),
    [iquote('para_into,8.1.1.2,9.1.1')] ).

cnf(156,plain,
    inverse(inverse(A)) = multiply(divide(B,B),A),
    inference(para_into,[status(thm),theory(equality)],[89,9]),
    [iquote('para_into,89.1.1,9.1.1')] ).

cnf(160,plain,
    multiply(divide(A,A),B) = inverse(inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[156])]),
    [iquote('copy,156,flip.1')] ).

cnf(164,plain,
    divide(multiply(inverse(A),A),B) = inverse(B),
    inference(para_from,[status(thm),theory(equality)],[89,9]),
    [iquote('para_from,89.1.1,9.1.1.1')] ).

cnf(165,plain,
    divide(A,multiply(divide(B,B),C)) = multiply(A,inverse(C)),
    inference(para_from,[status(thm),theory(equality)],[89,8]),
    [iquote('para_from,89.1.1,8.1.1.2')] ).

cnf(204,plain,
    divide(divide(divide(A,A),b1),divide(divide(B,B),b1)) != multiply(inverse(a1),a1),
    inference(para_into,[status(thm),theory(equality)],[11,6]),
    [iquote('para_into,11.1.1,6.1.1')] ).

cnf(208,plain,
    multiply(inverse(a1),a1) != divide(divide(divide(A,A),b1),divide(divide(B,B),b1)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[204])]),
    [iquote('copy,204,flip.1')] ).

cnf(220,plain,
    divide(inverse(inverse(inverse(multiply(inverse(A),A)))),B) = inverse(B),
    inference(para_from,[status(thm),theory(equality)],[164,16]),
    [iquote('para_from,164.1.1,16.1.1.1.1.1')] ).

cnf(392,plain,
    divide(divide(A,A),multiply(divide(inverse(A),B),B)) = A,
    inference(para_into,[status(thm),theory(equality)],[31,8]),
    [iquote('para_into,31.1.1.2,8.1.1')] ).

cnf(402,plain,
    multiply(divide(A,A),inverse(inverse(A))) = A,
    inference(para_into,[status(thm),theory(equality)],[392,165]),
    [iquote('para_into,392.1.1,165.1.1')] ).

cnf(407,plain,
    inverse(multiply(divide(inverse(A),B),B)) = A,
    inference(para_into,[status(thm),theory(equality)],[392,9]),
    [iquote('para_into,392.1.1,9.1.1')] ).

cnf(429,plain,
    inverse(inverse(inverse(inverse(A)))) = A,
    inference(para_into,[status(thm),theory(equality)],[402,160]),
    [iquote('para_into,402.1.1,160.1.1')] ).

cnf(526,plain,
    divide(A,A) = divide(B,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[407,21]),407]),
    [iquote('para_into,406.1.1.1.1,21.1.1,demod,407')] ).

cnf(543,plain,
    multiply(inverse(A),A) = divide(B,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[526,220]),429]),
    [iquote('para_into,526.1.1,220.1.1,demod,429')] ).

