TSTP Solution File: GRP509-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP509-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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 12:57:09 EDT 2022

% Result   : Unsatisfiable 1.92s 2.09s
% Output   : Refutation 1.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   50 (  50 unt;   0 nHn;   4 RR)
%            Number of literals    :   50 (  49 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   10 (   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   :  147 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
    file('GRP509-1.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(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B,
    file('GRP509-1.p',unknown),
    [] ).

cnf(6,plain,
    multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)),
    inference(para_into,[status(thm),theory(equality)],[5,5]),
    [iquote('para_into,4.1.1.1.1,4.1.1')] ).

cnf(8,plain,
    multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C,
    inference(para_into,[status(thm),theory(equality)],[5,5]),
    [iquote('para_into,4.1.1.1,4.1.1')] ).

cnf(10,plain,
    multiply(multiply(multiply(multiply(multiply(A,B),C),D),inverse(multiply(A,C))),inverse(B)) = D,
    inference(para_into,[status(thm),theory(equality)],[5,5]),
    [iquote('para_into,4.1.1.2.1,4.1.1')] ).

cnf(16,plain,
    multiply(A,inverse(multiply(multiply(B,A),inverse(C)))) = inverse(multiply(multiply(D,B),inverse(multiply(D,C)))),
    inference(para_into,[status(thm),theory(equality)],[8,8]),
    [iquote('para_into,8.1.1.2.1.2.1,8.1.1')] ).

cnf(19,plain,
    inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),
    [iquote('copy,16,flip.1')] ).

cnf(24,plain,
    multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(multiply(D,C),inverse(multiply(D,A)))),
    inference(para_from,[status(thm),theory(equality)],[8,5]),
    [iquote('para_from,8.1.1,4.1.1.1.1')] ).

cnf(25,plain,
    inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(multiply(C,D),inverse(multiply(B,D))),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24])]),
    [iquote('copy,24,flip.1')] ).

cnf(32,plain,
    multiply(multiply(inverse(multiply(multiply(A,B),inverse(multiply(A,C)))),D),inverse(multiply(multiply(C,E),D))) = inverse(multiply(B,E)),
    inference(para_into,[status(thm),theory(equality)],[6,8]),
    [iquote('para_into,6.1.1.2.1.1.1,8.1.1')] ).

cnf(35,plain,
    multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(D,inverse(multiply(multiply(E,multiply(D,A)),inverse(multiply(E,C)))))),
    inference(para_into,[status(thm),theory(equality)],[6,8]),
    [iquote('para_into,6.1.1.2.1.1,8.1.1')] ).

cnf(44,plain,
    inverse(multiply(A,multiply(B,inverse(multiply(multiply(A,B),C))))) = C,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,8])]),
    [iquote('para_into,6.1.1,8.1.1,flip.1')] ).

cnf(45,plain,
    inverse(multiply(A,B)) = multiply(multiply(inverse(multiply(multiply(C,A),inverse(multiply(C,D)))),E),inverse(multiply(multiply(D,B),E))),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),
    [iquote('copy,32,flip.1')] ).

cnf(63,plain,
    inverse(multiply(multiply(A,multiply(B,C)),inverse(multiply(A,D)))) = inverse(multiply(B,multiply(C,inverse(D)))),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[44,8])]),
    [iquote('para_into,43.1.1.1.2.2.1,8.1.1,flip.1')] ).

cnf(74,plain,
    multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(D,inverse(multiply(D,multiply(A,inverse(C)))))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[35]),63]),
    [iquote('back_demod,35,demod,63')] ).

cnf(81,plain,
    multiply(multiply(multiply(A,B),multiply(C,inverse(multiply(multiply(A,C),D)))),D) = B,
    inference(para_from,[status(thm),theory(equality)],[44,5]),
    [iquote('para_from,43.1.1,4.1.1.2')] ).

cnf(95,plain,
    multiply(multiply(A,inverse(B)),inverse(A)) = inverse(B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,10]),5]),
    [iquote('para_into,10.1.1.1.1,10.1.1,demod,5')] ).

cnf(103,plain,
    multiply(multiply(multiply(multiply(multiply(A,B),inverse(multiply(multiply(C,A),inverse(multiply(C,D))))),E),inverse(D)),inverse(B)) = E,
    inference(para_into,[status(thm),theory(equality)],[10,8]),
    [iquote('para_into,10.1.1.1.2.1,8.1.1')] ).

cnf(119,plain,
    multiply(inverse(A),inverse(multiply(B,inverse(multiply(multiply(multiply(multiply(multiply(C,A),D),B),inverse(multiply(C,D))),E))))) = E,
    inference(para_from,[status(thm),theory(equality)],[10,8]),
    [iquote('para_from,10.1.1,8.1.1.2.1.1')] ).

cnf(128,plain,
    multiply(multiply(A,B),inverse(A)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[95,44]),44]),
    [iquote('para_into,95.1.1.1.2,43.1.1,demod,44')] ).

cnf(134,plain,
    inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(C,inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[95,8])]),
    [iquote('para_into,95.1.1.1,8.1.1,flip.1')] ).

