TSTP Solution File: SET864-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET864-2 : TPTP v8.1.0. Released v3.2.0.
% 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 13:14:26 EDT 2022

% Result   : Unsatisfiable 2.02s 2.16s
% Output   : Refutation 2.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   6 unt;   0 nHn;  11 RR)
%            Number of literals    :   18 (   4 equ;   9 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_in(A,B,tc_set(C))
    | ~ c_in(D,c_Zorn_Omaxchain(B,C),tc_set(tc_set(C)))
    | ~ c_lesse_quals(c_Union(D,C),A,tc_set(C))
    | c_Union(D,C) = A ),
    file('SET864-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( c_in(v_x(A),v_S,tc_set(t_a))
    | ~ c_in(A,v_S,tc_set(t_a)) ),
    file('SET864-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( c_lesse_quals(A,v_x(A),tc_set(t_a))
    | ~ c_in(A,v_S,tc_set(t_a)) ),
    file('SET864-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( A != v_x(A)
    | ~ c_in(A,v_S,tc_set(t_a)) ),
    file('SET864-2.p',unknown),
    [] ).

cnf(5,plain,
    ( v_x(A) != A
    | ~ c_in(A,v_S,tc_set(t_a)) ),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
    [iquote('copy,4,flip.1')] ).

cnf(7,axiom,
    c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET864-2.p',unknown),
    [] ).

cnf(8,axiom,
    c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
    file('SET864-2.p',unknown),
    [] ).

cnf(9,plain,
    c_lesse_quals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)),
    inference(hyper,[status(thm)],[8,3]),
    [iquote('hyper,8,3')] ).

cnf(10,plain,
    c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)),
    inference(hyper,[status(thm)],[8,2]),
    [iquote('hyper,8,2')] ).

cnf(18,plain,
    v_x(c_Union(v_c,t_a)) = c_Union(v_c,t_a),
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[9,1,10,7])]),
    [iquote('hyper,9,1,10,7,flip.1')] ).

