TSTP Solution File: GRP430-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP430-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n014.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 12:57:00 EDT 2022

% Result   : Unsatisfiable 1.74s 1.98s
% Output   : Refutation 1.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   46 (  46 unt;   0 nHn;   3 RR)
%            Number of literals    :   46 (  45 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  144 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
    file('GRP430-1.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(5,axiom,
    multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D,
    file('GRP430-1.p',unknown),
    [] ).

cnf(6,plain,
    multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),E))),multiply(multiply(multiply(F,inverse(F)),inverse(D)),A)))) = E,
    inference(para_into,[status(thm),theory(equality)],[5,5]),
    [iquote('para_into,4.1.1.2.1.2.1.2.1,4.1.1')] ).

cnf(8,plain,
    multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,D))),multiply(E,inverse(E))),multiply(C,A)))) = D,
    inference(para_into,[status(thm),theory(equality)],[5,5]),
    [iquote('para_into,4.1.1.2.1.2.1,4.1.1')] ).

cnf(14,plain,
    multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,B))),multiply(F,inverse(F))),A)))) = multiply(E,multiply(G,inverse(G))),
    inference(para_into,[status(thm),theory(equality)],[8,8]),
    [iquote('para_into,8.1.1.2.1.1.1,8.1.1')] ).

cnf(15,plain,
    multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))) = multiply(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))),multiply(F,inverse(F))),
    inference(para_into,[status(thm),theory(equality)],[8,5]),
    [iquote('para_into,8.1.1.2.1.1.1,4.1.1')] ).

cnf(32,plain,
    multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,D))),C))),multiply(E,inverse(E))) = D,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,8])]),
    [iquote('para_into,15.1.1,8.1.1,flip.1')] ).

cnf(56,plain,
    multiply(multiply(multiply(A,inverse(A)),inverse(inverse(B))),multiply(C,inverse(C))) = B,
    inference(para_into,[status(thm),theory(equality)],[32,32]),
    [iquote('para_into,32.1.1.1.2.1,32.1.1')] ).

cnf(90,plain,
    multiply(A,inverse(A)) = multiply(B,inverse(B)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,32]),5]),
    [iquote('para_into,6.1.1.2.1.1.1.2,32.1.1,demod,5')] ).

cnf(138,plain,
    multiply(A,inverse(multiply(multiply(multiply(B,inverse(B)),multiply(C,inverse(C))),multiply(D,A)))) = inverse(D),
    inference(para_from,[status(thm),theory(equality)],[90,8]),
    [iquote('para_from,90.1.1,8.1.1.2.1.1.1')] ).

cnf(145,plain,
    multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(multiply(D,inverse(D)),B))),E))),multiply(multiply(F,inverse(F)),A)))) = E,
    inference(para_from,[status(thm),theory(equality)],[90,6]),
    [iquote('para_from,90.1.1,6.1.1.2.1.2.1')] ).

cnf(153,plain,
    multiply(A,inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),A)))) = B,
    inference(para_from,[status(thm),theory(equality)],[90,5]),
    [iquote('para_from,90.1.1,4.1.1.2.1.2.1')] ).

cnf(160,plain,
    multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),A))),D)) = D,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[145]),153]),
    [iquote('back_demod,145,demod,153')] ).

cnf(308,plain,
    multiply(inverse(multiply(A,inverse(A))),multiply(multiply(B,inverse(B)),C)) = C,
    inference(para_into,[status(thm),theory(equality)],[160,90]),
    [iquote('para_into,160.1.1.2.1,90.1.1')] ).

cnf(315,plain,
    inverse(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),multiply(multiply(C,inverse(C)),inverse(inverse(D))))))) = D,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[160,56])]),
    [iquote('para_into,160.1.1,55.1.1,flip.1')] ).

cnf(324,plain,
    multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))) = inverse(multiply(C,inverse(C))),
    inference(para_into,[status(thm),theory(equality)],[308,90]),
    [iquote('para_into,308.1.1.2,90.1.1')] ).

