TSTP Solution File: GRP680-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP680-1 : TPTP v8.1.0. Released v4.0.0.
% 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 12:57:38 EDT 2022

% Result   : Unsatisfiable 1.82s 2.00s
% Output   : Refutation 1.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   28 (  28 unt;   0 nHn;   4 RR)
%            Number of literals    :   28 (  27 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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    mult(i(op_c),a) != mult(a,i(op_c)),
    file('GRP680-1.p',unknown),
    [] ).

cnf(3,axiom,
    mult(A,ld(A,B)) = B,
    file('GRP680-1.p',unknown),
    [] ).

cnf(5,axiom,
    ld(A,mult(A,B)) = B,
    file('GRP680-1.p',unknown),
    [] ).

cnf(11,axiom,
    mult(A,unit) = A,
    file('GRP680-1.p',unknown),
    [] ).

cnf(13,axiom,
    mult(unit,A) = A,
    file('GRP680-1.p',unknown),
    [] ).

cnf(15,axiom,
    mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C),
    file('GRP680-1.p',unknown),
    [] ).

cnf(16,plain,
    mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
    [iquote('copy,15,flip.1')] ).

cnf(18,axiom,
    mult(i(A),mult(A,B)) = B,
    file('GRP680-1.p',unknown),
    [] ).

cnf(20,axiom,
    mult(op_c,A) = mult(A,op_c),
    file('GRP680-1.p',unknown),
    [] ).

cnf(21,plain,
    mult(A,op_c) = mult(op_c,A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
    [iquote('copy,20,flip.1')] ).

cnf(23,plain,
    ld(unit,A) = A,
    inference(para_into,[status(thm),theory(equality)],[3,13]),
    [iquote('para_into,3.1.1,13.1.1')] ).

cnf(25,plain,
    ld(A,A) = unit,
    inference(para_into,[status(thm),theory(equality)],[5,11]),
    [iquote('para_into,5.1.1.2,11.1.1')] ).

cnf(60,plain,
    mult(A,mult(B,mult(A,op_c))) = mult(op_c,mult(A,mult(B,A))),
    inference(para_into,[status(thm),theory(equality)],[21,16]),
    [iquote('para_into,21.1.1,16.1.1')] ).

cnf(63,plain,
    mult(op_c,mult(A,mult(B,A))) = mult(A,mult(B,mult(A,op_c))),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[60])]),
    [iquote('copy,60,flip.1')] ).

cnf(74,plain,
    mult(i(i(A)),B) = mult(A,B),
    inference(para_into,[status(thm),theory(equality)],[18,18]),
    [iquote('para_into,18.1.1.2,18.1.1')] ).

cnf(85,plain,
    mult(i(A),B) = ld(A,B),
    inference(para_into,[status(thm),theory(equality)],[18,3]),
    [iquote('para_into,18.1.1.2,3.1.1')] ).

cnf(86,plain,
    ld(i(A),B) = mult(A,B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[74]),85]),
    [iquote('back_demod,74,demod,85')] ).

cnf(87,plain,
    mult(a,i(op_c)) != ld(op_c,a),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),85])]),
    [iquote('back_demod,1,demod,85,flip.1')] ).

cnf(88,plain,
    mult(A,B) = ld(i(A),B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[86])]),
    [iquote('copy,86,flip.1')] ).

cnf(146,plain,
    i(A) = ld(A,unit),
    inference(para_into,[status(thm),theory(equality)],[85,11]),
    [iquote('para_into,84.1.1,11.1.1')] ).

cnf(152,plain,
    mult(A,B) = ld(ld(A,unit),B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[88]),146]),
    [iquote('back_demod,88,demod,146')] ).

cnf(153,plain,
    ld(ld(a,unit),ld(op_c,unit)) != ld(op_c,a),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[87]),146,152]),
    [iquote('back_demod,87,demod,146,152')] ).

cnf(208,plain,
    ld(ld(op_c,unit),ld(ld(A,unit),ld(ld(B,unit),A))) = ld(ld(A,unit),ld(ld(B,unit),ld(ld(A,unit),op_c))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[63]),152,152,152,152,152,152]),
    [iquote('back_demod,63,demod,152,152,152,152,152,152')] ).

cnf(235,plain,
    ld(ld(op_c,unit),A) = ld(ld(A,unit),op_c),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),152,152]),
    [iquote('back_demod,20,demod,152,152')] ).

