TSTP Solution File: GRP035-3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP035-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n011.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 12:55:55 EDT 2022

% Result   : Unsatisfiable 1.90s 2.09s
% Output   : Refutation 1.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   23 (  20 unt;   0 nHn;  15 RR)
%            Number of literals    :   31 (   4 equ;   9 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | C = D ),
    file('GRP035-3.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ product(A,B,C)
    | ~ product(B,D,E)
    | ~ product(A,E,F)
    | product(C,D,F) ),
    file('GRP035-3.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ subgroup_member(A)
    | ~ subgroup_member(B)
    | ~ product(A,inverse(B),C)
    | subgroup_member(C) ),
    file('GRP035-3.p',unknown),
    [] ).

cnf(5,axiom,
    ~ subgroup_member(c),
    file('GRP035-3.p',unknown),
    [] ).

cnf(7,axiom,
    product(identity,A,A),
    file('GRP035-3.p',unknown),
    [] ).

cnf(8,axiom,
    product(A,identity,A),
    file('GRP035-3.p',unknown),
    [] ).

cnf(9,axiom,
    product(inverse(A),A,identity),
    file('GRP035-3.p',unknown),
    [] ).

cnf(10,axiom,
    product(A,inverse(A),identity),
    file('GRP035-3.p',unknown),
    [] ).

cnf(11,axiom,
    product(A,B,multiply(A,B)),
    file('GRP035-3.p',unknown),
    [] ).

cnf(12,axiom,
    subgroup_member(a),
    file('GRP035-3.p',unknown),
    [] ).

cnf(13,axiom,
    subgroup_member(b),
    file('GRP035-3.p',unknown),
    [] ).

cnf(14,axiom,
    product(a,b,c),
    file('GRP035-3.p',unknown),
    [] ).

cnf(19,plain,
    product(identity,A,inverse(inverse(A))),
    inference(hyper,[status(thm)],[9,3,9,8]),
    [iquote('hyper,9,3,9,8')] ).

cnf(34,plain,
    subgroup_member(identity),
    inference(hyper,[status(thm)],[10,4,13,13]),
    [iquote('hyper,10,4,13,13')] ).

cnf(40,plain,
    subgroup_member(inverse(b)),
    inference(hyper,[status(thm)],[34,4,13,7]),
    [iquote('hyper,34,4,13,7')] ).

cnf(127,plain,
    multiply(a,b) = c,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[11,1,14])]),
    [iquote('hyper,11,1,14,flip.1')] ).

cnf(135,plain,
    multiply(identity,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[11,1,7])]),
    [iquote('hyper,11,1,7,flip.1')] ).

cnf(137,plain,
    subgroup_member(inverse(inverse(b))),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[40,4,34,11]),135]),
    [iquote('hyper,40,4,34,11,demod,135')] ).

cnf(155,plain,
    subgroup_member(inverse(inverse(inverse(b)))),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[137,4,34,11]),135]),
    [iquote('hyper,137,4,34,11,demod,135')] ).

cnf(264,plain,
    subgroup_member(multiply(a,inverse(inverse(inverse(inverse(b)))))),
    inference(hyper,[status(thm)],[155,4,12,11]),
    [iquote('hyper,155,4,12,11')] ).

cnf(333,plain,
    inverse(inverse(A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[19,1,11]),135])]),
    [iquote('hyper,19,1,11,demod,135,flip.1')] ).

cnf(340,plain,
    subgroup_member(c),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[264]),333,333,127]),
    [iquote('back_demod,264,demod,333,333,127')] ).

