TSTP Solution File: GRP568-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n012.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 12:57:16 EDT 2022

% Result   : Unsatisfiable 1.68s 1.88s
% Output   : Refutation 1.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   27 (  27 unt;   0 nHn;   6 RR)
%            Number of literals    :   27 (  26 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(a,b) != multiply(b,a),
    file('GRP568-1.p',unknown),
    [] ).

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

cnf(4,axiom,
    double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B,
    file('GRP568-1.p',unknown),
    [] ).

cnf(7,axiom,
    multiply(A,B) = double_divide(double_divide(B,A),identity),
    file('GRP568-1.p',unknown),
    [] ).

cnf(9,axiom,
    inverse(A) = double_divide(A,identity),
    file('GRP568-1.p',unknown),
    [] ).

cnf(10,axiom,
    identity = double_divide(A,inverse(A)),
    file('GRP568-1.p',unknown),
    [] ).

cnf(12,plain,
    double_divide(A,double_divide(A,identity)) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10]),9])]),
    [iquote('copy,10,demod,9,flip.1')] ).

cnf(13,plain,
    double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),7,7])]),
    [iquote('back_demod,2,demod,7,7,flip.1')] ).

cnf(19,plain,
    double_divide(double_divide(A,identity),double_divide(identity,identity)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),12]),
    [iquote('para_into,4.1.1.1.2.1,11.1.1,demod,12')] ).

cnf(20,plain,
    double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(identity,C))),
    inference(para_into,[status(thm),theory(equality)],[4,4]),
    [iquote('para_into,4.1.1.1.2.1,4.1.1')] ).

cnf(23,plain,
    double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
    [iquote('copy,20,flip.1')] ).

cnf(25,plain,
    double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(A,identity),
    inference(para_from,[status(thm),theory(equality)],[19,4]),
    [iquote('para_from,18.1.1,4.1.1.1.2.1')] ).

cnf(28,plain,
    double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(B,identity),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),25]),
    [iquote('back_demod,23,demod,25')] ).

cnf(32,plain,
    double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(A,identity),identity),
    inference(para_into,[status(thm),theory(equality)],[25,19]),
    [iquote('para_into,24.1.1.1.2,18.1.1')] ).

cnf(34,plain,
    double_divide(identity,identity) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,12]),19])]),
    [iquote('para_into,24.1.1.1.2,11.1.1,demod,19,flip.1')] ).

cnf(35,plain,
    double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),identity),
    inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),34]),
    [iquote('copy,32,flip.1,demod,34')] ).

cnf(44,plain,
    double_divide(double_divide(A,identity),identity) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),34]),
    [iquote('back_demod,18,demod,34')] ).

cnf(47,plain,
    double_divide(double_divide(identity,A),identity) = A,
    inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[35])]),44]),
    [iquote('copy,35,flip.1,demod,44')] ).

cnf(51,plain,
    double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)) = double_divide(B,identity),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,44]),34]),
    [iquote('para_into,28.1.1.2.1.2,43.1.1,demod,34')] ).

cnf(53,plain,
    double_divide(identity,A) = double_divide(A,identity),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,34]),34,44]),
    [iquote('para_into,28.1.1.2.1.2,33.1.1,demod,34,44')] ).

cnf(64,plain,
    double_divide(A,identity) = double_divide(identity,A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[53])]),
    [iquote('copy,53,flip.1')] ).

cnf(86,plain,
    double_divide(identity,double_divide(identity,A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[64,47])]),
    [iquote('para_into,64.1.1,47.1.1,flip.1')] ).

cnf(91,plain,
    double_divide(double_divide(a,b),identity) != double_divide(identity,double_divide(b,a)),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,13])]),
    [iquote('para_from,64.1.1,13.1.1,flip.1')] ).

cnf(94,plain,
    double_divide(double_divide(A,B),A) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[51,51]),44,44,44]),
    [iquote('para_into,51.1.1.2.1,51.1.1,demod,44,44,44')] ).

cnf(104,plain,
    double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[86,28]),86]),
    [iquote('para_from,85.1.1,28.1.1.2.1.2,demod,86')] ).

cnf(194,plain,
    double_divide(double_divide(A,B),identity) = double_divide(identity,double_divide(B,A)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[104,94])]),
    [iquote('para_into,104.1.1.2.1,94.1.1,flip.1')] ).