cnf(544,plain,
    $false,
    inference(binary,[status(thm)],[543,208]),
    [iquote('binary,543.1,208.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP448-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n018.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 05:07:31 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.79/1.98  ----- Otter 3.3f, August 2004 -----
% 1.79/1.98  The process was started by sandbox on n018.cluster.edu,
% 1.79/1.98  Wed Jul 27 05:07:31 2022
% 1.79/1.98  The command was "./otter".  The process ID is 25178.
% 1.79/1.98  
% 1.79/1.98  set(prolog_style_variables).
% 1.79/1.98  set(auto).
% 1.79/1.98     dependent: set(auto1).
% 1.79/1.98     dependent: set(process_input).
% 1.79/1.98     dependent: clear(print_kept).
% 1.79/1.98     dependent: clear(print_new_demod).
% 1.79/1.98     dependent: clear(print_back_demod).
% 1.79/1.98     dependent: clear(print_back_sub).
% 1.79/1.98     dependent: set(control_memory).
% 1.79/1.98     dependent: assign(max_mem, 12000).
% 1.79/1.98     dependent: assign(pick_given_ratio, 4).
% 1.79/1.98     dependent: assign(stats_level, 1).
% 1.79/1.98     dependent: assign(max_seconds, 10800).
% 1.79/1.98  clear(print_given).
% 1.79/1.98  
% 1.79/1.98  list(usable).
% 1.79/1.98  0 [] A=A.
% 1.79/1.98  0 [] divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C)))=B.
% 1.79/1.98  0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.79/1.98  0 [] inverse(A)=divide(divide(B,B),A).
% 1.79/1.98  0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.79/1.98  end_of_list.
% 1.79/1.98  
% 1.79/1.98  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.79/1.98  
% 1.79/1.98  All clauses are units, and equality is present; the
% 1.79/1.98  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.79/1.98  
% 1.79/1.98     dependent: set(knuth_bendix).
% 1.79/1.98     dependent: set(anl_eq).
% 1.79/1.98     dependent: set(para_from).
% 1.79/1.98     dependent: set(para_into).
% 1.79/1.98     dependent: clear(para_from_right).
% 1.79/1.98     dependent: clear(para_into_right).
% 1.79/1.98     dependent: set(para_from_vars).
% 1.79/1.98     dependent: set(eq_units_both_ways).
% 1.79/1.98     dependent: set(dynamic_demod_all).
% 1.79/1.98     dependent: set(dynamic_demod).
% 1.79/1.98     dependent: set(order_eq).
% 1.79/1.98     dependent: set(back_demod).
% 1.79/1.98     dependent: set(lrpo).
% 1.79/1.98  
% 1.79/1.98  ------------> process usable:
% 1.79/1.98  ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.79/1.98  
% 1.79/1.98  ------------> process sos:
% 1.79/1.98  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.79/1.98  ** KEPT (pick-wt=19): 4 [] divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C)))=B.
% 1.79/1.98  ---> New Demodulator: 5 [new_demod,4] divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C)))=B.
% 1.79/1.98  ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.79/1.98  ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.79/1.98    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.79/1.98  >>>> Starting back demodulation with 5.
% 1.79/1.98  ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.79/1.98  ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.79/1.98    Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.79/1.98    Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.79/1.98  
% 1.79/1.98  ======= end of input processing =======
% 1.79/1.98  
% 1.79/1.98  =========== start of search ===========
% 1.79/1.98  
% 1.79/1.98  
% 1.79/1.98  Resetting weight limit to 12.
% 1.79/1.98  
% 1.79/1.98  
% 1.79/1.98  Resetting weight limit to 12.
% 1.79/1.98  
% 1.79/1.98  sos_size=311
% 1.79/1.98  
% 1.79/1.98  
% 1.79/1.98  Resetting weight limit to 10.
% 1.79/1.98  
% 1.79/1.98  
% 1.79/1.98  Resetting weight limit to 10.
% 1.79/1.98  
% 1.79/1.98  sos_size=314
% 1.79/1.98  
% 1.79/1.98  -------- PROOF -------- 
% 1.79/1.98  
% 1.79/1.98  ----> UNIT CONFLICT at   0.09 sec ----> 544 [binary,543.1,208.1] $F.
% 1.79/1.98  
% 1.79/1.98  Length of proof is 23.  Level of proof is 6.
% 1.79/1.98  
% 1.79/1.98  ---------------- PROOF ----------------
% 1.79/1.98  % SZS status Unsatisfiable
% 1.79/1.98  % SZS output start Refutation
% See solution above
% 1.79/1.98  ------------ end of proof -------------
% 1.79/1.98  
% 1.79/1.98  
% 1.79/1.98  Search stopped by max_proofs option.
% 1.79/1.98  
% 1.79/1.98  
% 1.79/1.98  Search stopped by max_proofs option.
% 1.79/1.98  
% 1.79/1.98  ============ end of search ============
% 1.79/1.98  
% 1.79/1.98  -------------- statistics -------------
% 1.79/1.98  clauses given                105
% 1.79/1.98  clauses generated           8362
% 1.79/1.98  clauses kept                 444
% 1.79/1.98  clauses forward subsumed     768
% 1.79/1.98  clauses back subsumed          0
% 1.79/1.98  Kbytes malloced             5859
% 1.79/1.98  
% 1.79/1.98  ----------- times (seconds) -----------
% 1.79/1.98  user CPU time          0.09          (0 hr, 0 min, 0 sec)
% 1.79/1.98  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 1.79/1.98  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.79/1.98  
% 1.79/1.98  That finishes the proof of the theorem.
% 1.79/1.98  
% 1.79/1.98  Process 25178 finished Wed Jul 27 05:07:32 2022
% 1.79/1.98  Otter interrupted
% 1.79/1.98  PROOF FOUND
%------------------------------------------------------------------------------