cnf(341,plain,
    $false,
    inference(binary,[status(thm)],[340,5]),
    [iquote('binary,340.1,5.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP035-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n011.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 05:15:40 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.90/2.09  ----- Otter 3.3f, August 2004 -----
% 1.90/2.09  The process was started by sandbox on n011.cluster.edu,
% 1.90/2.09  Wed Jul 27 05:15:40 2022
% 1.90/2.09  The command was "./otter".  The process ID is 11943.
% 1.90/2.09  
% 1.90/2.09  set(prolog_style_variables).
% 1.90/2.09  set(auto).
% 1.90/2.09     dependent: set(auto1).
% 1.90/2.09     dependent: set(process_input).
% 1.90/2.09     dependent: clear(print_kept).
% 1.90/2.09     dependent: clear(print_new_demod).
% 1.90/2.09     dependent: clear(print_back_demod).
% 1.90/2.09     dependent: clear(print_back_sub).
% 1.90/2.09     dependent: set(control_memory).
% 1.90/2.09     dependent: assign(max_mem, 12000).
% 1.90/2.09     dependent: assign(pick_given_ratio, 4).
% 1.90/2.09     dependent: assign(stats_level, 1).
% 1.90/2.09     dependent: assign(max_seconds, 10800).
% 1.90/2.09  clear(print_given).
% 1.90/2.09  
% 1.90/2.09  list(usable).
% 1.90/2.09  0 [] A=A.
% 1.90/2.09  0 [] product(identity,X,X).
% 1.90/2.09  0 [] product(X,identity,X).
% 1.90/2.09  0 [] product(inverse(X),X,identity).
% 1.90/2.09  0 [] product(X,inverse(X),identity).
% 1.90/2.09  0 [] product(X,Y,multiply(X,Y)).
% 1.90/2.09  0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.90/2.09  0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.90/2.09  0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.90/2.09  0 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.90/2.09  0 [] subgroup_member(a).
% 1.90/2.09  0 [] subgroup_member(b).
% 1.90/2.09  0 [] product(a,b,c).
% 1.90/2.09  0 [] -subgroup_member(c).
% 1.90/2.09  end_of_list.
% 1.90/2.09  
% 1.90/2.09  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.90/2.09  
% 1.90/2.09  This is a Horn set with equality.  The strategy will be
% 1.90/2.09  Knuth-Bendix and hyper_res, with positive clauses in
% 1.90/2.09  sos and nonpositive clauses in usable.
% 1.90/2.09  
% 1.90/2.09     dependent: set(knuth_bendix).
% 1.90/2.09     dependent: set(anl_eq).
% 1.90/2.09     dependent: set(para_from).
% 1.90/2.09     dependent: set(para_into).
% 1.90/2.09     dependent: clear(para_from_right).
% 1.90/2.09     dependent: clear(para_into_right).
% 1.90/2.09     dependent: set(para_from_vars).
% 1.90/2.09     dependent: set(eq_units_both_ways).
% 1.90/2.09     dependent: set(dynamic_demod_all).
% 1.90/2.09     dependent: set(dynamic_demod).
% 1.90/2.09     dependent: set(order_eq).
% 1.90/2.09     dependent: set(back_demod).
% 1.90/2.09     dependent: set(lrpo).
% 1.90/2.09     dependent: set(hyper_res).
% 1.90/2.09     dependent: clear(order_hyper).
% 1.90/2.09  
% 1.90/2.09  ------------> process usable:
% 1.90/2.09  ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.90/2.09  ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.90/2.09  ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.90/2.09  ** KEPT (pick-wt=11): 4 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.90/2.09  ** KEPT (pick-wt=2): 5 [] -subgroup_member(c).
% 1.90/2.09  
% 1.90/2.09  ------------> process sos:
% 1.90/2.09  ** KEPT (pick-wt=3): 6 [] A=A.
% 1.90/2.09  ** KEPT (pick-wt=4): 7 [] product(identity,A,A).
% 1.90/2.09  ** KEPT (pick-wt=4): 8 [] product(A,identity,A).
% 1.90/2.09  ** KEPT (pick-wt=5): 9 [] product(inverse(A),A,identity).
% 1.90/2.09  ** KEPT (pick-wt=5): 10 [] product(A,inverse(A),identity).
% 1.90/2.09  ** KEPT (pick-wt=6): 11 [] product(A,B,multiply(A,B)).
% 1.90/2.09  ** KEPT (pick-wt=2): 12 [] subgroup_member(a).
% 1.90/2.09  ** KEPT (pick-wt=2): 13 [] subgroup_member(b).
% 1.90/2.09  ** KEPT (pick-wt=4): 14 [] product(a,b,c).
% 1.90/2.09    Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.90/2.09  
% 1.90/2.09  ======= end of input processing =======
% 1.90/2.09  
% 1.90/2.09  =========== start of search ===========
% 1.90/2.09  
% 1.90/2.09  -------- PROOF -------- 
% 1.90/2.09  
% 1.90/2.09  ----> UNIT CONFLICT at   0.01 sec ----> 341 [binary,340.1,5.1] $F.
% 1.90/2.09  
% 1.90/2.09  Length of proof is 10.  Level of proof is 6.
% 1.90/2.09  
% 1.90/2.09  ---------------- PROOF ----------------
% 1.90/2.09  % SZS status Unsatisfiable
% 1.90/2.09  % SZS output start Refutation
% See solution above
% 1.90/2.09  ------------ end of proof -------------
% 1.90/2.09  
% 1.90/2.09  
% 1.90/2.09  Search stopped by max_proofs option.
% 1.90/2.09  
% 1.90/2.09  
% 1.90/2.09  Search stopped by max_proofs option.
% 1.90/2.09  
% 1.90/2.09  ============ end of search ============
% 1.90/2.09  
% 1.90/2.09  -------------- statistics -------------
% 1.90/2.09  clauses given                 28
% 1.90/2.09  clauses generated            800
% 1.90/2.09  clauses kept                 331
% 1.90/2.09  clauses forward subsumed     619
% 1.90/2.09  clauses back subsumed          8
% 1.90/2.09  Kbytes malloced             1953
% 1.90/2.09  
% 1.90/2.09  ----------- times (seconds) -----------
% 1.90/2.09  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.90/2.09  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.90/2.09  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.90/2.09  
% 1.90/2.09  That finishes the proof of the theorem.
% 1.90/2.09  
% 1.90/2.09  Process 11943 finished Wed Jul 27 05:15:42 2022
% 1.90/2.09  Otter interrupted
% 1.90/2.09  PROOF FOUND
%------------------------------------------------------------------------------