cnf(136,plain,
    inverse(multiply(multiply(multiply(A,B),C),D)) = multiply(inverse(multiply(A,C)),inverse(multiply(B,D))),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[95,6])]),
    [iquote('para_into,95.1.1.1,6.1.1,flip.1')] ).

cnf(138,plain,
    multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)),
    inference(para_into,[status(thm),theory(equality)],[95,5]),
    [iquote('para_into,95.1.1.1,4.1.1')] ).

cnf(143,plain,
    multiply(multiply(multiply(multiply(multiply(A,B),multiply(C,inverse(A))),D),inverse(C)),inverse(B)) = D,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[103]),134]),
    [iquote('back_demod,103,demod,134')] ).

cnf(148,plain,
    inverse(multiply(A,multiply(B,inverse(C)))) = multiply(C,inverse(multiply(A,B))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[63]),134])]),
    [iquote('back_demod,62,demod,134,flip.1')] ).

cnf(151,plain,
    inverse(multiply(A,B)) = multiply(multiply(multiply(C,inverse(A)),D),inverse(multiply(multiply(C,B),D))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[45]),134]),
    [iquote('back_demod,45,demod,134')] ).

cnf(156,plain,
    multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(A,inverse(C)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),134])]),
    [iquote('back_demod,25,demod,134,flip.1')] ).

cnf(160,plain,
    inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),134,138])]),
    [iquote('back_demod,19,demod,134,138,flip.1')] ).

cnf(164,plain,
    multiply(A,multiply(multiply(B,C),inverse(multiply(B,A)))) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[8]),160]),
    [iquote('back_demod,8,demod,160')] ).

cnf(168,plain,
    multiply(inverse(A),multiply(multiply(B,C),multiply(A,inverse(B)))) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[119]),136,156,128,148,160]),
    [iquote('back_demod,119,demod,136,156,128,148,160')] ).

cnf(186,plain,
    multiply(multiply(multiply(A,B),inverse(multiply(A,C))),C) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[81]),138]),
    [iquote('back_demod,81,demod,138')] ).

cnf(194,plain,
    multiply(multiply(A,B),inverse(multiply(A,C))) = multiply(B,inverse(C)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[74]),156,148,148])]),
    [iquote('back_demod,74,demod,156,148,148,flip.1')] ).

cnf(196,plain,
    inverse(multiply(A,B)) = multiply(inverse(A),inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[151])]),156,194])]),
    [iquote('copy,151,flip.1,demod,156,194,flip.1')] ).

cnf(219,plain,
    multiply(multiply(multiply(A,B),multiply(inverse(A),inverse(C))),C) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[186]),196]),
    [iquote('back_demod,186,demod,196')] ).

cnf(223,plain,
    multiply(A,multiply(multiply(B,C),multiply(inverse(B),inverse(A)))) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[164]),196]),
    [iquote('back_demod,164,demod,196')] ).

cnf(229,plain,
    multiply(multiply(A,B),multiply(inverse(A),inverse(C))) = multiply(B,inverse(C)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[194]),196]),
    [iquote('back_demod,193,demod,196')] ).

cnf(272,plain,
    multiply(A,multiply(B,inverse(A))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[223]),229]),
    [iquote('back_demod,223,demod,229')] ).

cnf(276,plain,
    multiply(multiply(A,inverse(B)),B) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[219]),229]),
    [iquote('back_demod,219,demod,229')] ).

cnf(285,plain,
    multiply(A,B) = multiply(B,A),
    inference(para_into,[status(thm),theory(equality)],[276,128]),
    [iquote('para_into,276.1.1.1,127.1.1')] ).

cnf(287,plain,
    inverse(inverse(A)) = A,
    inference(para_into,[status(thm),theory(equality)],[276,128]),
    [iquote('para_into,276.1.1,127.1.1')] ).

cnf(327,plain,
    multiply(multiply(multiply(A,B),multiply(inverse(B),inverse(A))),C) = C,
    inference(para_into,[status(thm),theory(equality)],[143,276]),
    [iquote('para_into,143.1.1,276.1.1')] ).

cnf(332,plain,
    multiply(inverse(A),multiply(B,A)) = B,
    inference(para_from,[status(thm),theory(equality)],[287,272]),
    [iquote('para_from,286.1.1,272.1.1.2.2')] ).

cnf(340,plain,
    multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
    inference(para_from,[status(thm),theory(equality)],[285,2]),
    [iquote('para_from,285.1.1,2.1.1')] ).

cnf(363,plain,
    multiply(inverse(A),multiply(B,multiply(A,C))) = multiply(B,C),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[168,332]),287]),
    [iquote('para_into,168.1.1.2.1,332.1.1,demod,287')] ).

cnf(365,plain,
    multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(B,C),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[168,168]),287,363])]),
    [iquote('para_into,168.1.1.2.1,168.1.1,demod,287,363,flip.1')] ).

cnf(376,plain,
    multiply(multiply(A,inverse(A)),B) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[327]),365]),
    [iquote('back_demod,327,demod,365')] ).

