TSTP Solution File: GRP116-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP116-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n022.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 12:56:05 EDT 2022

% Result   : Unsatisfiable 1.71s 1.94s
% Output   : Refutation 1.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   23 (  23 unt;   0 nHn;   2 RR)
%            Number of literals    :   23 (  22 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   51 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(identity,a) != a,
    file('GRP116-1.p',unknown),
    [] ).

cnf(4,axiom,
    multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C)))) = B,
    file('GRP116-1.p',unknown),
    [] ).

cnf(9,plain,
    multiply(A,multiply(multiply(A,multiply(multiply(A,B),multiply(identity,multiply(multiply(identity,C),multiply(identity,C))))),C)) = B,
    inference(para_into,[status(thm),theory(equality)],[4,4]),
    [iquote('para_into,3.1.1.2.2,3.1.1')] ).

cnf(17,plain,
    multiply(A,multiply(multiply(A,multiply(multiply(A,B),multiply(identity,multiply(C,C)))),multiply(multiply(identity,multiply(multiply(identity,C),D)),multiply(identity,multiply(D,D))))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,4]),4]),
    [iquote('para_into,9.1.1.2.1.2.2.2.1,3.1.1,demod,4')] ).

cnf(19,plain,
    multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(multiply(identity,C),multiply(identity,C)))) = B,
    inference(para_into,[status(thm),theory(equality)],[9,4]),
    [iquote('para_into,9.1.1.2.1.2.2,3.1.1')] ).

cnf(24,plain,
    multiply(multiply(A,B),multiply(identity,C)) = multiply(A,multiply(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,4])]),
    [iquote('para_into,9.1.1.2.1,3.1.1,flip.1')] ).

cnf(29,plain,
    multiply(A,multiply(A,multiply(multiply(multiply(A,B),C),multiply(C,C)))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),24,24]),
    [iquote('back_demod,19,demod,24,24')] ).

cnf(32,plain,
    multiply(A,multiply(A,multiply(multiply(A,multiply(B,multiply(C,C))),multiply(multiply(multiply(identity,C),D),multiply(D,D))))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),24,24,24]),
    [iquote('back_demod,17,demod,24,24,24')] ).

cnf(52,plain,
    multiply(A,multiply(A,multiply(A,multiply(B,identity)))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,24]),24]),
    [iquote('para_into,29.1.1.2.2,23.1.1,demod,24')] ).

cnf(68,plain,
    multiply(multiply(A,B),multiply(multiply(A,B),multiply(A,multiply(B,identity)))) = identity,
    inference(para_into,[status(thm),theory(equality)],[52,24]),
    [iquote('para_into,51.1.1.2.2,23.1.1')] ).

cnf(76,plain,
    multiply(A,multiply(A,multiply(multiply(B,C),multiply(C,C)))) = multiply(A,multiply(A,multiply(B,identity))),
    inference(para_from,[status(thm),theory(equality)],[52,29]),
    [iquote('para_from,51.1.1,29.1.1.2.2.1.1')] ).

cnf(99,plain,
    multiply(identity,multiply(A,multiply(A,multiply(A,identity)))) = identity,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[68,24]),24]),
    [iquote('para_into,68.1.1.2,23.1.1,demod,24')] ).

cnf(102,plain,
    multiply(multiply(A,B),identity) = multiply(A,multiply(B,multiply(C,multiply(C,multiply(C,identity))))),
    inference(para_from,[status(thm),theory(equality)],[99,24]),
    [iquote('para_from,98.1.1,23.1.1.2')] ).

cnf(104,plain,
    multiply(A,multiply(A,multiply(A,identity))) = identity,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[99,68]),99,52]),
    [iquote('para_from,98.1.1,68.1.1.2.1,demod,99,52')] ).

cnf(108,plain,
    multiply(multiply(A,B),identity) = multiply(A,multiply(B,identity)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[102])]),104])]),
    [iquote('copy,102,flip.1,demod,104,flip.1')] ).

cnf(127,plain,
    multiply(multiply(A,identity),multiply(multiply(A,identity),multiply(A,multiply(multiply(multiply(identity,multiply(A,identity)),B),multiply(B,B))))) = multiply(A,identity),
    inference(para_into,[status(thm),theory(equality)],[32,52]),
    [iquote('para_into,31.1.1.2.2.1,51.1.1')] ).

cnf(137,plain,
    multiply(A,multiply(A,multiply(A,multiply(B,multiply(multiply(C,C),multiply(multiply(C,multiply(C,identity)),multiply(C,multiply(C,identity)))))))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,68]),24,24,24,24,24]),
    [iquote('para_into,31.1.1.2.2.2.1,68.1.1,demod,24,24,24,24,24')] ).

cnf(148,plain,
    multiply(A,multiply(A,multiply(B,multiply(B,multiply(multiply(B,multiply(A,multiply(C,C))),multiply(multiply(multiply(identity,C),D),multiply(D,multiply(D,identity)))))))) = identity,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[32,68]),32,108,108,108,108]),
    [iquote('para_from,31.1.1,68.1.1.2.1,demod,32,108,108,108,108')] ).

cnf(154,plain,
    multiply(A,identity) = A,
    inference(para_from,[status(thm),theory(equality)],[104,52]),
    [iquote('para_from,103.1.1,51.1.1.2')] ).

cnf(166,plain,
    multiply(A,multiply(A,A)) = identity,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[148]),154,32]),
    [iquote('back_demod,148,demod,154,32')] ).