cnf(334,plain,
    inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
    inference(para_into,[status(thm),theory(equality)],[324,324]),
    [iquote('para_into,324.1.1,324.1.1')] ).

cnf(343,plain,
    multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
    inference(para_from,[status(thm),theory(equality)],[334,90]),
    [iquote('para_from,334.1.1,90.1.1.2')] ).

cnf(485,plain,
    inverse(multiply(multiply(multiply(A,inverse(A)),inverse(B)),multiply(C,inverse(C)))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,56]),138,56]),
    [iquote('para_into,14.1.1.2.1.2.1.1.2.1,55.1.1,demod,138,56')] ).

cnf(487,plain,
    multiply(A,multiply(B,inverse(B))) = multiply(A,multiply(C,inverse(C))),
    inference(para_into,[status(thm),theory(equality)],[14,14]),
    [iquote('para_into,14.1.1,14.1.1')] ).

cnf(525,plain,
    inverse(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),multiply(multiply(C,inverse(C)),inverse(D))))))) = D,
    inference(para_into,[status(thm),theory(equality)],[485,160]),
    [iquote('para_into,484.1.1.1,160.1.1')] ).

cnf(527,plain,
    multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),B) = inverse(C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[485,32])]),
    [iquote('para_into,484.1.1.1,32.1.1,flip.1')] ).

cnf(549,plain,
    multiply(A,multiply(multiply(multiply(multiply(B,inverse(B)),inverse(C)),multiply(D,inverse(D))),C)) = multiply(A,multiply(E,inverse(E))),
    inference(para_from,[status(thm),theory(equality)],[485,487]),
    [iquote('para_from,484.1.1,487.1.1.2.2')] ).

cnf(564,plain,
    multiply(A,multiply(B,inverse(B))) = multiply(A,multiply(multiply(multiply(multiply(C,inverse(C)),inverse(D)),multiply(E,inverse(E))),D)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[549])]),
    [iquote('copy,549,flip.1')] ).

cnf(588,plain,
    multiply(multiply(multiply(A,inverse(A)),multiply(B,C)),D) = inverse(inverse(multiply(multiply(B,multiply(E,inverse(E))),multiply(C,D)))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[527,15]),485]),
    [iquote('para_into,527.1.1.1.2.1,15.1.1,demod,485')] ).

cnf(595,plain,
    multiply(multiply(A,inverse(A)),B) = inverse(inverse(B)),
    inference(para_into,[status(thm),theory(equality)],[527,343]),
    [iquote('para_into,527.1.1.1,343.1.1')] ).

cnf(609,plain,
    inverse(inverse(multiply(multiply(A,multiply(B,inverse(B))),multiply(C,D)))) = multiply(multiply(multiply(E,inverse(E)),multiply(A,C)),D),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[588])]),
    [iquote('copy,588,flip.1')] ).

cnf(625,plain,
    multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))) = B,
    inference(para_from,[status(thm),theory(equality)],[527,308]),
    [iquote('para_from,527.1.1,308.1.1.2')] ).

cnf(629,plain,
    multiply(inverse(inverse(inverse(inverse(A)))),multiply(B,inverse(B))) = A,
    inference(para_from,[status(thm),theory(equality)],[527,56]),
    [iquote('para_from,527.1.1,55.1.1.1')] ).

cnf(633,plain,
    multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(multiply(B,C)))),multiply(D,inverse(D))),multiply(B,A)))) = C,
    inference(para_from,[status(thm),theory(equality)],[527,8]),
    [iquote('para_from,527.1.1,8.1.1.2.1.1.1')] ).

cnf(640,plain,
    multiply(A,inverse(multiply(B,inverse(B)))) = A,
    inference(para_from,[status(thm),theory(equality)],[527,5]),
    [iquote('para_from,527.1.1,4.1.1.2.1.2')] ).

cnf(698,plain,
    multiply(A,inverse(A)) = inverse(multiply(B,inverse(B))),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[595,324]),629]),
    [iquote('para_from,595.1.1,324.1.1.1.1,demod,629')] ).