cnf(385,plain,
    multiply(inverse(A),A) = multiply(B,inverse(B)),
    inference(para_from,[status(thm),theory(equality)],[376,276]),
    [iquote('para_from,376.1.1,276.1.1.1')] ).

cnf(386,plain,
    multiply(A,inverse(A)) = multiply(inverse(B),B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[385])]),
    [iquote('copy,385,flip.1')] ).

cnf(387,plain,
    $false,
    inference(binary,[status(thm)],[386,340]),
    [iquote('binary,386.1,340.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GRP509-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n023.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 05:49:33 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.92/2.09  ----- Otter 3.3f, August 2004 -----
% 1.92/2.09  The process was started by sandbox2 on n023.cluster.edu,
% 1.92/2.09  Wed Jul 27 05:49:33 2022
% 1.92/2.09  The command was "./otter".  The process ID is 32510.
% 1.92/2.09  
% 1.92/2.09  set(prolog_style_variables).
% 1.92/2.09  set(auto).
% 1.92/2.09     dependent: set(auto1).
% 1.92/2.09     dependent: set(process_input).
% 1.92/2.09     dependent: clear(print_kept).
% 1.92/2.09     dependent: clear(print_new_demod).
% 1.92/2.09     dependent: clear(print_back_demod).
% 1.92/2.09     dependent: clear(print_back_sub).
% 1.92/2.09     dependent: set(control_memory).
% 1.92/2.09     dependent: assign(max_mem, 12000).
% 1.92/2.09     dependent: assign(pick_given_ratio, 4).
% 1.92/2.09     dependent: assign(stats_level, 1).
% 1.92/2.09     dependent: assign(max_seconds, 10800).
% 1.92/2.09  clear(print_given).
% 1.92/2.09  
% 1.92/2.09  list(usable).
% 1.92/2.09  0 [] A=A.
% 1.92/2.09  0 [] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.92/2.09  0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.92/2.09  end_of_list.
% 1.92/2.09  
% 1.92/2.09  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.92/2.09  
% 1.92/2.09  All clauses are units, and equality is present; the
% 1.92/2.09  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.92/2.09  
% 1.92/2.09     dependent: set(knuth_bendix).
% 1.92/2.09     dependent: set(anl_eq).
% 1.92/2.09     dependent: set(para_from).
% 1.92/2.09     dependent: set(para_into).
% 1.92/2.09     dependent: clear(para_from_right).
% 1.92/2.09     dependent: clear(para_into_right).
% 1.92/2.09     dependent: set(para_from_vars).
% 1.92/2.09     dependent: set(eq_units_both_ways).
% 1.92/2.09     dependent: set(dynamic_demod_all).
% 1.92/2.09     dependent: set(dynamic_demod).
% 1.92/2.09     dependent: set(order_eq).
% 1.92/2.09     dependent: set(back_demod).
% 1.92/2.09     dependent: set(lrpo).
% 1.92/2.09  
% 1.92/2.09  ------------> process usable:
% 1.92/2.09  ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.92/2.09  
% 1.92/2.09  ------------> process sos:
% 1.92/2.09  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.92/2.09  ** KEPT (pick-wt=12): 4 [] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.92/2.09  ---> New Demodulator: 5 [new_demod,4] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.92/2.09    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.92/2.09  >>>> Starting back demodulation with 5.
% 1.92/2.09  
% 1.92/2.09  ======= end of input processing =======
% 1.92/2.09  
% 1.92/2.09  =========== start of search ===========
% 1.92/2.09  
% 1.92/2.09  -------- PROOF -------- 
% 1.92/2.09  
% 1.92/2.09  ----> UNIT CONFLICT at   0.01 sec ----> 387 [binary,386.1,340.1] $F.
% 1.92/2.09  
% 1.92/2.09  Length of proof is 47.  Level of proof is 15.
% 1.92/2.09  
% 1.92/2.09  ---------------- PROOF ----------------
% 1.92/2.09  % SZS status Unsatisfiable
% 1.92/2.09  % SZS output start Refutation
% See solution above
% 1.92/2.09  ------------ end of proof -------------
% 1.92/2.09  
% 1.92/2.09  
% 1.92/2.09  Search stopped by max_proofs option.
% 1.92/2.09  
% 1.92/2.09  
% 1.92/2.09  Search stopped by max_proofs option.
% 1.92/2.09  
% 1.92/2.09  ============ end of search ============
% 1.92/2.09  
% 1.92/2.09  -------------- statistics -------------
% 1.92/2.09  clauses given                 22
% 1.92/2.09  clauses generated            319
% 1.92/2.09  clauses kept                 220
% 1.92/2.09  clauses forward subsumed     304
% 1.92/2.09  clauses back subsumed          2
% 1.92/2.09  Kbytes malloced             2929
% 1.92/2.09  
% 1.92/2.09  ----------- times (seconds) -----------
% 1.92/2.09  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.92/2.09  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.92/2.09  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.92/2.09  
% 1.92/2.09  That finishes the proof of the theorem.
% 1.92/2.09  
% 1.92/2.09  Process 32510 finished Wed Jul 27 05:49:35 2022
% 1.92/2.09  Otter interrupted
% 1.92/2.09  PROOF FOUND
%------------------------------------------------------------------------------