TSTP Solution File: GRP482-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP482-1 : TPTP v8.1.0. Released v2.6.0.
% 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 12:57:05 EDT 2022

% Result   : Unsatisfiable 1.78s 1.97s
% Output   : Refutation 1.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   24 (  24 unt;   0 nHn;   4 RR)
%            Number of literals    :   24 (  23 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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   40 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(identity,a2) != a2,
    file('GRP482-1.p',unknown),
    [] ).

cnf(3,axiom,
    double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = C,
    file('GRP482-1.p',unknown),
    [] ).

cnf(6,axiom,
    multiply(A,B) = double_divide(double_divide(B,A),identity),
    file('GRP482-1.p',unknown),
    [] ).

cnf(8,axiom,
    inverse(A) = double_divide(A,identity),
    file('GRP482-1.p',unknown),
    [] ).

cnf(9,axiom,
    identity = double_divide(A,inverse(A)),
    file('GRP482-1.p',unknown),
    [] ).

cnf(11,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)],[9]),8])]),
    [iquote('copy,9,demod,8,flip.1')] ).

cnf(12,plain,
    double_divide(double_divide(a2,identity),identity) != a2,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6]),
    [iquote('back_demod,1,demod,6')] ).

cnf(13,plain,
    double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,identity),double_divide(A,identity))),B) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),11]),
    [iquote('back_demod,3,demod,11')] ).

cnf(19,plain,
    double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),B) = A,
    inference(para_into,[status(thm),theory(equality)],[13,11]),
    [iquote('para_into,13.1.1.1.1,10.1.1')] ).

cnf(21,plain,
    double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(double_divide(D,double_divide(identity,identity)),double_divide(double_divide(C,identity),double_divide(D,identity))),
    inference(para_into,[status(thm),theory(equality)],[13,13]),
    [iquote('para_into,13.1.1.1.2.1,13.1.1')] ).

cnf(26,plain,
    double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(double_divide(double_divide(C,double_divide(D,identity)),double_divide(B,double_divide(C,identity))),D),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
    [iquote('copy,21,flip.1')] ).

cnf(30,plain,
    double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),B) = double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))),
    inference(para_into,[status(thm),theory(equality)],[19,19]),
    [iquote('para_into,19.1.1.1.2.1,19.1.1')] ).

cnf(31,plain,
    double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))) = double_divide(double_divide(B,double_divide(identity,identity)),double_divide(double_divide(A,identity),double_divide(B,identity))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,13]),30]),
    [iquote('para_into,19.1.1.1.2.1,13.1.1,demod,30')] ).

cnf(36,plain,
    double_divide(double_divide(identity,identity),double_divide(A,identity)) = A,
    inference(para_into,[status(thm),theory(equality)],[19,11]),
    [iquote('para_into,19.1.1.1.2,10.1.1')] ).

cnf(38,plain,
    double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),double_divide(identity,identity))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),30]),
    [iquote('back_demod,19,demod,30')] ).

cnf(40,plain,
    double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity))),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[31])]),
    [iquote('copy,31,flip.1')] ).

cnf(41,plain,
    double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(double_divide(identity,identity),B),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[36,13])]),
    [iquote('para_into,36.1.1.2,13.1.1,flip.1')] ).

cnf(44,plain,
    double_divide(identity,identity) = identity,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[36,11])]),
    [iquote('para_into,36.1.1,10.1.1,flip.1')] ).

cnf(46,plain,
    double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),identity)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),44,44]),
    [iquote('back_demod,40,demod,44,44')] ).

cnf(52,plain,
    double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(C,double_divide(A,identity))),B) = double_divide(identity,double_divide(double_divide(C,identity),identity)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),44,46])]),
    [iquote('back_demod,26,demod,44,46,flip.1')] ).

cnf(58,plain,
    double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(identity,A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),44,46,44]),
    [iquote('back_demod,41,demod,44,46,44')] ).

cnf(60,plain,
    double_divide(identity,double_divide(A,identity)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[38]),44,58]),
    [iquote('back_demod,38,demod,44,58')] ).

cnf(65,plain,
    double_divide(double_divide(A,identity),identity) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),52,60]),
    [iquote('back_demod,13,demod,52,60')] ).