cnf(239,plain,
    ld(ld(A,unit),unit) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),152]),
    [iquote('back_demod,11,demod,152')] ).

cnf(245,plain,
    ld(ld(A,unit),ld(A,B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),152]),
    [iquote('back_demod,3,demod,152')] ).

cnf(461,plain,
    ld(ld(A,unit),ld(op_c,unit)) = ld(op_c,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[208,235]),25,23,245,239,239,25,239]),
    [iquote('para_into,208.1.1.2.1,235.1.1,demod,25,23,245,239,239,25,239')] ).

cnf(463,plain,
    $false,
    inference(binary,[status(thm)],[461,153]),
    [iquote('binary,461.1,153.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GRP680-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % 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 05:33:48 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.82/2.00  ----- Otter 3.3f, August 2004 -----
% 1.82/2.00  The process was started by sandbox on n028.cluster.edu,
% 1.82/2.00  Wed Jul 27 05:33:48 2022
% 1.82/2.00  The command was "./otter".  The process ID is 25860.
% 1.82/2.00  
% 1.82/2.00  set(prolog_style_variables).
% 1.82/2.00  set(auto).
% 1.82/2.00     dependent: set(auto1).
% 1.82/2.00     dependent: set(process_input).
% 1.82/2.00     dependent: clear(print_kept).
% 1.82/2.00     dependent: clear(print_new_demod).
% 1.82/2.00     dependent: clear(print_back_demod).
% 1.82/2.00     dependent: clear(print_back_sub).
% 1.82/2.00     dependent: set(control_memory).
% 1.82/2.00     dependent: assign(max_mem, 12000).
% 1.82/2.00     dependent: assign(pick_given_ratio, 4).
% 1.82/2.00     dependent: assign(stats_level, 1).
% 1.82/2.00     dependent: assign(max_seconds, 10800).
% 1.82/2.00  clear(print_given).
% 1.82/2.00  
% 1.82/2.00  list(usable).
% 1.82/2.00  0 [] A=A.
% 1.82/2.00  0 [] mult(A,ld(A,B))=B.
% 1.82/2.00  0 [] ld(A,mult(A,B))=B.
% 1.82/2.00  0 [] mult(rd(A,B),B)=A.
% 1.82/2.00  0 [] rd(mult(A,B),B)=A.
% 1.82/2.00  0 [] mult(A,unit)=A.
% 1.82/2.00  0 [] mult(unit,A)=A.
% 1.82/2.00  0 [] mult(A,mult(B,mult(A,C)))=mult(mult(A,mult(B,A)),C).
% 1.82/2.00  0 [] mult(i(A),mult(A,B))=B.
% 1.82/2.00  0 [] mult(op_c,A)=mult(A,op_c).
% 1.82/2.00  0 [] mult(i(op_c),a)!=mult(a,i(op_c)).
% 1.82/2.00  end_of_list.
% 1.82/2.00  
% 1.82/2.00  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.82/2.00  
% 1.82/2.00  All clauses are units, and equality is present; the
% 1.82/2.00  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.82/2.00  
% 1.82/2.00     dependent: set(knuth_bendix).
% 1.82/2.00     dependent: set(anl_eq).
% 1.82/2.00     dependent: set(para_from).
% 1.82/2.00     dependent: set(para_into).
% 1.82/2.00     dependent: clear(para_from_right).
% 1.82/2.00     dependent: clear(para_into_right).
% 1.82/2.00     dependent: set(para_from_vars).
% 1.82/2.00     dependent: set(eq_units_both_ways).
% 1.82/2.00     dependent: set(dynamic_demod_all).
% 1.82/2.00     dependent: set(dynamic_demod).
% 1.82/2.00     dependent: set(order_eq).
% 1.82/2.00     dependent: set(back_demod).
% 1.82/2.00     dependent: set(lrpo).
% 1.82/2.00  
% 1.82/2.00  ------------> process usable:
% 1.82/2.00  ** KEPT (pick-wt=9): 1 [] mult(i(op_c),a)!=mult(a,i(op_c)).
% 1.82/2.00  
% 1.82/2.00  ------------> process sos:
