TSTP Solution File: GRP518-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n028.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 12:57:10 EDT 2022

% Result   : Unsatisfiable 1.67s 1.87s
% Output   : Refutation 1.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   20 (  20 unt;   0 nHn;   3 RR)
%            Number of literals    :   20 (  19 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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   50 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    file('GRP518-1.p',unknown),
    [] ).

cnf(3,axiom,
    multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C,
    file('GRP518-1.p',unknown),
    [] ).

cnf(5,plain,
    multiply(A,multiply(multiply(inverse(B),C),multiply(multiply(inverse(multiply(A,D)),B),D))) = C,
    inference(para_into,[status(thm),theory(equality)],[3,3]),
    [iquote('para_into,3.1.1.2.1.1.1,3.1.1')] ).

cnf(7,plain,
    multiply(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D),C) = multiply(A,multiply(D,B)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,3])]),
    [iquote('para_into,3.1.1.2.1,3.1.1,flip.1')] ).

cnf(17,plain,
    multiply(multiply(inverse(A),B),A) = B,
    inference(para_into,[status(thm),theory(equality)],[5,3]),
    [iquote('para_into,5.1.1.2,3.1.1')] ).

cnf(23,plain,
    multiply(multiply(inverse(A),B),multiply(multiply(inverse(multiply(inverse(C),D)),A),D)) = multiply(B,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,5])]),
    [iquote('para_into,17.1.1.1,5.1.1,flip.1')] ).

cnf(26,plain,
    multiply(multiply(inverse(multiply(inverse(A),B)),C),B) = multiply(C,A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,3])]),
    [iquote('para_into,17.1.1.1,3.1.1,flip.1')] ).

cnf(29,plain,
    multiply(multiply(inverse(A),B),multiply(A,C)) = multiply(B,C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),26]),
    [iquote('back_demod,23,demod,26')] ).

cnf(33,plain,
    multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),26]),
    [iquote('back_demod,7,demod,26')] ).

cnf(34,plain,
    multiply(multiply(inverse(A),B),multiply(multiply(inverse(B),C),A)) = C,
    inference(para_from,[status(thm),theory(equality)],[17,3]),
    [iquote('para_from,17.1.1,3.1.1.2.1.1.1')] ).

cnf(37,plain,
    multiply(A,B) = multiply(multiply(inverse(C),B),multiply(A,C)),
    inference(para_into,[status(thm),theory(equality)],[33,17]),
    [iquote('para_into,33.1.1.2,17.1.1')] ).

cnf(85,plain,
    multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,3]),26])]),
    [iquote('para_into,29.1.1.1,3.1.1,demod,26,flip.1')] ).

cnf(92,plain,
    multiply(A,multiply(inverse(A),multiply(B,C))) = multiply(B,C),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,33]),85]),
    [iquote('para_into,29.1.1,33.1.1,demod,85')] ).

cnf(120,plain,
    multiply(A,B) = multiply(inverse(C),multiply(B,multiply(A,C))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),85]),
    [iquote('back_demod,37,demod,85')] ).

cnf(121,plain,
    multiply(inverse(A),multiply(B,A)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[34]),85,85,92]),
    [iquote('back_demod,34,demod,85,85,92')] ).

cnf(127,plain,
    multiply(inverse(b2),multiply(b2,a2)) != a2,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),85]),
    [iquote('back_demod,1,demod,85')] ).

cnf(138,plain,
    multiply(inverse(A),multiply(B,multiply(C,A))) = multiply(B,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[121,33])]),
    [iquote('para_from,121.1.1,33.1.1.2,flip.1')] ).

cnf(139,plain,
    multiply(A,B) = multiply(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[120]),138]),
    [iquote('back_demod,120,demod,138')] ).

cnf(143,plain,
    multiply(inverse(A),multiply(A,B)) = B,
    inference(para_from,[status(thm),theory(equality)],[139,121]),
    [iquote('para_from,139.1.1,121.1.1.2')] ).

