TSTP Solution File: SCT026-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SCT026-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:38:11 EDT 2024

% Result   : Unsatisfiable 9.36s 1.60s
% Output   : CNFRefutation 9.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   39 (  12 unt;   0 def)
%            Number of atoms       :   73 (   9 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   65 (  31   ~;  32   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-4 aty)
%            Number of variables   :   46 (  46   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f359,axiom,
    ! [V_b,V_a,T_b,T_a,V_r] :
      ( c_in(c_Pair(V_b,V_a,T_b,T_a),c_Relation_Oconverse(V_r,T_a,T_b),tc_prod(T_b,T_a))
      | ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f448,axiom,
    c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f450,axiom,
    ! [V_L] :
      ( c_in(c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
      | ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f505,axiom,
    v_a != v_b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f507,axiom,
    ! [V_y,V_x,V_L] :
      ( c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | V_x = V_y
      | ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f508,axiom,
    ! [V_x,V_S,T_a] :
      ( c_in(V_x,V_S,T_a)
      | ~ hBOOL(hAPP(V_S,V_x)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f509,axiom,
    ! [V_S,V_x,T_a] :
      ( hBOOL(hAPP(V_S,V_x))
      | ~ c_in(V_x,V_S,T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f511,negated_conjecture,
    ! [V_x] :
      ( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | ~ c_in(V_x,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1068,plain,
    ! [X0,X1,X2,X3,X4] :
      ( c_in(c_Pair(X0,X1,X2,X3),c_Relation_Oconverse(X4,X3,X2),tc_prod(X2,X3))
      | ~ c_in(c_Pair(X1,X0,X3,X2),X4,tc_prod(X3,X2)) ),
    inference(cnf_transformation,[status(esa)],[f359]) ).

fof(f1193,plain,
    c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
    inference(cnf_transformation,[status(esa)],[f448]) ).

fof(f1195,plain,
    ! [X0] :
      ( c_in(c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
      | ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    inference(cnf_transformation,[status(esa)],[f450]) ).

fof(f1293,plain,
    v_a != v_b,
    inference(cnf_transformation,[status(esa)],[f505]) ).

fof(f1296,plain,
    ! [V_L] :
      ( ! [V_y,V_x] :
          ( c_in(c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
          | c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
          | V_x = V_y )
      | ~ c_in(V_L,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    inference(miniscoping,[status(esa)],[f507]) ).

fof(f1297,plain,
    ! [X0,X1,X2] :
      ( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | X1 = X0
      | ~ c_in(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    inference(cnf_transformation,[status(esa)],[f1296]) ).

fof(f1298,plain,
    ! [V_x,V_S] :
      ( ! [T_a] : c_in(V_x,V_S,T_a)
      | ~ hBOOL(hAPP(V_S,V_x)) ),
    inference(miniscoping,[status(esa)],[f508]) ).

fof(f1299,plain,
    ! [X0,X1,X2] :
      ( c_in(X0,X1,X2)
      | ~ hBOOL(hAPP(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f1298]) ).

fof(f1300,plain,
    ! [V_S,V_x] :
      ( hBOOL(hAPP(V_S,V_x))
      | ! [T_a] : ~ c_in(V_x,V_S,T_a) ),
    inference(miniscoping,[status(esa)],[f509]) ).

fof(f1301,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(X0,X1))
      | ~ c_in(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f1300]) ).

fof(f1304,plain,
    ! [X0] :
      ( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    inference(cnf_transformation,[status(esa)],[f511]) ).

fof(f1364,plain,
    ! [X0] :
      ( ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | ~ c_in(c_Relation_Oconverse(X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    inference(resolution,[status(thm)],[f1068,f1304]) ).

fof(f1526,plain,
    ( spl0_5
  <=> v_a = v_b ),
    introduced(split_symbol_definition) ).

fof(f1527,plain,
    ( v_a = v_b
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f1526]) ).

fof(f1545,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1527,f1293]) ).

fof(f1546,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f1545]) ).

fof(f3938,plain,
    c_in(c_Relation_Oconverse(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
    inference(resolution,[status(thm)],[f1193,f1195]) ).

fof(f3944,plain,
    ( spl0_203
  <=> c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(split_symbol_definition) ).

fof(f3945,plain,
    ( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_203 ),
    inference(component_clause,[status(thm)],[f3944]) ).

fof(f3950,plain,
    ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
    inference(resolution,[status(thm)],[f1193,f1304]) ).

fof(f3953,plain,
    hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1)),
    inference(resolution,[status(thm)],[f1193,f1301]) ).

fof(f3955,plain,
    ! [X0] : c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,X0),
    inference(resolution,[status(thm)],[f3953,f1299]) ).

fof(f3959,plain,
    ! [X0,X1] :
      ( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f3955,f1297]) ).

fof(f4899,plain,
    ( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | v_a = v_b ),
    inference(resolution,[status(thm)],[f3959,f3950]) ).

fof(f4900,plain,
    ( spl0_203
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f4899,f3944,f1526]) ).

fof(f4909,plain,
    ( hBOOL(hAPP(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_203 ),
    inference(resolution,[status(thm)],[f3945,f1301]) ).

fof(f4911,plain,
    ! [X0] :
      ( c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,X0)
      | ~ spl0_203 ),
    inference(resolution,[status(thm)],[f4909,f1299]) ).

fof(f5000,plain,
    ~ c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
    inference(resolution,[status(thm)],[f3938,f1364]) ).

fof(f5001,plain,
    ( $false
    | ~ spl0_203 ),
    inference(forward_subsumption_resolution,[status(thm)],[f5000,f4911]) ).

fof(f5002,plain,
    ~ spl0_203,
    inference(contradiction_clause,[status(thm)],[f5001]) ).

fof(f5003,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1546,f4900,f5002]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SCT026-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 20:08:56 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.39  % Drodi V3.6.0
% 9.36/1.60  % Refutation found
% 9.36/1.60  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.36/1.60  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.36/1.67  % Elapsed time: 1.299657 seconds
% 9.36/1.67  % CPU time: 9.827108 seconds
% 9.36/1.67  % Total memory used: 225.439 MB
% 9.36/1.67  % Net memory used: 219.859 MB
%------------------------------------------------------------------------------