% 1.82/2.00  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.82/2.00  ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.82/2.00  ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.82/2.00  ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.82/2.00  ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.82/2.00  ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.82/2.00  ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.82/2.00  ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.82/2.00  ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.82/2.00  ** KEPT (pick-wt=5): 11 [] mult(A,unit)=A.
% 1.82/2.00  ---> New Demodulator: 12 [new_demod,11] mult(A,unit)=A.
% 1.82/2.00  ** KEPT (pick-wt=5): 13 [] mult(unit,A)=A.
% 1.82/2.00  ---> New Demodulator: 14 [new_demod,13] mult(unit,A)=A.
% 1.82/2.00  ** KEPT (pick-wt=15): 16 [copy,15,flip.1] mult(mult(A,mult(B,A)),C)=mult(A,mult(B,mult(A,C))).
% 1.82/2.00  ---> New Demodulator: 17 [new_demod,16] mult(mult(A,mult(B,A)),C)=mult(A,mult(B,mult(A,C))).
% 1.82/2.00  ** KEPT (pick-wt=8): 18 [] mult(i(A),mult(A,B))=B.
% 1.82/2.00  ---> New Demodulator: 19 [new_demod,18] mult(i(A),mult(A,B))=B.
% 1.82/2.00  ** KEPT (pick-wt=7): 20 [] mult(op_c,A)=mult(A,op_c).
% 1.82/2.00    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.82/2.00  >>>> Starting back demodulation with 4.
% 1.82/2.00  >>>> Starting back demodulation with 6.
% 1.82/2.00  >>>> Starting back demodulation with 8.
% 1.82/2.00  >>>> Starting back demodulation with 10.
% 1.82/2.00  >>>> Starting back demodulation with 12.
% 1.82/2.00  >>>> Starting back demodulation with 14.
% 1.82/2.00  >>>> Starting back demodulation with 17.
% 1.82/2.00  >>>> Starting back demodulation with 19.
% 1.82/2.00  ** KEPT (pick-wt=7): 21 [copy,20,flip.1] mult(A,op_c)=mult(op_c,A).
% 1.82/2.00    Following clause subsumed by 20 during input processing: 0 [copy,21,flip.1] mult(op_c,A)=mult(A,op_c).
% 1.82/2.00  
% 1.82/2.00  ======= end of input processing =======
% 1.82/2.00  
% 1.82/2.00  =========== start of search ===========
% 1.82/2.00  
% 1.82/2.00  
% 1.82/2.00  Resetting weight limit to 11.
% 1.82/2.00  
% 1.82/2.00  
% 1.82/2.00  Resetting weight limit to 11.
% 1.82/2.00  
% 1.82/2.00  sos_size=122
% 1.82/2.00  
% 1.82/2.00  -------- PROOF -------- 
% 1.82/2.00  
% 1.82/2.00  ----> UNIT CONFLICT at   0.07 sec ----> 463 [binary,461.1,153.1] $F.
% 1.82/2.00  
% 1.82/2.00  Length of proof is 19.  Level of proof is 6.
% 1.82/2.00  
% 1.82/2.00  ---------------- PROOF ----------------
% 1.82/2.00  % SZS status Unsatisfiable
% 1.82/2.00  % SZS output start Refutation
% See solution above
% 1.82/2.00  ------------ end of proof -------------
% 1.82/2.00  
% 1.82/2.00  
% 1.82/2.00  Search stopped by max_proofs option.
% 1.82/2.00  
% 1.82/2.00  
% 1.82/2.00  Search stopped by max_proofs option.
% 1.82/2.00  
% 1.82/2.00  ============ end of search ============
% 1.82/2.00  
% 1.82/2.00  -------------- statistics -------------
% 1.82/2.00  clauses given                 82
% 1.82/2.00  clauses generated           3512
% 1.82/2.00  clauses kept                 248
% 1.82/2.00  clauses forward subsumed    1498
% 1.82/2.00  clauses back subsumed          0
% 1.82/2.00  Kbytes malloced             4882
% 1.82/2.00  
% 1.82/2.00  ----------- times (seconds) -----------
% 1.82/2.00  user CPU time          0.07          (0 hr, 0 min, 0 sec)
% 1.82/2.00  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.82/2.00  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.82/2.00  
% 1.82/2.00  That finishes the proof of the theorem.
% 1.82/2.00  
% 1.82/2.00  Process 25860 finished Wed Jul 27 05:33:50 2022
% 1.82/2.00  Otter interrupted
% 1.82/2.00  PROOF FOUND
%------------------------------------------------------------------------------