TSTP Solution File: GRP700-10 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP700-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n015.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 12:57:40 EDT 2022

% Result   : Unsatisfiable 1.97s 2.14s
% Output   : Refutation 1.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (  16 unt;   0 nHn;   4 RR)
%            Number of literals    :   16 (  15 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   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   :   21 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    tuple(mult(A,x0),mult(x0,A)) != tuple(unit,unit),
    file('GRP700-10.p',unknown),
    [] ).

cnf(2,axiom,
    A = A,
    file('GRP700-10.p',unknown),
    [] ).

cnf(7,axiom,
    mult(rd(A,B),B) = A,
    file('GRP700-10.p',unknown),
    [] ).

cnf(10,axiom,
    rd(mult(A,B),B) = A,
    file('GRP700-10.p',unknown),
    [] ).

cnf(12,axiom,
    mult(A,unit) = A,
    file('GRP700-10.p',unknown),
    [] ).

cnf(13,axiom,
    mult(unit,A) = A,
    file('GRP700-10.p',unknown),
    [] ).

cnf(15,axiom,
    mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
    file('GRP700-10.p',unknown),
    [] ).

cnf(30,plain,
    tuple(A,mult(x0,rd(A,x0))) != tuple(unit,unit),
    inference(para_from,[status(thm),theory(equality)],[7,1]),
    [iquote('para_from,7.1.1,1.1.1.1')] ).

cnf(33,plain,
    rd(A,A) = unit,
    inference(para_into,[status(thm),theory(equality)],[10,13]),
    [iquote('para_into,9.1.1.1,13.1.1')] ).

cnf(46,plain,
    mult(mult(mult(A,B),A),A) = mult(A,mult(mult(B,A),A)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,12]),12]),
    [iquote('para_into,15.1.1.2,11.1.1,demod,12')] ).

cnf(171,plain,
    rd(mult(A,mult(mult(B,A),A)),A) = mult(mult(A,B),A),
    inference(para_from,[status(thm),theory(equality)],[46,10]),
    [iquote('para_from,46.1.1,9.1.1.1')] ).

cnf(271,plain,
    rd(mult(A,mult(B,A)),A) = mult(mult(A,rd(B,A)),A),
    inference(para_into,[status(thm),theory(equality)],[171,7]),
    [iquote('para_into,171.1.1.1.2.1,7.1.1')] ).

cnf(307,plain,
    mult(mult(A,rd(unit,A)),A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[271,13]),10])]),
    [iquote('para_into,271.1.1.1.2,13.1.1,demod,10,flip.1')] ).

cnf(318,plain,
    mult(A,rd(unit,A)) = unit,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[307,10]),33])]),
    [iquote('para_from,307.1.1,9.1.1.1,demod,33,flip.1')] ).

cnf(324,plain,
    tuple(unit,unit) != tuple(unit,unit),
    inference(para_from,[status(thm),theory(equality)],[318,30]),
    [iquote('para_from,318.1.1,30.1.1.2')] ).