cnf(172,plain,
    multiply(A,multiply(A,multiply(A,B))) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[137]),154,154,166,154]),
    [iquote('back_demod,137,demod,154,154,166,154')] ).

cnf(177,plain,
    multiply(identity,A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[127]),154,154,154,76,154,172,154]),
    [iquote('back_demod,127,demod,154,154,154,76,154,172,154')] ).

cnf(179,plain,
    $false,
    inference(binary,[status(thm)],[177,1]),
    [iquote('binary,177.1,1.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP116-1 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13  % Command  : otter-tptp-script %s
% 0.14/0.33  % Computer : n022.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 05:13:50 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 1.71/1.94  ----- Otter 3.3f, August 2004 -----
% 1.71/1.94  The process was started by sandbox2 on n022.cluster.edu,
% 1.71/1.94  Wed Jul 27 05:13:50 2022
% 1.71/1.94  The command was "./otter".  The process ID is 4341.
% 1.71/1.94  
% 1.71/1.94  set(prolog_style_variables).
% 1.71/1.94  set(auto).
% 1.71/1.94     dependent: set(auto1).
% 1.71/1.94     dependent: set(process_input).
% 1.71/1.94     dependent: clear(print_kept).
% 1.71/1.94     dependent: clear(print_new_demod).
% 1.71/1.94     dependent: clear(print_back_demod).
% 1.71/1.94     dependent: clear(print_back_sub).
% 1.71/1.94     dependent: set(control_memory).
% 1.71/1.94     dependent: assign(max_mem, 12000).
% 1.71/1.94     dependent: assign(pick_given_ratio, 4).
% 1.71/1.94     dependent: assign(stats_level, 1).
% 1.71/1.94     dependent: assign(max_seconds, 10800).
% 1.71/1.94  clear(print_given).
% 1.71/1.94  
% 1.71/1.94  list(usable).
% 1.71/1.94  0 [] A=A.
% 1.71/1.94  0 [] multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z))))=Y.
% 1.71/1.94  0 [] multiply(identity,a)!=a.
% 1.71/1.94  end_of_list.
% 1.71/1.94  
% 1.71/1.94  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.94  
% 1.71/1.94  All clauses are units, and equality is present; the
% 1.71/1.94  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.94  
% 1.71/1.94     dependent: set(knuth_bendix).
% 1.71/1.94     dependent: set(anl_eq).
% 1.71/1.94     dependent: set(para_from).
% 1.71/1.94     dependent: set(para_into).
% 1.71/1.94     dependent: clear(para_from_right).
% 1.71/1.94     dependent: clear(para_into_right).
% 1.71/1.94     dependent: set(para_from_vars).
% 1.71/1.94     dependent: set(eq_units_both_ways).
% 1.71/1.94     dependent: set(dynamic_demod_all).
% 1.71/1.94     dependent: set(dynamic_demod).
% 1.71/1.94     dependent: set(order_eq).
% 1.71/1.94     dependent: set(back_demod).
% 1.71/1.94     dependent: set(lrpo).
% 1.71/1.94  
% 1.71/1.94  ------------> process usable:
% 1.71/1.94  ** KEPT (pick-wt=5): 1 [] multiply(identity,a)!=a.
% 1.71/1.94  
% 1.71/1.94  ------------> process sos:
% 1.71/1.94  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.71/1.94  ** KEPT (pick-wt=17): 3 [] multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C))))=B.
% 1.71/1.94  ---> New Demodulator: 4 [new_demod,3] multiply(A,multiply(multiply(A,multiply(multiply(A,B),C)),multiply(identity,multiply(C,C))))=B.
% 1.71/1.94    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.71/1.94  >>>> Starting back demodulation with 4.
% 1.71/1.94  
% 1.71/1.94  ======= end of input processing =======
% 1.71/1.94  
% 1.71/1.94  =========== start of search ===========
% 1.71/1.94  
% 1.71/1.94  -------- PROOF -------- 
% 1.71/1.94  
% 1.71/1.94  ----> UNIT CONFLICT at   0.01 sec ----> 179 [binary,177.1,1.1] $F.
% 1.71/1.94  
% 1.71/1.94  Length of proof is 20.  Level of proof is 12.
% 1.71/1.94  
% 1.71/1.94  ---------------- PROOF ----------------
% 1.71/1.94  % SZS status Unsatisfiable
% 1.71/1.94  % SZS output start Refutation
% See solution above
% 1.71/1.94  ------------ end of proof -------------
% 1.71/1.94  
% 1.71/1.94  
% 1.71/1.94  Search stopped by max_proofs option.
% 1.71/1.94  
% 1.71/1.94  
% 1.71/1.94  Search stopped by max_proofs option.
% 1.71/1.94  
% 1.71/1.94  ============ end of search ============
% 1.71/1.94  
% 1.71/1.94  -------------- statistics -------------
% 1.71/1.94  clauses given                 12
% 1.71/1.94  clauses generated            117
% 1.71/1.94  clauses kept                 109
% 1.71/1.94  clauses forward subsumed     100
% 1.71/1.94  clauses back subsumed          2
% 1.71/1.94  Kbytes malloced             1953
% 1.71/1.94  
% 1.71/1.94  ----------- times (seconds) -----------
% 1.71/1.94  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.71/1.94  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.71/1.94  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.71/1.94  
% 1.71/1.94  That finishes the proof of the theorem.
% 1.71/1.94  
% 1.71/1.94  Process 4341 finished Wed Jul 27 05:13:52 2022
% 1.71/1.94  Otter interrupted
% 1.71/1.94  PROOF FOUND
%------------------------------------------------------------------------------