TSTP Solution File: SET825-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% 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 13:14:19 EDT 2022

% Result   : Unsatisfiable 1.66s 1.89s
% Output   : Refutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   8 unt;   2 nHn;  12 RR)
%            Number of literals    :   20 (   2 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-4 aty)
%            Number of variables   :    9 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_in(c_Pair(A,B,C,C),c_Relation_OId,tc_prod(C,C))
    | A = B ),
    file('SET825-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ v_Q(v_m),
    file('SET825-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
    file('SET825-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(c_Suc(v_x(A)),c_Suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
    file('SET825-2.p',unknown),
    [] ).

cnf(6,axiom,
    c_in(c_Pair(A,A,B,B),c_Relation_OId,tc_prod(B,B)),
    file('SET825-2.p',unknown),
    [] ).

cnf(7,axiom,
    v_Q(v_n),
    file('SET825-2.p',unknown),
    [] ).

cnf(8,plain,
    ( v_Q(A)
    | ~ c_in(c_Pair(v_n,A,B,B),c_Relation_OId,tc_prod(B,B)) ),
    inference(para_into,[status(thm),theory(equality)],[7,1]),
    [iquote('para_into,7.1.1,1.2.1')] ).

cnf(9,plain,
    ( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
    inference(hyper,[status(thm)],[6,3]),
    [iquote('hyper,6,3')] ).

cnf(23,plain,
    c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[9,8]),2]),
    [iquote('hyper,9,8,unit_del,2')] ).

cnf(25,plain,
    v_xa(c_Relation_OId) = v_x(c_Relation_OId),
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[23,1])]),
    [iquote('hyper,23,1,flip.1')] ).

cnf(29,plain,
    c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
    inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[25,4]),6,6]),
    [iquote('para_from,25.1.1,4.2.1.2.1,unit_del,6,6')] ).

cnf(30,plain,
    v_Q(v_m),
    inference(hyper,[status(thm)],[29,8]),
    [iquote('hyper,29,8')] ).