cnf(724,plain,
    multiply(A,multiply(B,inverse(B))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,56]),625]),
    [iquote('para_from,698.1.1,55.1.1.1.1,demod,625')] ).

cnf(728,plain,
    multiply(multiply(A,inverse(A)),inverse(multiply(B,C))) = multiply(inverse(C),inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,15]),724,640,724])]),
    [iquote('para_from,698.1.1,15.1.1.2.1.2,demod,724,640,724,flip.1')] ).

cnf(732,plain,
    multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(C,inverse(C))),A)))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,14]),724,724,724]),
    [iquote('para_from,698.1.1,14.1.1.2.1.2.1.1,demod,724,724,724')] ).

cnf(744,plain,
    multiply(A,multiply(inverse(A),B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,6]),728,640,732]),
    [iquote('para_from,698.1.1,6.1.1.2.1.2.1,demod,728,640,732')] ).

cnf(748,plain,
    inverse(multiply(multiply(A,inverse(A)),inverse(B))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,485]),640]),
    [iquote('para_from,698.1.1,484.1.1.1.2,demod,640')] ).

cnf(752,plain,
    multiply(A,inverse(multiply(B,multiply(C,A)))) = multiply(inverse(C),inverse(B)),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,15]),640,728,724]),
    [iquote('para_from,698.1.1,15.1.1.2.1.1.2,demod,640,728,724')] ).

cnf(754,plain,
    inverse(inverse(A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[525]),728,748,640]),
    [iquote('back_demod,525,demod,728,748,640')] ).

cnf(756,plain,
    multiply(multiply(A,inverse(A)),B) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[315]),754,728,640,754]),
    [iquote('back_demod,315,demod,754,728,640,754')] ).

cnf(769,plain,
    multiply(inverse(A),multiply(A,B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[633]),754,724,752,754]),
    [iquote('back_demod,633,demod,754,724,752,754')] ).

cnf(772,plain,
    multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[609]),724,754,756])]),
    [iquote('back_demod,609,demod,724,754,756,flip.1')] ).

cnf(775,plain,
    multiply(A,multiply(inverse(B),B)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[564]),724,772,744,724])]),
    [iquote('back_demod,564,demod,724,772,744,724,flip.1')] ).

cnf(794,plain,
    multiply(inverse(A),A) = multiply(inverse(B),B),
    inference(para_from,[status(thm),theory(equality)],[775,769]),
    [iquote('para_from,775.1.1,769.1.1.2')] ).

