TSTP Solution File: SET843-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET843-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 : Tue Apr 30 20:40:30 EDT 2024

% Result   : Unsatisfiable 1.89s 0.65s
% Output   : CNFRefutation 2.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   68 (  12 unt;   0 def)
%            Number of atoms       :  150 (  41 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  153 (  71   ~;  75   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   11 (   9 usr;   8 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   75 (  75   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f309,axiom,
    ! [V_B,V_A,T_a] :
      ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
      | ~ c_lessequals(V_A,V_B,tc_set(T_a))
      | V_A = V_B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f310,axiom,
    ! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1360,axiom,
    ! [V_B,V_A,T_a] :
      ( ~ c_in(V_B,V_A,tc_set(T_a))
      | c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1361,axiom,
    ! [V_x,V_S,T_a] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1362,axiom,
    ! [V_x,V_S,T_a] :
      ( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
      | c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1363,axiom,
    ! [V_Y,V_S,T_a] :
      ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a))))
      | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1364,axiom,
    ! [V_m,V_S,T_a,V_n] :
      ( ~ 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)))
      | V_m != c_Zorn_Osucc(V_S,V_m,T_a)
      | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1365,negated_conjecture,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1366,negated_conjecture,
    ( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1367,negated_conjecture,
    ( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
    | v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1784,plain,
    ! [V_B,V_A] :
      ( ! [T_a] :
          ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
          | ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
      | V_A = V_B ),
    inference(miniscoping,[status(esa)],[f309]) ).

fof(f1785,plain,
    ! [X0,X1,X2] :
      ( ~ c_lessequals(X0,X1,tc_set(X2))
      | ~ c_lessequals(X1,X0,tc_set(X2))
      | X1 = X0 ),
    inference(cnf_transformation,[status(esa)],[f1784]) ).

fof(f1786,plain,
    ! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
    inference(cnf_transformation,[status(esa)],[f310]) ).

fof(f2845,plain,
    ! [X0,X1,X2] :
      ( ~ c_in(X0,X1,tc_set(X2))
      | c_lessequals(X0,c_Union(X1,X2),tc_set(X2)) ),
    inference(cnf_transformation,[status(esa)],[f1360]) ).

fof(f2846,plain,
    ! [X0,X1,X2] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
    inference(cnf_transformation,[status(esa)],[f1361]) ).

fof(f2847,plain,
    ! [X0,X1,X2] :
      ( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
      | c_in(c_Zorn_Osucc(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
    inference(cnf_transformation,[status(esa)],[f1362]) ).

fof(f2848,plain,
    ! [X0,X1,X2] :
      ( ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2))))
      | c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
    inference(cnf_transformation,[status(esa)],[f1363]) ).

fof(f2849,plain,
    ! [V_m,T_a,V_n] :
      ( ! [V_S] :
          ( ~ 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)))
          | V_m != c_Zorn_Osucc(V_S,V_m,T_a) )
      | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) ),
    inference(miniscoping,[status(esa)],[f1364]) ).

fof(f2850,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
      | ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
      | X0 != c_Zorn_Osucc(X1,X0,X2)
      | c_lessequals(X3,X0,tc_set(tc_set(X2))) ),
    inference(cnf_transformation,[status(esa)],[f2849]) ).

fof(f2851,plain,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    inference(cnf_transformation,[status(esa)],[f1365]) ).

fof(f2852,plain,
    ( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
    inference(cnf_transformation,[status(esa)],[f1366]) ).

fof(f2853,plain,
    ( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
    | v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
    inference(cnf_transformation,[status(esa)],[f1367]) ).

fof(f2854,plain,
    ( spl0_0
  <=> v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
    introduced(split_symbol_definition) ).

fof(f2855,plain,
    ( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f2854]) ).

fof(f2857,plain,
    ( spl0_1
  <=> v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
    introduced(split_symbol_definition) ).

fof(f2860,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f2852,f2854,f2857]) ).

fof(f2861,plain,
    ( spl0_1
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f2853,f2857,f2854]) ).

fof(f2863,plain,
    ( spl0_2
  <=> c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
    introduced(split_symbol_definition) ).

fof(f2865,plain,
    ( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f2863]) ).

fof(f2870,plain,
    ! [X0,X1,X2] :
      ( ~ c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
      | X2 = c_Union(X0,X1)
      | ~ c_in(X2,X0,tc_set(X1)) ),
    inference(resolution,[status(thm)],[f1785,f2845]) ).

fof(f2871,plain,
    ! [X0,X1,X2] :
      ( ~ c_lessequals(c_Zorn_Osucc(X0,X1,X2),X1,tc_set(tc_set(X2)))
      | X1 = c_Zorn_Osucc(X0,X1,X2) ),
    inference(resolution,[status(thm)],[f1785,f2846]) ).

fof(f2872,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_lessequals(X0,X1,tc_set(tc_set(X2)))
      | X1 = X0
      | ~ c_in(X0,c_Zorn_OTFin(X3,X2),tc_set(tc_set(X2)))
      | ~ c_in(X1,c_Zorn_OTFin(X3,X2),tc_set(tc_set(X2)))
      | X0 != c_Zorn_Osucc(X3,X0,X2) ),
    inference(resolution,[status(thm)],[f1785,f2850]) ).

fof(f2874,plain,
    ! [X0,X1,X2] :
      ( c_Union(X0,tc_set(X1)) = c_Zorn_Osucc(X2,c_Union(X0,tc_set(X1)),X1)
      | ~ c_in(c_Zorn_Osucc(X2,c_Union(X0,tc_set(X1)),X1),X0,tc_set(tc_set(X1))) ),
    inference(resolution,[status(thm)],[f2871,f2845]) ).