cnf(325,plain,
    $false,
    inference(binary,[status(thm)],[324,2]),
    [iquote('binary,324.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : GRP700-10 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n015.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 05:31:56 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.97/2.14  ----- Otter 3.3f, August 2004 -----
% 1.97/2.14  The process was started by sandbox on n015.cluster.edu,
% 1.97/2.14  Wed Jul 27 05:31:56 2022
% 1.97/2.14  The command was "./otter".  The process ID is 9032.
% 1.97/2.14  
% 1.97/2.14  set(prolog_style_variables).
% 1.97/2.14  set(auto).
% 1.97/2.14     dependent: set(auto1).
% 1.97/2.14     dependent: set(process_input).
% 1.97/2.14     dependent: clear(print_kept).
% 1.97/2.14     dependent: clear(print_new_demod).
% 1.97/2.14     dependent: clear(print_back_demod).
% 1.97/2.14     dependent: clear(print_back_sub).
% 1.97/2.14     dependent: set(control_memory).
% 1.97/2.14     dependent: assign(max_mem, 12000).
% 1.97/2.14     dependent: assign(pick_given_ratio, 4).
% 1.97/2.14     dependent: assign(stats_level, 1).
% 1.97/2.14     dependent: assign(max_seconds, 10800).
% 1.97/2.14  clear(print_given).
% 1.97/2.14  
% 1.97/2.14  list(usable).
% 1.97/2.14  0 [] A=A.
% 1.97/2.14  0 [] mult(A,ld(A,B))=B.
% 1.97/2.14  0 [] ld(A,mult(A,B))=B.
% 1.97/2.14  0 [] mult(rd(A,B),B)=A.
% 1.97/2.14  0 [] rd(mult(A,B),B)=A.
% 1.97/2.14  0 [] mult(A,unit)=A.
% 1.97/2.14  0 [] mult(unit,A)=A.
% 1.97/2.14  0 [] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.97/2.14  0 [] mult(mult(A,B),mult(B,mult(C,B)))=mult(mult(A,mult(B,mult(B,C))),B).
% 1.97/2.14  0 [] tuple(mult(X1,x0),mult(x0,X1))!=tuple(unit,unit).
% 1.97/2.14  end_of_list.
% 1.97/2.14  
% 1.97/2.14  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.97/2.14  
% 1.97/2.14  All clauses are units, and equality is present; the
% 1.97/2.14  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.97/2.14  
% 1.97/2.14     dependent: set(knuth_bendix).
% 1.97/2.14     dependent: set(anl_eq).
% 1.97/2.14     dependent: set(para_from).
% 1.97/2.14     dependent: set(para_into).
% 1.97/2.14     dependent: clear(para_from_right).
% 1.97/2.14     dependent: clear(para_into_right).
% 1.97/2.14     dependent: set(para_from_vars).
% 1.97/2.14     dependent: set(eq_units_both_ways).
% 1.97/2.14     dependent: set(dynamic_demod_all).
% 1.97/2.14     dependent: set(dynamic_demod).
% 1.97/2.14     dependent: set(order_eq).
% 1.97/2.14     dependent: set(back_demod).
% 1.97/2.14     dependent: set(lrpo).
% 1.97/2.14  
% 1.97/2.14  ------------> process usable:
% 1.97/2.14  ** KEPT (pick-wt=11): 1 [] tuple(mult(A,x0),mult(x0,A))!=tuple(unit,unit).
% 1.97/2.14  
% 1.97/2.14  ------------> process sos:
% 1.97/2.14  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.97/2.14  ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.97/2.14  ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.97/2.14  ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.97/2.14  ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.97/2.14  ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.97/2.14  ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.97/2.14  ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.97/2.14  ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.97/2.14  ** KEPT (pick-wt=5): 11 [] mult(A,unit)=A.
% 1.97/2.14  ---> New Demodulator: 12 [new_demod,11] mult(A,unit)=A.
% 1.97/2.14  ** KEPT (pick-wt=5): 13 [] mult(unit,A)=A.
% 1.97/2.14  ---> New Demodulator: 14 [new_demod,13] mult(unit,A)=A.
% 1.97/2.14  ** KEPT (pick-wt=19): 15 [] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.97/2.14  ** KEPT (pick-wt=19): 17 [copy,16,flip.1] mult(mult(A,mult(B,mult(B,C))),B)=mult(mult(A,B),mult(B,mult(C,B))).
% 1.97/2.14  ---> New Demodulator: 18 [new_demod,17] mult(mult(A,mult(B,mult(B,C))),B)=mult(mult(A,B),mult(B,mult(C,B))).
% 1.97/2.14    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.97/2.14  >>>> Starting back demodulation with 4.
% 1.97/2.14  >>>> Starting back demodulation with 6.
% 1.97/2.14  >>>> Starting back demodulation with 8.
% 1.97/2.14  >>>> Starting back demodulation with 10.
% 1.97/2.14  >>>> Starting back demodulation with 12.
% 1.97/2.14  >>>> Starting back demodulation with 14.
% 1.97/2.14  ** KEPT (pick-wt=19): 19 [copy,15,flip.1] mult(A,mult(mult(mult(B,A),A),C))=mult(mult(mult(A,B),A),mult(A,C)).
% 1.97/2.14  >>>> Starting back demodulation with 18.
% 1.97/2.14    Following clause subsumed by 15 during input processing: 0 [copy,19,flip.1] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.97/2.14  
% 1.97/2.14  ======= end of input processing =======
% 1.97/2.14  
% 1.97/2.14  =========== start of search ===========
% 1.97/2.14  
% 1.97/2.14  
% 1.97/2.14  Resetting weight limit to 19.
% 1.97/2.14  
% 1.97/2.14  
% 1.97/2.14  Resetting weight limit to 19.
% 1.97/2.14  
% 1.97/2.14  sos_size=132
% 1.97/2.14  
% 1.97/2.14  -------- PROOF -------- 
% 1.97/2.14  
% 1.97/2.14  ----> UNIT CONFLICT at   0.04 sec ----> 325 [binary,324.1,2.1] $F.
% 1.97/2.14  
% 1.97/2.14  Length of proof is 8.  Level of proof is 6.
% 1.97/2.14  
% 1.97/2.14  ---------------- PROOF ----------------
% 1.97/2.14  % SZS status Unsatisfiable
% 1.97/2.14  % SZS output start Refutation
% See solution above
% 1.97/2.14  ------------ end of proof -------------
% 1.97/2.14  
% 1.97/2.14  
% 1.97/2.14  Search stopped by max_proofs option.
% 1.97/2.14  
% 1.97/2.14  
% 1.97/2.14  Search stopped by max_proofs option.
% 1.97/2.14  
% 1.97/2.14  ============ end of search ============
% 1.97/2.14  
% 1.97/2.14  -------------- statistics -------------
% 1.97/2.14  clauses given                 44
% 1.97/2.14  clauses generated            832
% 1.97/2.14  clauses kept                 210
% 1.97/2.14  clauses forward subsumed     396
% 1.97/2.14  clauses back subsumed          0
% 1.97/2.14  Kbytes malloced             4882
% 1.97/2.14  
% 1.97/2.14  ----------- times (seconds) -----------
% 1.97/2.14  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.97/2.14  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.97/2.14  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.97/2.14  
% 1.97/2.14  That finishes the proof of the theorem.
% 1.97/2.14  
% 1.97/2.14  Process 9032 finished Wed Jul 27 05:31:58 2022
% 1.97/2.14  Otter interrupted
% 1.97/2.14  PROOF FOUND
%------------------------------------------------------------------------------