TSTP Solution File: SCT024-1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SCT024-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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 0.21s 0.43s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   41 (  16 unt;   0 def)
%            Number of atoms       :   84 (   6 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   81 (  38   ~;  38   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   6 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-4 aty)
%            Number of variables   :   24 (  24   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f672,axiom,
    ! [V_x,T_a,V_r] :
      ( ~ hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ c_Relation_Oirrefl(V_r,T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f679,negated_conjecture,
    ! [V_x] : c_Relation_Otrans(hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f680,negated_conjecture,
    ! [V_x] : c_Relation_Oirrefl(hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f681,negated_conjecture,
    ! [V_x] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,V_x),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f682,negated_conjecture,
    hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f683,negated_conjecture,
    ~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f687,negated_conjecture,
    ! [V_a,V_b,V_P] :
      ( hBOOL(c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ hBOOL(c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | V_a = V_b
      | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(V_P,v_Pa(V_P)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Oirrefl(hAPP(V_P,v_Pa(V_P)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Otrans(hAPP(V_P,v_Pa(V_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1705,plain,
    ! [T_a,V_r] :
      ( ! [V_x] : ~ hBOOL(c_in(c_Pair(V_x,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)))
      | ~ c_Relation_Oirrefl(V_r,T_a) ),
    inference(miniscoping,[status(esa)],[f672]) ).

fof(f1706,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)))
      | ~ c_Relation_Oirrefl(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f1705]) ).

fof(f1716,plain,
    ! [X0] : c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
    inference(cnf_transformation,[status(esa)],[f679]) ).

fof(f1717,plain,
    ! [X0] : c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
    inference(cnf_transformation,[status(esa)],[f680]) ).

fof(f1718,plain,
    ! [X0] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
    inference(cnf_transformation,[status(esa)],[f681]) ).

fof(f1719,plain,
    hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(cnf_transformation,[status(esa)],[f682]) ).

fof(f1720,plain,
    ~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(cnf_transformation,[status(esa)],[f683]) ).

fof(f1724,plain,
    ! [V_P] :
      ( ! [V_a,V_b] :
          ( hBOOL(c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(V_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
          | ~ hBOOL(c_in(c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(V_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
          | V_a = V_b )
      | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(V_P,v_Pa(V_P)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Oirrefl(hAPP(V_P,v_Pa(V_P)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Otrans(hAPP(V_P,v_Pa(V_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    inference(miniscoping,[status(esa)],[f687]) ).

fof(f1725,plain,
    ! [X0,X1,X2] :
      ( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | X0 = X1
      | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Oirrefl(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Otrans(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt) ),
    inference(cnf_transformation,[status(esa)],[f1724]) ).

fof(f1795,plain,
    ( spl0_5
  <=> hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(split_symbol_definition) ).

fof(f1796,plain,
    ( hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f1795]) ).

fof(f1798,plain,
    ( spl0_6
  <=> v_a = v_b ),
    introduced(split_symbol_definition) ).

fof(f1799,plain,
    ( v_a = v_b
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f1798]) ).

fof(f1801,plain,
    ( spl0_7
  <=> c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(split_symbol_definition) ).

fof(f1803,plain,
    ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f1801]) ).

fof(f1804,plain,
    ( spl0_8
  <=> c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(split_symbol_definition) ).

fof(f1806,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f1804]) ).

fof(f1807,plain,
    ( spl0_9
  <=> c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(split_symbol_definition) ).

fof(f1809,plain,
    ( ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f1807]) ).

fof(f1810,plain,
    ( hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | v_a = v_b
    | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    inference(resolution,[status(thm)],[f1725,f1719]) ).

fof(f1811,plain,
    ( spl0_5
    | spl0_6
    | ~ spl0_7
    | ~ spl0_8
    | ~ spl0_9 ),
    inference(split_clause,[status(thm)],[f1810,f1795,f1798,f1801,f1804,f1807]) ).

fof(f1813,plain,
    ( $false
    | spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1809,f1716]) ).

fof(f1814,plain,
    spl0_9,
    inference(contradiction_clause,[status(thm)],[f1813]) ).

fof(f1815,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1806,f1717]) ).

fof(f1816,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f1815]) ).

fof(f1817,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1803,f1718]) ).

fof(f1818,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f1817]) ).

fof(f1819,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1796,f1720]) ).

fof(f1820,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f1819]) ).

fof(f1823,plain,
    ( hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_6 ),
    inference(backward_demodulation,[status(thm)],[f1799,f1719]) ).

fof(f1872,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f1706,f1823]) ).

fof(f1873,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1872,f1717]) ).

fof(f1874,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f1873]) ).

fof(f1875,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1811,f1814,f1816,f1818,f1820,f1874]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SCT024-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n014.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 20:05:04 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.21/0.42  % Drodi V3.6.0
% 0.21/0.43  % Refutation found
% 0.21/0.43  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.43  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.46  % Elapsed time: 0.092279 seconds
% 0.21/0.46  % CPU time: 0.146347 seconds
% 0.21/0.46  % Total memory used: 33.788 MB
% 0.21/0.46  % Net memory used: 33.682 MB
%------------------------------------------------------------------------------