TSTP Solution File: SET858-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n018.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 13:14:25 EDT 2022

% Result   : Unsatisfiable 1.94s 2.14s
% Output   : Refutation 1.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   20 (  10 unt;   9 nHn;  19 RR)
%            Number of literals    :   46 (   3 equ;  17 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   27 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ c_lesse_quals(v_n,v_m,tc_set(tc_set(t_a))),
    file('SET858-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ c_lesse_quals(v_m,v_n,tc_set(tc_set(t_a))),
    file('SET858-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ c_lesse_quals(A,B,tc_set(C))
    | ~ c_lesse_quals(D,A,tc_set(C))
    | c_lesse_quals(D,B,tc_set(C)) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | ~ c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | c_in(c_Zorn_OTFin__linear__lemma1__1(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | c_lesse_quals(D,A,tc_set(tc_set(C)))
    | c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | ~ c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | c_lesse_quals(D,A,tc_set(tc_set(C)))
    | c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(B,A,C),A,tc_set(tc_set(C)))
    | c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | ~ c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | c_Zorn_OTFin__linear__lemma1__1(B,A,C) != A
    | c_lesse_quals(D,A,tc_set(tc_set(C)))
    | c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | ~ c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | ~ c_lesse_quals(c_Zorn_Osucc(B,c_Zorn_OTFin__linear__lemma1__1(B,A,C),C),A,tc_set(tc_set(C)))
    | c_lesse_quals(D,A,tc_set(tc_set(C)))
    | c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | ~ c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
    | ~ c_lesse_quals(A,D,tc_set(tc_set(C)))
    | c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
    | A = D ),
    file('SET858-2.p',unknown),
    [] ).

cnf(16,axiom,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET858-2.p',unknown),
    [] ).

cnf(17,axiom,
    c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET858-2.p',unknown),
    [] ).

cnf(18,axiom,
    c_lesse_quals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))),
    file('SET858-2.p',unknown),
    [] ).

cnf(30,plain,
    ( c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[17,5,16]),1]),
    [iquote('hyper,17,5,16,unit_del,1')] ).

cnf(32,plain,
    ( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[17,4,16]),1]),
    [iquote('hyper,17,4,16,unit_del,1')] ).

cnf(87,plain,
    c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[30,3,18]),2]),
    [iquote('hyper,30,3,18,unit_del,2')] ).

cnf(376,plain,
    c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[32,3,18]),2]),
    [iquote('hyper,32,3,18,unit_del,2')] ).

cnf(379,plain,
    ( c_lesse_quals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a)))
    | c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m ),
    inference(hyper,[status(thm)],[376,8,16,87]),
    [iquote('hyper,376,8,16,87')] ).

cnf(459,plain,
    ( c_lesse_quals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a)))
    | c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[379,6,16,17]),1]),
    [iquote('hyper,379,6,16,17,unit_del,1')] ).

cnf(856,plain,
    c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))),
    inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[459,7,16,17]),1])]),
    [iquote('hyper,459,7,16,17,unit_del,1,factor_simp')] ).

cnf(870,plain,
    c_lesse_quals(v_m,v_n,tc_set(tc_set(t_a))),
    inference(hyper,[status(thm)],[856,3,18]),
    [iquote('hyper,856,3,18')] ).