cnf(31,plain,
    $false,
    inference(binary,[status(thm)],[30,2]),
    [iquote('binary,30.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12  % 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 10:44:04 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.66/1.89  ----- Otter 3.3f, August 2004 -----
% 1.66/1.89  The process was started by sandbox on n028.cluster.edu,
% 1.66/1.89  Wed Jul 27 10:44:04 2022
% 1.66/1.89  The command was "./otter".  The process ID is 26330.
% 1.66/1.89  
% 1.66/1.89  set(prolog_style_variables).
% 1.66/1.89  set(auto).
% 1.66/1.89     dependent: set(auto1).
% 1.66/1.89     dependent: set(process_input).
% 1.66/1.89     dependent: clear(print_kept).
% 1.66/1.89     dependent: clear(print_new_demod).
% 1.66/1.89     dependent: clear(print_back_demod).
% 1.66/1.89     dependent: clear(print_back_sub).
% 1.66/1.89     dependent: set(control_memory).
% 1.66/1.89     dependent: assign(max_mem, 12000).
% 1.66/1.89     dependent: assign(pick_given_ratio, 4).
% 1.66/1.89     dependent: assign(stats_level, 1).
% 1.66/1.89     dependent: assign(max_seconds, 10800).
% 1.66/1.89  clear(print_given).
% 1.66/1.89  
% 1.66/1.89  list(usable).
% 1.66/1.89  0 [] A=A.
% 1.66/1.89  0 [] c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)).
% 1.66/1.89  0 [] -c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a))|V_a=V_b.
% 1.66/1.89  0 [] v_Q(v_n).
% 1.66/1.89  0 [] -v_Q(v_m).
% 1.66/1.89  0 [] c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))|c_in(c_Pair(v_x(V_U),v_xa(V_U),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)).
% 1.66/1.89  0 [] c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_Suc(v_x(V_U)),c_Suc(v_xa(V_U)),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)).
% 1.66/1.89  end_of_list.
% 1.66/1.89  
% 1.66/1.89  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.66/1.89  
% 1.66/1.89  This ia a non-Horn set with equality.  The strategy will be
% 1.66/1.89  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.66/1.89  deletion, with positive clauses in sos and nonpositive
% 1.66/1.89  clauses in usable.
% 1.66/1.89  
% 1.66/1.89     dependent: set(knuth_bendix).
% 1.66/1.89     dependent: set(anl_eq).
% 1.66/1.89     dependent: set(para_from).
% 1.66/1.89     dependent: set(para_into).
% 1.66/1.89     dependent: clear(para_from_right).
% 1.66/1.89     dependent: clear(para_into_right).
% 1.66/1.89     dependent: set(para_from_vars).
% 1.66/1.89     dependent: set(eq_units_both_ways).
% 1.66/1.89     dependent: set(dynamic_demod_all).
% 1.66/1.89     dependent: set(dynamic_demod).
% 1.66/1.89     dependent: set(order_eq).
% 1.66/1.89     dependent: set(back_demod).
% 1.66/1.89     dependent: set(lrpo).
% 1.66/1.89     dependent: set(hyper_res).
% 1.66/1.89     dependent: set(unit_deletion).
% 1.66/1.89     dependent: set(factor).
% 1.66/1.89  
% 1.66/1.89  ------------> process usable:
% 1.66/1.89  ** KEPT (pick-wt=13): 1 [] -c_in(c_Pair(A,B,C,C),c_Relation_OId,tc_prod(C,C))|A=B.
% 1.66/1.89  ** KEPT (pick-wt=2): 2 [] -v_Q(v_m).
% 1.66/1.89  ** KEPT (pick-wt=32): 3 [] c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|c_in(c_Pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)).
% 1.66/1.89  ** KEPT (pick-wt=34): 4 [] c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_Suc(v_x(A)),c_Suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))| -c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)).
% 1.66/1.89  
% 1.66/1.89  ------------> process sos:
% 1.66/1.89  ** KEPT (pick-wt=3): 5 [] A=A.
% 1.66/1.89  ** KEPT (pick-wt=10): 6 [] c_in(c_Pair(A,A,B,B),c_Relation_OId,tc_prod(B,B)).
% 1.66/1.89  ** KEPT (pick-wt=2): 7 [] v_Q(v_n).
% 1.66/1.89    Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.66/1.89  
% 1.66/1.89  ======= end of input processing =======
% 1.66/1.89  
% 1.66/1.89  =========== start of search ===========
% 1.66/1.89  
% 1.66/1.89  -------- PROOF -------- 
% 1.66/1.89  
% 1.66/1.89  ----> UNIT CONFLICT at   0.00 sec ----> 31 [binary,30.1,2.1] $F.
% 1.66/1.89  
% 1.66/1.89  Length of proof is 6.  Level of proof is 5.
% 1.66/1.89  
% 1.66/1.89  ---------------- PROOF ----------------
% 1.66/1.89  % SZS status Unsatisfiable
% 1.66/1.89  % SZS output start Refutation
% See solution above
% 1.66/1.89  ------------ end of proof -------------
% 1.66/1.89  
% 1.66/1.89  
% 1.66/1.89  Search stopped by max_proofs option.
% 1.66/1.89  
% 1.66/1.89  
% 1.66/1.89  Search stopped by max_proofs option.
% 1.66/1.89  
% 1.66/1.89  ============ end of search ============
% 1.66/1.89  
% 1.66/1.89  -------------- statistics -------------
% 1.66/1.89  clauses given                  9
% 1.66/1.89  clauses generated             31
% 1.66/1.89  clauses kept                  29
% 1.66/1.89  clauses forward subsumed      12
% 1.66/1.89  clauses back subsumed          1
% 1.66/1.89  Kbytes malloced              976
% 1.66/1.89  
% 1.66/1.89  ----------- times (seconds) -----------
% 1.66/1.89  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.89  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.89  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.66/1.89  
% 1.66/1.89  That finishes the proof of the theorem.
% 1.66/1.89  
% 1.66/1.89  Process 26330 finished Wed Jul 27 10:44:05 2022
% 1.66/1.89  Otter interrupted
% 1.66/1.89  PROOF FOUND
%------------------------------------------------------------------------------