TSTP Solution File: COM011-2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : COM011-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n001.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 May 31 12:03:54 EDT 2023

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   45 (   9 unt;   0 def)
%            Number of atoms       :   92 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   88 (  41   ~;  45   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   73 (;  73   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
    c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,negated_conjecture,
    ~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [V_c,V_A,V_B,T_a] :
      ( ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
      | c_in(V_c,V_A,T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [V_A,V_B,T_a] :
      ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
      | c_lessequals(V_A,V_B,tc_set(T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [V_A,V_B,T_a] :
      ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
      | c_lessequals(V_A,V_B,tc_set(T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [V_F,V_A,V_A_H,T_a,V_B] :
      ( ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
      | ~ c_lessequals(V_B,V_A,tc_set(T_a))
      | c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [V_F,V_A,V_B,T_a] :
      ( ~ c_in(V_F,c_UNITY_Oconstrains(c_minus(V_A,V_B,tc_set(T_a)),c_union(V_A,V_B,T_a),T_a),tc_UNITY_Oprogram(T_a))
      | ~ c_in(V_F,c_WFair_Otransient(c_minus(V_A,V_B,tc_set(T_a)),T_a),tc_UNITY_Oprogram(T_a))
      | c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [V_F,V_A,V_B,T_a] :
      ( ~ c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
      | c_in(V_F,c_WFair_OleadsTo(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [V_F,V_A,T_a,V_B] :
      ( ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a))
      | ~ c_lessequals(V_B,V_A,tc_set(T_a))
      | c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,plain,
    c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f13,plain,
    ~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f14,plain,
    ! [V_c,V_A,T_a] :
      ( ! [V_B] : ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
      | c_in(V_c,V_A,T_a) ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f15,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,c_minus(X1,X2,tc_set(X3)),X3)
      | c_in(X0,X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2)
      | c_lessequals(X0,X1,tc_set(X2)) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2)
      | c_lessequals(X0,X1,tc_set(X2)) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f18,plain,
    ! [V_F,V_A_H,T_a,V_B] :
      ( ! [V_A] :
          ( ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
          | ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
      | c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f19,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ c_in(X0,c_UNITY_Oconstrains(X1,X2,X3),tc_UNITY_Oprogram(X3))
      | ~ c_lessequals(X4,X1,tc_set(X3))
      | c_in(X0,c_UNITY_Oconstrains(X4,X2,X3),tc_UNITY_Oprogram(X3)) ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,c_UNITY_Oconstrains(c_minus(X1,X2,tc_set(X3)),c_union(X1,X2,X3),X3),tc_UNITY_Oprogram(X3))
      | ~ c_in(X0,c_WFair_Otransient(c_minus(X1,X2,tc_set(X3)),X3),tc_UNITY_Oprogram(X3))
      | c_in(X0,c_WFair_Oensures(X1,X2,X3),tc_UNITY_Oprogram(X3)) ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,c_WFair_Oensures(X1,X2,X3),tc_UNITY_Oprogram(X3))
      | c_in(X0,c_WFair_OleadsTo(X1,X2,X3),tc_UNITY_Oprogram(X3)) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f22,plain,
    ! [V_F,T_a,V_B] :
      ( ! [V_A] :
          ( ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a))
          | ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
      | c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,c_WFair_Otransient(X1,X2),tc_UNITY_Oprogram(X2))
      | ~ c_lessequals(X3,X1,tc_set(X2))
      | c_in(X0,c_WFair_Otransient(X3,X2),tc_UNITY_Oprogram(X2)) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,c_UNITY_Oconstrains(c_minus(X1,X2,tc_set(X3)),c_union(X1,X2,X3),X3),tc_UNITY_Oprogram(X3))
      | ~ c_in(X0,c_WFair_Otransient(c_minus(X1,X2,tc_set(X3)),X3),tc_UNITY_Oprogram(X3))
      | c_in(X0,c_WFair_OleadsTo(X1,X2,X3),tc_UNITY_Oprogram(X3)) ),
    inference(resolution,[status(thm)],[f20,f21]) ).

fof(f27,plain,
    ( spl0_0
  <=> c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
    introduced(split_symbol_definition) ).

fof(f29,plain,
    ( ~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f27]) ).

fof(f30,plain,
    ( spl0_1
  <=> c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
    introduced(split_symbol_definition) ).

fof(f32,plain,
    ( ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f30]) ).

fof(f33,plain,
    ( ~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
    | ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
    inference(resolution,[status(thm)],[f25,f13]) ).

fof(f34,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f33,f27,f30]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
      | ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),X0,tc_set(t_a))
      | spl0_0 ),
    inference(resolution,[status(thm)],[f29,f19]) ).

fof(f54,plain,
    ( ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),v_A,tc_set(t_a))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f53,f11]) ).

fof(f56,plain,
    ( ~ c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f54,f17]) ).

fof(f57,plain,
    ( c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),c_minus(v_A,v_B,tc_set(t_a)),t_a)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f54,f16]) ).

fof(f58,plain,
    ( c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f57,f15]) ).

fof(f59,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f58,f56]) ).

fof(f60,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f59]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ c_in(v_F,c_WFair_Otransient(X0,t_a),tc_UNITY_Oprogram(t_a))
      | ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),X0,tc_set(t_a))
      | spl0_1 ),
    inference(resolution,[status(thm)],[f32,f23]) ).

fof(f62,plain,
    ( ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),v_A,tc_set(t_a))
    | spl0_1 ),
    inference(resolution,[status(thm)],[f61,f12]) ).

fof(f64,plain,
    ( ~ c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f62,f17]) ).

fof(f65,plain,
    ( c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),c_minus(v_A,v_B,tc_set(t_a)),t_a)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f62,f16]) ).

fof(f66,plain,
    ( c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f65,f15]) ).

fof(f67,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f66,f64]) ).

fof(f68,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f67]) ).

fof(f69,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f34,f60,f68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM011-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n001.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 : Tue May 30 12:19:15 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.36  % Elapsed time: 0.020478 seconds
% 0.12/0.36  % CPU time: 0.037448 seconds
% 0.12/0.36  % Memory used: 2.084 MB
%------------------------------------------------------------------------------