cnf(871,plain,
    $false,
    inference(binary,[status(thm)],[870,2]),
    [iquote('binary,870.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n018.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 10:52:46 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.71/1.92  ----- Otter 3.3f, August 2004 -----
% 1.71/1.92  The process was started by sandbox on n018.cluster.edu,
% 1.71/1.92  Wed Jul 27 10:52:46 2022
% 1.71/1.92  The command was "./otter".  The process ID is 13437.
% 1.71/1.92  
% 1.71/1.92  set(prolog_style_variables).
% 1.71/1.92  set(auto).
% 1.71/1.92     dependent: set(auto1).
% 1.71/1.92     dependent: set(process_input).
% 1.71/1.92     dependent: clear(print_kept).
% 1.71/1.92     dependent: clear(print_new_demod).
% 1.71/1.92     dependent: clear(print_back_demod).
% 1.71/1.92     dependent: clear(print_back_sub).
% 1.71/1.92     dependent: set(control_memory).
% 1.71/1.92     dependent: assign(max_mem, 12000).
% 1.71/1.92     dependent: assign(pick_given_ratio, 4).
% 1.71/1.92     dependent: assign(stats_level, 1).
% 1.71/1.92     dependent: assign(max_seconds, 10800).
% 1.71/1.92  clear(print_given).
% 1.71/1.92  
% 1.71/1.92  list(usable).
% 1.71/1.92  0 [] A=A.
% 1.71/1.92  0 [] c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.71/1.92  0 [] c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.71/1.92  0 [] -c_lesse_quals(v_n,v_m,tc_set(tc_set(t_a))).
% 1.71/1.92  0 [] -c_lesse_quals(v_m,v_n,tc_set(tc_set(t_a))).
% 1.71/1.92  0 [] -c_lesse_quals(V_B,V_C,tc_set(T_a))| -c_lesse_quals(V_A,V_B,tc_set(T_a))|c_lesse_quals(V_A,V_C,tc_set(T_a)).
% 1.71/1.92  0 [] c_lesse_quals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))).
% 1.71/1.92  0 [] -c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))).
% 1.71/1.92  0 [] -c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))).
% 1.71/1.92  0 [] -c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a)!=V_m|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))).
% 1.71/1.92  0 [] -c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_lesse_quals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))).
% 1.71/1.92  0 [] -c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_lesse_quals(V_U,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))|V_U=V_m.
% 1.71/1.92  end_of_list.
% 1.71/1.92  
% 1.71/1.92  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.71/1.92  
% 1.71/1.92  This ia a non-Horn set with equality.  The strategy will be
% 1.71/1.92  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.92  deletion, with positive clauses in sos and nonpositive
% 1.71/1.92  clauses in usable.
% 1.71/1.92  
% 1.71/1.92     dependent: set(knuth_bendix).
% 1.71/1.92     dependent: set(anl_eq).
% 1.71/1.92     dependent: set(para_from).
% 1.71/1.92     dependent: set(para_into).
% 1.71/1.92     dependent: clear(para_from_right).
% 1.71/1.92     dependent: clear(para_into_right).
% 1.71/1.92     dependent: set(para_from_vars).
% 1.71/1.92     dependent: set(eq_units_both_ways).
% 1.71/1.92     dependent: set(dynamic_demod_all).
% 1.71/1.92     dependent: set(dynamic_demod).
% 1.71/1.92     dependent: set(order_eq).
% 1.71/1.92     dependent: set(back_demod).
% 1.71/1.92     dependent: set(lrpo).
% 1.71/1.92     dependent: set(hyper_res).
% 1.71/1.92     dependent: set(unit_deletion).
% 1.71/1.92     dependent: set(factor).
% 1.71/1.92  
% 1.71/1.92  ------------> process usable:
% 1.71/1.92  ** KEPT (pick-wt=6): 1 [] -c_lesse_quals(v_n,v_m,tc_set(tc_set(t_a))).
% 1.71/1.92  ** KEPT (pick-wt=6): 2 [] -c_lesse_quals(v_m,v_n,tc_set(tc_set(t_a))).
% 1.71/1.92  ** KEPT (pick-wt=15): 3 [] -c_lesse_quals(A,B,tc_set(C))| -c_lesse_quals(D,A,tc_set(C))|c_lesse_quals(D,B,tc_set(C)).
% 1.71/1.92  ** KEPT (pick-wt=42): 4 [] -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))| -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))|c_in(c_Zorn_OTFin__linear__lemma1__1(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(C)))|c_lesse_quals(D,A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))).
% 1.71/1.92  ** KEPT (pick-wt=40): 5 [] -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))| -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))|c_lesse_quals(D,A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(B,A,C),A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))).
% 1.94/2.14  ** KEPT (pick-wt=37): 6 [] -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))| -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))|c_Zorn_OTFin__linear__lemma1__1(B,A,C)!=A|c_lesse_quals(D,A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))).
% 1.94/2.14  ** KEPT (pick-wt=43): 7 [] -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))| -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))| -c_lesse_quals(c_Zorn_Osucc(B,c_Zorn_OTFin__linear__lemma1__1(B,A,C),C),A,tc_set(tc_set(C)))|c_lesse_quals(D,A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))).
% 1.94/2.14  ** KEPT (pick-wt=34): 8 [] -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))| -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))| -c_lesse_quals(A,D,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))|A=D.
% 1.94/2.14  
% 1.94/2.14  ------------> process sos:
% 1.94/2.14  ** KEPT (pick-wt=3): 15 [] A=A.
% 1.94/2.14  ** KEPT (pick-wt=8): 16 [] c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.94/2.14  ** KEPT (pick-wt=8): 17 [] c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.94/2.14  ** KEPT (pick-wt=9): 18 [] c_lesse_quals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))).
% 1.94/2.14    Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.94/2.14  15 back subsumes 14.
% 1.94/2.14  
% 1.94/2.14  ======= end of input processing =======
% 1.94/2.14  
% 1.94/2.14  =========== start of search ===========
% 1.94/2.14  
% 1.94/2.14  -------- PROOF -------- 
% 1.94/2.14  
% 1.94/2.14  ----> UNIT CONFLICT at   0.21 sec ----> 871 [binary,870.1,2.1] $F.
% 1.94/2.14  
% 1.94/2.14  Length of proof is 8.  Level of proof is 6.
% 1.94/2.14  
% 1.94/2.14  ---------------- PROOF ----------------
% 1.94/2.14  % SZS status Unsatisfiable
% 1.94/2.14  % SZS output start Refutation
% See solution above
% 1.94/2.14  ------------ end of proof -------------
% 1.94/2.14  
% 1.94/2.14  
% 1.94/2.14  Search stopped by max_proofs option.
% 1.94/2.14  
% 1.94/2.14  
% 1.94/2.14  Search stopped by max_proofs option.
% 1.94/2.14  
% 1.94/2.14  ============ end of search ============
% 1.94/2.14  
% 1.94/2.14  -------------- statistics -------------
% 1.94/2.14  clauses given                 44
% 1.94/2.14  clauses generated           2255
% 1.94/2.14  clauses kept                 870
% 1.94/2.14  clauses forward subsumed    1371
% 1.94/2.14  clauses back subsumed        155
% 1.94/2.14  Kbytes malloced             2929
% 1.94/2.14  
% 1.94/2.14  ----------- times (seconds) -----------
% 1.94/2.14  user CPU time          0.21          (0 hr, 0 min, 0 sec)
% 1.94/2.14  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.94/2.14  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.94/2.14  
% 1.94/2.14  That finishes the proof of the theorem.
% 1.94/2.14  
% 1.94/2.14  Process 13437 finished Wed Jul 27 10:52:48 2022
% 1.94/2.14  Otter interrupted
% 1.94/2.14  PROOF FOUND
%------------------------------------------------------------------------------