cnf(196,plain,
    $false,
    inference(binary,[status(thm)],[194,91]),
    [iquote('binary,194.1,91.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.00/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n012.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 05:14:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.68/1.88  ----- Otter 3.3f, August 2004 -----
% 1.68/1.88  The process was started by sandbox2 on n012.cluster.edu,
% 1.68/1.88  Wed Jul 27 05:14:35 2022
% 1.68/1.88  The command was "./otter".  The process ID is 11368.
% 1.68/1.88  
% 1.68/1.88  set(prolog_style_variables).
% 1.68/1.88  set(auto).
% 1.68/1.88     dependent: set(auto1).
% 1.68/1.88     dependent: set(process_input).
% 1.68/1.88     dependent: clear(print_kept).
% 1.68/1.88     dependent: clear(print_new_demod).
% 1.68/1.88     dependent: clear(print_back_demod).
% 1.68/1.88     dependent: clear(print_back_sub).
% 1.68/1.88     dependent: set(control_memory).
% 1.68/1.88     dependent: assign(max_mem, 12000).
% 1.68/1.88     dependent: assign(pick_given_ratio, 4).
% 1.68/1.88     dependent: assign(stats_level, 1).
% 1.68/1.88     dependent: assign(max_seconds, 10800).
% 1.68/1.88  clear(print_given).
% 1.68/1.88  
% 1.68/1.88  list(usable).
% 1.68/1.88  0 [] A=A.
% 1.68/1.88  0 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))=B.
% 1.68/1.88  0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.88  0 [] inverse(A)=double_divide(A,identity).
% 1.68/1.88  0 [] identity=double_divide(A,inverse(A)).
% 1.68/1.88  0 [] multiply(a,b)!=multiply(b,a).
% 1.68/1.88  end_of_list.
% 1.68/1.88  
% 1.68/1.88  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.88  
% 1.68/1.88  All clauses are units, and equality is present; the
% 1.68/1.88  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.88  
% 1.68/1.88     dependent: set(knuth_bendix).
% 1.68/1.88     dependent: set(anl_eq).
% 1.68/1.88     dependent: set(para_from).
% 1.68/1.88     dependent: set(para_into).
% 1.68/1.88     dependent: clear(para_from_right).
% 1.68/1.88     dependent: clear(para_into_right).
% 1.68/1.88     dependent: set(para_from_vars).
% 1.68/1.88     dependent: set(eq_units_both_ways).
% 1.68/1.88     dependent: set(dynamic_demod_all).
% 1.68/1.88     dependent: set(dynamic_demod).
% 1.68/1.88     dependent: set(order_eq).
% 1.68/1.88     dependent: set(back_demod).
% 1.68/1.88     dependent: set(lrpo).
% 1.68/1.88  
% 1.68/1.88  ------------> process usable:
% 1.68/1.88  ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.68/1.88  
% 1.68/1.88  ------------> process sos:
% 1.68/1.88  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.68/1.88  ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))=B.
% 1.68/1.88  ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))=B.
% 1.68/1.88  ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.88  ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.88  ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 1.68/1.88  ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 1.68/1.88  ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.68/1.88  ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 1.68/1.88    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.68/1.88  >>>> Starting back demodulation with 5.
% 1.68/1.88  >>>> Starting back demodulation with 7.
% 1.68/1.88      >> back demodulating 2 with 7.
% 1.68/1.88  >>>> Starting back demodulation with 9.
% 1.68/1.88  >>>> Starting back demodulation with 12.
% 1.68/1.88  
% 1.68/1.88  ======= end of input processing =======
% 1.68/1.88  
% 1.68/1.88  =========== start of search ===========
% 1.68/1.88  
% 1.68/1.88  -------- PROOF -------- 
% 1.68/1.88  
% 1.68/1.88  ----> UNIT CONFLICT at   0.01 sec ----> 196 [binary,194.1,91.1] $F.
% 1.68/1.88  
% 1.68/1.88  Length of proof is 21.  Level of proof is 10.
% 1.68/1.88  
% 1.68/1.88  ---------------- PROOF ----------------
% 1.68/1.88  % SZS status Unsatisfiable
% 1.68/1.88  % SZS output start Refutation
% See solution above
% 1.68/1.88  ------------ end of proof -------------
% 1.68/1.88  
% 1.68/1.88  
% 1.68/1.88  Search stopped by max_proofs option.
% 1.68/1.88  
% 1.68/1.88  
% 1.68/1.88  Search stopped by max_proofs option.
% 1.68/1.88  
% 1.68/1.88  ============ end of search ============
% 1.68/1.88  
% 1.68/1.88  -------------- statistics -------------
% 1.68/1.88  clauses given                 25
% 1.68/1.88  clauses generated            326
% 1.68/1.88  clauses kept                 106
% 1.68/1.88  clauses forward subsumed     291
% 1.68/1.88  clauses back subsumed          0
% 1.68/1.88  Kbytes malloced             1953
% 1.68/1.88  
% 1.68/1.88  ----------- times (seconds) -----------
% 1.68/1.88  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.68/1.88  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.68/1.88  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.68/1.88  
% 1.68/1.88  That finishes the proof of the theorem.
% 1.68/1.88  
% 1.68/1.88  Process 11368 finished Wed Jul 27 05:14:37 2022
% 1.68/1.88  Otter interrupted
% 1.68/1.88  PROOF FOUND
%------------------------------------------------------------------------------