fof(f2877,plain,
    ( spl0_3
  <=> c_lessequals(v_m,v_m,tc_set(tc_set(t_a))) ),
    introduced(split_symbol_definition) ).

fof(f2879,plain,
    ( ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a)))
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f2877]) ).

fof(f2889,plain,
    ! [X0,X1,X2] :
      ( c_Union(X0,X1) = c_Union(X2,X1)
      | ~ c_in(c_Union(X0,X1),X2,tc_set(X1))
      | ~ c_in(c_Union(X2,X1),X0,tc_set(X1)) ),
    inference(resolution,[status(thm)],[f2870,f2845]) ).

fof(f2906,plain,
    ! [X0] :
      ( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
      | c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
      | ~ spl0_0 ),
    inference(paramodulation,[status(thm)],[f2855,f2845]) ).

fof(f2910,plain,
    ! [X0] :
      ( ~ c_in(c_Zorn_Osucc(X0,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
      | v_m = c_Zorn_Osucc(X0,v_m,t_a)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f2906,f2871]) ).

fof(f2916,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2879,f1786]) ).

fof(f2917,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f2916]) ).

fof(f2934,plain,
    ( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
    | ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f2910,f2847]) ).

fof(f2935,plain,
    ( spl0_1
    | ~ spl0_2
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f2934,f2857,f2863,f2854]) ).

fof(f2936,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2865,f2851]) ).

fof(f2937,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f2936]) ).

fof(f2979,plain,
    ! [X0,X1] :
      ( c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)) = c_Zorn_Osucc(X0,c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),X1)
      | ~ c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_OTFin(X0,X1),tc_set(tc_set(X1))) ),
    inference(resolution,[status(thm)],[f2874,f2847]) ).

fof(f2981,plain,
    ! [X0,X1] :
      ( c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)) = c_Zorn_Osucc(X0,c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),X1)
      | ~ c_lessequals(c_Zorn_OTFin(X0,X1),c_Zorn_OTFin(X0,X1),tc_set(tc_set(tc_set(X1)))) ),
    inference(resolution,[status(thm)],[f2979,f2848]) ).

fof(f2982,plain,
    ! [X0,X1] : c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)) = c_Zorn_Osucc(X0,c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),X1),
    inference(forward_subsumption_resolution,[status(thm)],[f2981,f1786]) ).

fof(f2986,plain,
    ( spl0_10
  <=> c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),t_a) ),
    introduced(split_symbol_definition) ).

fof(f2988,plain,
    ( c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),t_a)
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f2986]) ).

fof(f2989,plain,
    ( spl0_11
  <=> c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
    introduced(split_symbol_definition) ).

fof(f2990,plain,
    ( c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f2989]) ).

fof(f2991,plain,
    ( ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f2989]) ).

fof(f3012,plain,
    ( ~ c_lessequals(c_Zorn_OTFin(v_S,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
    | spl0_11 ),
    inference(resolution,[status(thm)],[f2991,f2848]) ).

fof(f3013,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3012,f1786]) ).

fof(f3014,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f3013]) ).

fof(f3015,plain,
    ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),t_a)
    | spl0_10 ),
    inference(forward_demodulation,[status(thm)],[f2982,f2988]) ).

fof(f3016,plain,
    ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a)
    | spl0_10 ),
    inference(forward_demodulation,[status(thm)],[f2982,f3015]) ).

fof(f3017,plain,
    ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | spl0_10 ),
    inference(forward_demodulation,[status(thm)],[f2982,f3016]) ).

fof(f3018,plain,
    ( $false
    | spl0_10 ),
    inference(trivial_equality_resolution,[status(esa)],[f3017]) ).

fof(f3019,plain,
    spl0_10,
    inference(contradiction_clause,[status(thm)],[f3018]) ).

fof(f3025,plain,
    ( spl0_14
  <=> c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
    introduced(split_symbol_definition) ).

fof(f3028,plain,
    ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
    | ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f2990,f2889]) ).

fof(f3029,plain,
    ( spl0_14
    | ~ spl0_11 ),
    inference(split_clause,[status(thm)],[f3028,f3025,f2989]) ).

fof(f3035,plain,
    ! [X0] :
      ( ~ c_lessequals(X0,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))
      | c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = X0
      | ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
      | X0 != c_Zorn_Osucc(v_S,X0,t_a)
      | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f2990,f2872]) ).

fof(f3036,plain,
    ! [X0] :
      ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = X0
      | ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
      | X0 != c_Zorn_Osucc(v_S,X0,t_a)
      | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3035,f2845]) ).

fof(f3041,plain,
    ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m
    | v_m != c_Zorn_Osucc(v_S,v_m,t_a)
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f3036,f2851]) ).

fof(f3042,plain,
    ( spl0_0
    | ~ spl0_1
    | ~ spl0_11 ),
    inference(split_clause,[status(thm)],[f3041,f2854,f2857,f2989]) ).

fof(f3043,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f2860,f2861,f2917,f2935,f2937,f3014,f3019,f3029,f3042]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET843-1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 21:21:35 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.39  % Drodi V3.6.0
% 1.89/0.65  % Refutation found
% 1.89/0.65  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.89/0.65  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.08/0.68  % Elapsed time: 0.318847 seconds
% 2.08/0.68  % CPU time: 2.103901 seconds
% 2.08/0.68  % Total memory used: 132.789 MB
% 2.08/0.68  % Net memory used: 132.426 MB
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