cnf(795,plain,
    $false,
    inference(binary,[status(thm)],[794,2]),
    [iquote('binary,794.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP430-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n014.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 05:31:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.74/1.97  ----- Otter 3.3f, August 2004 -----
% 1.74/1.97  The process was started by sandbox on n014.cluster.edu,
% 1.74/1.97  Wed Jul 27 05:31:39 2022
% 1.74/1.97  The command was "./otter".  The process ID is 16214.
% 1.74/1.97  
% 1.74/1.97  set(prolog_style_variables).
% 1.74/1.97  set(auto).
% 1.74/1.97     dependent: set(auto1).
% 1.74/1.97     dependent: set(process_input).
% 1.74/1.97     dependent: clear(print_kept).
% 1.74/1.97     dependent: clear(print_new_demod).
% 1.74/1.97     dependent: clear(print_back_demod).
% 1.74/1.97     dependent: clear(print_back_sub).
% 1.74/1.97     dependent: set(control_memory).
% 1.74/1.97     dependent: assign(max_mem, 12000).
% 1.74/1.97     dependent: assign(pick_given_ratio, 4).
% 1.74/1.97     dependent: assign(stats_level, 1).
% 1.74/1.97     dependent: assign(max_seconds, 10800).
% 1.74/1.97  clear(print_given).
% 1.74/1.97  
% 1.74/1.97  list(usable).
% 1.74/1.97  0 [] A=A.
% 1.74/1.97  0 [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.74/1.97  0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.74/1.97  end_of_list.
% 1.74/1.97  
% 1.74/1.97  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.97  
% 1.74/1.97  All clauses are units, and equality is present; the
% 1.74/1.97  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.74/1.97  
% 1.74/1.97     dependent: set(knuth_bendix).
% 1.74/1.97     dependent: set(anl_eq).
% 1.74/1.97     dependent: set(para_from).
% 1.74/1.97     dependent: set(para_into).
% 1.74/1.97     dependent: clear(para_from_right).
% 1.74/1.97     dependent: clear(para_into_right).
% 1.74/1.97     dependent: set(para_from_vars).
% 1.74/1.97     dependent: set(eq_units_both_ways).
% 1.74/1.97     dependent: set(dynamic_demod_all).
% 1.74/1.97     dependent: set(dynamic_demod).
% 1.74/1.97     dependent: set(order_eq).
% 1.74/1.97     dependent: set(back_demod).
% 1.74/1.97     dependent: set(lrpo).
% 1.74/1.97  
% 1.74/1.97  ------------> process usable:
% 1.74/1.97  ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.74/1.97  
% 1.74/1.97  ------------> process sos:
% 1.74/1.97  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.74/1.97  ** KEPT (pick-wt=18): 4 [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.74/1.97  ---> New Demodulator: 5 [new_demod,4] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.74/1.97    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.74/1.97  >>>> Starting back demodulation with 5.
% 1.74/1.97  
% 1.74/1.97  ======= end of input processing =======
% 1.74/1.98  
% 1.74/1.98  =========== start of search ===========
% 1.74/1.98  
% 1.74/1.98  
% 1.74/1.98  Resetting weight limit to 25.
% 1.74/1.98  
% 1.74/1.98  
% 1.74/1.98  Resetting weight limit to 25.
% 1.74/1.98  
% 1.74/1.98  sos_size=192
% 1.74/1.98  
% 1.74/1.98  
% 1.74/1.98  Resetting weight limit to 15.
% 1.74/1.98  
% 1.74/1.98  
% 1.74/1.98  Resetting weight limit to 15.
% 1.74/1.98  
% 1.74/1.98  sos_size=294
% 1.74/1.98  
% 1.74/1.98  -------- PROOF -------- 
% 1.74/1.98  
% 1.74/1.98  ----> UNIT CONFLICT at   0.08 sec ----> 795 [binary,794.1,2.1] $F.
% 1.74/1.98  
% 1.74/1.98  Length of proof is 43.  Level of proof is 19.
% 1.74/1.98  
% 1.74/1.98  ---------------- PROOF ----------------
% 1.74/1.98  % SZS status Unsatisfiable
% 1.74/1.98  % SZS output start Refutation
% See solution above
% 1.74/1.98  ------------ end of proof -------------
% 1.74/1.98  
% 1.74/1.98  
% 1.74/1.98  Search stopped by max_proofs option.
% 1.74/1.98  
% 1.74/1.98  
% 1.74/1.98  Search stopped by max_proofs option.
% 1.74/1.98  
% 1.74/1.98  ============ end of search ============
% 1.74/1.98  
% 1.74/1.98  -------------- statistics -------------
% 1.74/1.98  clauses given                 39
% 1.74/1.98  clauses generated           2003
% 1.74/1.98  clauses kept                 566
% 1.74/1.98  clauses forward subsumed    1355
% 1.74/1.98  clauses back subsumed          6
% 1.74/1.98  Kbytes malloced             7812
% 1.74/1.98  
% 1.74/1.98  ----------- times (seconds) -----------
% 1.74/1.98  user CPU time          0.08          (0 hr, 0 min, 0 sec)
% 1.74/1.98  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 1.74/1.98  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.74/1.98  
% 1.74/1.98  That finishes the proof of the theorem.
% 1.74/1.98  
% 1.74/1.98  Process 16214 finished Wed Jul 27 05:31:41 2022
% 1.74/1.98  Otter interrupted
% 1.74/1.98  PROOF FOUND
%------------------------------------------------------------------------------