cnf(67,plain,
    $false,
    inference(binary,[status(thm)],[65,12]),
    [iquote('binary,65.1,12.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP482-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 04:59:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.78/1.96  ----- Otter 3.3f, August 2004 -----
% 1.78/1.96  The process was started by sandbox2 on n022.cluster.edu,
% 1.78/1.96  Wed Jul 27 04:59:50 2022
% 1.78/1.96  The command was "./otter".  The process ID is 16853.
% 1.78/1.96  
% 1.78/1.96  set(prolog_style_variables).
% 1.78/1.96  set(auto).
% 1.78/1.96     dependent: set(auto1).
% 1.78/1.96     dependent: set(process_input).
% 1.78/1.96     dependent: clear(print_kept).
% 1.78/1.96     dependent: clear(print_new_demod).
% 1.78/1.96     dependent: clear(print_back_demod).
% 1.78/1.96     dependent: clear(print_back_sub).
% 1.78/1.96     dependent: set(control_memory).
% 1.78/1.96     dependent: assign(max_mem, 12000).
% 1.78/1.96     dependent: assign(pick_given_ratio, 4).
% 1.78/1.96     dependent: assign(stats_level, 1).
% 1.78/1.96     dependent: assign(max_seconds, 10800).
% 1.78/1.96  clear(print_given).
% 1.78/1.96  
% 1.78/1.96  list(usable).
% 1.78/1.96  0 [] A=A.
% 1.78/1.96  0 [] double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)=C.
% 1.78/1.96  0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.78/1.96  0 [] inverse(A)=double_divide(A,identity).
% 1.78/1.96  0 [] identity=double_divide(A,inverse(A)).
% 1.78/1.96  0 [] multiply(identity,a2)!=a2.
% 1.78/1.97  end_of_list.
% 1.78/1.97  
% 1.78/1.97  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.78/1.97  
% 1.78/1.97  All clauses are units, and equality is present; the
% 1.78/1.97  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.78/1.97  
% 1.78/1.97     dependent: set(knuth_bendix).
% 1.78/1.97     dependent: set(anl_eq).
% 1.78/1.97     dependent: set(para_from).
% 1.78/1.97     dependent: set(para_into).
% 1.78/1.97     dependent: clear(para_from_right).
% 1.78/1.97     dependent: clear(para_into_right).
% 1.78/1.97     dependent: set(para_from_vars).
% 1.78/1.97     dependent: set(eq_units_both_ways).
% 1.78/1.97     dependent: set(dynamic_demod_all).
% 1.78/1.97     dependent: set(dynamic_demod).
% 1.78/1.97     dependent: set(order_eq).
% 1.78/1.97     dependent: set(back_demod).
% 1.78/1.97     dependent: set(lrpo).
% 1.78/1.97  
% 1.78/1.97  ------------> process usable:
% 1.78/1.97  ** KEPT (pick-wt=5): 1 [] multiply(identity,a2)!=a2.
% 1.78/1.97  
% 1.78/1.97  ------------> process sos:
% 1.78/1.97  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.78/1.97  ** KEPT (pick-wt=21): 3 [] double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)=C.
% 1.78/1.97  ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)=C.
% 1.78/1.97  ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.78/1.97  ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.78/1.97  ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.78/1.97  ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.78/1.97  ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.78/1.97  ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.78/1.97    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.78/1.97  >>>> Starting back demodulation with 4.
% 1.78/1.97  >>>> Starting back demodulation with 6.
% 1.78/1.97      >> back demodulating 1 with 6.
% 1.78/1.97  >>>> Starting back demodulation with 8.
% 1.78/1.97  >>>> Starting back demodulation with 11.
% 1.78/1.97      >> back demodulating 3 with 11.
% 1.78/1.97  >>>> Starting back demodulation with 14.
% 1.78/1.97  
% 1.78/1.97  ======= end of input processing =======
% 1.78/1.97  
% 1.78/1.97  =========== start of search ===========
% 1.78/1.97  
% 1.78/1.97  -------- PROOF -------- 
% 1.78/1.97  
% 1.78/1.97  ----> UNIT CONFLICT at   0.00 sec ----> 67 [binary,65.1,12.1] $F.
% 1.78/1.97  
% 1.78/1.97  Length of proof is 18.  Level of proof is 10.
% 1.78/1.97  
% 1.78/1.97  ---------------- PROOF ----------------
% 1.78/1.97  % SZS status Unsatisfiable
% 1.78/1.97  % SZS output start Refutation
% See solution above
% 1.78/1.97  ------------ end of proof -------------
% 1.78/1.97  
% 1.78/1.97  
% 1.78/1.97  Search stopped by max_proofs option.
% 1.78/1.97  
% 1.78/1.97  
% 1.78/1.97  Search stopped by max_proofs option.
% 1.78/1.97  
% 1.78/1.97  ============ end of search ============
% 1.78/1.97  
% 1.78/1.97  -------------- statistics -------------
% 1.78/1.97  clauses given                  8
% 1.78/1.97  clauses generated             28
% 1.78/1.97  clauses kept                  36
% 1.78/1.97  clauses forward subsumed      20
% 1.78/1.97  clauses back subsumed          0
% 1.78/1.97  Kbytes malloced              976
% 1.78/1.97  
% 1.78/1.97  ----------- times (seconds) -----------
% 1.78/1.97  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.78/1.97  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.78/1.97  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.78/1.97  
% 1.78/1.97  That finishes the proof of the theorem.
% 1.78/1.97  
% 1.78/1.97  Process 16853 finished Wed Jul 27 04:59:52 2022
% 1.78/1.97  Otter interrupted
% 1.78/1.97  PROOF FOUND
%------------------------------------------------------------------------------