cnf(145,plain,
    $false,
    inference(binary,[status(thm)],[143,127]),
    [iquote('binary,143.1,127.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP518-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n028.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 05:41:03 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.67/1.87  ----- Otter 3.3f, August 2004 -----
% 1.67/1.87  The process was started by sandbox2 on n028.cluster.edu,
% 1.67/1.87  Wed Jul 27 05:41:03 2022
% 1.67/1.87  The command was "./otter".  The process ID is 862.
% 1.67/1.87  
% 1.67/1.87  set(prolog_style_variables).
% 1.67/1.87  set(auto).
% 1.67/1.87     dependent: set(auto1).
% 1.67/1.87     dependent: set(process_input).
% 1.67/1.87     dependent: clear(print_kept).
% 1.67/1.87     dependent: clear(print_new_demod).
% 1.67/1.87     dependent: clear(print_back_demod).
% 1.67/1.87     dependent: clear(print_back_sub).
% 1.67/1.87     dependent: set(control_memory).
% 1.67/1.87     dependent: assign(max_mem, 12000).
% 1.67/1.87     dependent: assign(pick_given_ratio, 4).
% 1.67/1.87     dependent: assign(stats_level, 1).
% 1.67/1.87     dependent: assign(max_seconds, 10800).
% 1.67/1.87  clear(print_given).
% 1.67/1.87  
% 1.67/1.87  list(usable).
% 1.67/1.87  0 [] A=A.
% 1.67/1.87  0 [] multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))=C.
% 1.67/1.87  0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.67/1.87  end_of_list.
% 1.67/1.87  
% 1.67/1.87  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.67/1.87  
% 1.67/1.87  All clauses are units, and equality is present; the
% 1.67/1.87  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.67/1.87  
% 1.67/1.87     dependent: set(knuth_bendix).
% 1.67/1.87     dependent: set(anl_eq).
% 1.67/1.87     dependent: set(para_from).
% 1.67/1.87     dependent: set(para_into).
% 1.67/1.87     dependent: clear(para_from_right).
% 1.67/1.87     dependent: clear(para_into_right).
% 1.67/1.87     dependent: set(para_from_vars).
% 1.67/1.87     dependent: set(eq_units_both_ways).
% 1.67/1.87     dependent: set(dynamic_demod_all).
% 1.67/1.87     dependent: set(dynamic_demod).
% 1.67/1.87     dependent: set(order_eq).
% 1.67/1.87     dependent: set(back_demod).
% 1.67/1.87     dependent: set(lrpo).
% 1.67/1.87  
% 1.67/1.87  ------------> process usable:
% 1.67/1.87  ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.67/1.87  
% 1.67/1.87  ------------> process sos:
% 1.67/1.87  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.67/1.87  ** KEPT (pick-wt=12): 3 [] multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))=C.
% 1.67/1.87  ---> New Demodulator: 4 [new_demod,3] multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))=C.
% 1.67/1.87    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.67/1.87  >>>> Starting back demodulation with 4.
% 1.67/1.87  
% 1.67/1.87  ======= end of input processing =======
% 1.67/1.87  
% 1.67/1.87  =========== start of search ===========
% 1.67/1.87  
% 1.67/1.87  -------- PROOF -------- 
% 1.67/1.87  
% 1.67/1.87  ----> UNIT CONFLICT at   0.01 sec ----> 145 [binary,143.1,127.1] $F.
% 1.67/1.87  
% 1.67/1.87  Length of proof is 17.  Level of proof is 10.
% 1.67/1.87  
% 1.67/1.87  ---------------- PROOF ----------------
% 1.67/1.87  % SZS status Unsatisfiable
% 1.67/1.87  % SZS output start Refutation
% See solution above
% 1.67/1.87  ------------ end of proof -------------
% 1.67/1.87  
% 1.67/1.87  
% 1.67/1.87  Search stopped by max_proofs option.
% 1.67/1.87  
% 1.67/1.87  
% 1.67/1.87  Search stopped by max_proofs option.
% 1.67/1.87  
% 1.67/1.87  ============ end of search ============
% 1.67/1.87  
% 1.67/1.87  -------------- statistics -------------
% 1.67/1.87  clauses given                  9
% 1.67/1.87  clauses generated             83
% 1.67/1.87  clauses kept                  85
% 1.67/1.87  clauses forward subsumed      74
% 1.67/1.87  clauses back subsumed          0
% 1.67/1.87  Kbytes malloced             1953
% 1.67/1.87  
% 1.67/1.87  ----------- times (seconds) -----------
% 1.67/1.87  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.67/1.87  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.67/1.87  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.67/1.87  
% 1.67/1.87  That finishes the proof of the theorem.
% 1.67/1.87  
% 1.67/1.87  Process 862 finished Wed Jul 27 05:41:05 2022
% 1.67/1.87  Otter interrupted
% 1.67/1.87  PROOF FOUND
%------------------------------------------------------------------------------