cnf(21,plain,
    $false,
    inference(hyper,[status(thm)],[18,5,8]),
    [iquote('hyper,18,5,8')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET864-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 11:01:27 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 2.02/2.16  ----- Otter 3.3f, August 2004 -----
% 2.02/2.16  The process was started by sandbox2 on n015.cluster.edu,
% 2.02/2.16  Wed Jul 27 11:01:27 2022
% 2.02/2.16  The command was "./otter".  The process ID is 3130.
% 2.02/2.16  
% 2.02/2.16  set(prolog_style_variables).
% 2.02/2.16  set(auto).
% 2.02/2.16     dependent: set(auto1).
% 2.02/2.16     dependent: set(process_input).
% 2.02/2.16     dependent: clear(print_kept).
% 2.02/2.16     dependent: clear(print_new_demod).
% 2.02/2.16     dependent: clear(print_back_demod).
% 2.02/2.16     dependent: clear(print_back_sub).
% 2.02/2.16     dependent: set(control_memory).
% 2.02/2.16     dependent: assign(max_mem, 12000).
% 2.02/2.16     dependent: assign(pick_given_ratio, 4).
% 2.02/2.16     dependent: assign(stats_level, 1).
% 2.02/2.16     dependent: assign(max_seconds, 10800).
% 2.02/2.16  clear(print_given).
% 2.02/2.16  
% 2.02/2.16  list(usable).
% 2.02/2.16  0 [] A=A.
% 2.02/2.16  0 [] -c_in(V_u,V_S,tc_set(T_a))| -c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))| -c_lesse_quals(c_Union(V_c,T_a),V_u,tc_set(T_a))|c_Union(V_c,T_a)=V_u.
% 2.02/2.16  0 [] c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 2.02/2.16  0 [] c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)).
% 2.02/2.16  0 [] c_in(v_x(V_U),v_S,tc_set(t_a))| -c_in(V_U,v_S,tc_set(t_a)).
% 2.02/2.16  0 [] c_lesse_quals(V_U,v_x(V_U),tc_set(t_a))| -c_in(V_U,v_S,tc_set(t_a)).
% 2.02/2.16  0 [] V_U!=v_x(V_U)| -c_in(V_U,v_S,tc_set(t_a)).
% 2.02/2.16  end_of_list.
% 2.02/2.16  
% 2.02/2.16  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.02/2.16  
% 2.02/2.16  This is a Horn set with equality.  The strategy will be
% 2.02/2.16  Knuth-Bendix and hyper_res, with positive clauses in
% 2.02/2.16  sos and nonpositive clauses in usable.
% 2.02/2.16  
% 2.02/2.16     dependent: set(knuth_bendix).
% 2.02/2.16     dependent: set(anl_eq).
% 2.02/2.16     dependent: set(para_from).
% 2.02/2.16     dependent: set(para_into).
% 2.02/2.16     dependent: clear(para_from_right).
% 2.02/2.16     dependent: clear(para_into_right).
% 2.02/2.16     dependent: set(para_from_vars).
% 2.02/2.16     dependent: set(eq_units_both_ways).
% 2.02/2.16     dependent: set(dynamic_demod_all).
% 2.02/2.16     dependent: set(dynamic_demod).
% 2.02/2.16     dependent: set(order_eq).
% 2.02/2.16     dependent: set(back_demod).
% 2.02/2.16     dependent: set(lrpo).
% 2.02/2.16     dependent: set(hyper_res).
% 2.02/2.16     dependent: clear(order_hyper).
% 2.02/2.16  
% 2.02/2.16  ------------> process usable:
% 2.02/2.16  ** KEPT (pick-wt=25): 1 [] -c_in(A,B,tc_set(C))| -c_in(D,c_Zorn_Omaxchain(B,C),tc_set(tc_set(C)))| -c_lesse_quals(c_Union(D,C),A,tc_set(C))|c_Union(D,C)=A.
% 2.02/2.16  ** KEPT (pick-wt=11): 2 [] c_in(v_x(A),v_S,tc_set(t_a))| -c_in(A,v_S,tc_set(t_a)).
% 2.02/2.16  ** KEPT (pick-wt=11): 3 [] c_lesse_quals(A,v_x(A),tc_set(t_a))| -c_in(A,v_S,tc_set(t_a)).
% 2.02/2.16  ** KEPT (pick-wt=9): 5 [copy,4,flip.1] v_x(A)!=A| -c_in(A,v_S,tc_set(t_a)).
% 2.02/2.16  
% 2.02/2.16  ------------> process sos:
% 2.02/2.16  ** KEPT (pick-wt=3): 6 [] A=A.
% 2.02/2.16  ** KEPT (pick-wt=8): 7 [] c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 2.02/2.16  ** KEPT (pick-wt=7): 8 [] c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)).
% 2.02/2.16    Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 2.02/2.16  
% 2.02/2.16  ======= end of input processing =======
% 2.02/2.16  
% 2.02/2.16  =========== start of search ===========
% 2.02/2.16  
% 2.02/2.16  -------- PROOF -------- 
% 2.02/2.16  
% 2.02/2.16  -----> EMPTY CLAUSE at   0.00 sec ----> 21 [hyper,18,5,8] $F.
% 2.02/2.16  
% 2.02/2.16  Length of proof is 4.  Level of proof is 2.
% 2.02/2.16  
% 2.02/2.16  ---------------- PROOF ----------------
% 2.02/2.16  % SZS status Unsatisfiable
% 2.02/2.16  % SZS output start Refutation
% See solution above
% 2.02/2.16  ------------ end of proof -------------
% 2.02/2.16  
% 2.02/2.16  
% 2.02/2.16  Search stopped by max_proofs option.
% 2.02/2.16  
% 2.02/2.16  
% 2.02/2.16  Search stopped by max_proofs option.
% 2.02/2.16  
% 2.02/2.16  ============ end of search ============
% 2.02/2.16  
% 2.02/2.16  -------------- statistics -------------
% 2.02/2.16  clauses given                  7
% 2.02/2.16  clauses generated             11
% 2.02/2.16  clauses kept                  18
% 2.02/2.16  clauses forward subsumed       6
% 2.02/2.16  clauses back subsumed          0
% 2.02/2.16  Kbytes malloced              976
% 2.02/2.16  
% 2.02/2.16  ----------- times (seconds) -----------
% 2.02/2.16  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 2.02/2.16  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.02/2.16  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 2.02/2.16  
% 2.02/2.16  That finishes the proof of the theorem.
% 2.02/2.16  
% 2.02/2.16  Process 3130 finished Wed Jul 27 11:01:28 2022
% 2.02/2.16  Otter interrupted
% 2.02/2.16  PROOF FOUND
%------------------------------------------------------------------------------