TSTP Solution File: ANA014-2 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : ANA014-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 12:01:25 EDT 2023

% Result   : Unsatisfiable 0.18s 0.36s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   55 (  20 unt;   0 def)
%            Number of atoms       :   92 (  27 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   73 (  36   ~;  35   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   11 (   9 usr;   3 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   63 (;  63   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
    v_c != c_0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ! [V_U] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,negated_conjecture,
    class_Ring__and__Field_Oordered__field(t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [T_a,V_y] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | c_times(c_1,V_y,T_a) = V_y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [T_a,V_a,V_b,V_c] :
      ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
      | c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [T_a,V_x] :
      ( ~ class_Orderings_Oorder(T_a)
      | c_lessequals(V_x,V_x,T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [T_a,V_a,V_b] :
      ( ~ class_Ring__and__Field_Oordered__idom(T_a)
      | c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [T_a,V_a] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | V_a = c_0
      | c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Ofield(T)
      | class_OrderedGroup_Omonoid__mult(T) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Ofield(T)
      | class_OrderedGroup_Osemigroup__mult(T) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__field(T)
      | class_Ring__and__Field_Ofield(T) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__field(T)
      | class_Ring__and__Field_Oordered__idom(T) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [T] :
      ( ~ class_Ring__and__Field_Oordered__field(T)
      | class_Orderings_Oorder(T) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,plain,
    v_c != c_0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f15,plain,
    ! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),t_a),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f16,plain,
    class_Ring__and__Field_Oordered__field(t_a),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f17,plain,
    ! [T_a] :
      ( ~ class_OrderedGroup_Omonoid__mult(T_a)
      | ! [V_y] : c_times(c_1,V_y,T_a) = V_y ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_times(c_1,X1,X0) = X1 ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    ! [T_a] :
      ( ~ class_OrderedGroup_Osemigroup__mult(T_a)
      | ! [V_a,V_b,V_c] : c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ),
    inference(miniscoping,[status(esa)],[f5]) ).

fof(f20,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_OrderedGroup_Osemigroup__mult(X0)
      | c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f21,plain,
    ! [T_a] :
      ( ~ class_Orderings_Oorder(T_a)
      | ! [V_x] : c_lessequals(V_x,V_x,T_a) ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X1,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [T_a] :
      ( ~ class_Ring__and__Field_Oordered__idom(T_a)
      | ! [V_a,V_b] : c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | X1 = c_0
      | c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1 ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f26,plain,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | class_OrderedGroup_Omonoid__mult(X0) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f27,plain,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | class_OrderedGroup_Osemigroup__mult(X0) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f28,plain,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__field(X0)
      | class_Ring__and__Field_Ofield(X0) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f29,plain,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__field(X0)
      | class_Ring__and__Field_Oordered__idom(X0) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f30,plain,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__field(X0)
      | class_Orderings_Oorder(X0) ),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f31,plain,
    class_Ring__and__Field_Ofield(t_a),
    inference(resolution,[status(thm)],[f28,f16]) ).

fof(f32,plain,
    class_OrderedGroup_Omonoid__mult(t_a),
    inference(resolution,[status(thm)],[f26,f31]) ).

fof(f33,plain,
    class_OrderedGroup_Osemigroup__mult(t_a),
    inference(resolution,[status(thm)],[f27,f31]) ).

fof(f34,plain,
    class_Ring__and__Field_Oordered__idom(t_a),
    inference(resolution,[status(thm)],[f29,f16]) ).

fof(f35,plain,
    class_Orderings_Oorder(t_a),
    inference(resolution,[status(thm)],[f30,f16]) ).

fof(f36,plain,
    ! [X0] : c_lessequals(X0,X0,t_a),
    inference(resolution,[status(thm)],[f35,f22]) ).

fof(f37,plain,
    ! [X0] : c_times(c_1,X0,t_a) = X0,
    inference(resolution,[status(thm)],[f18,f32]) ).

fof(f39,plain,
    ! [X0,X1,X2] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
    inference(resolution,[status(thm)],[f20,f33]) ).

fof(f40,plain,
    ! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_a),t_a) = c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a),
    inference(resolution,[status(thm)],[f24,f34]) ).

fof(f47,plain,
    ! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_HOL_Oabs(c_times(v_c,v_f(v_x(X0)),t_a),t_a),t_a),t_a),
    inference(backward_demodulation,[status(thm)],[f40,f15]) ).

fof(f49,plain,
    ! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),c_HOL_Oabs(c_times(X0,c_times(v_c,v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),t_a),t_a),t_a),
    inference(paramodulation,[status(thm)],[f40,f47]) ).

fof(f237,plain,
    ! [X0] :
      ( X0 = c_0
      | c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) = c_1 ),
    inference(resolution,[status(thm)],[f25,f31]) ).

fof(f259,plain,
    ! [X0,X1] :
      ( c_times(c_1,X0,t_a) = c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X0,t_a),t_a)
      | X1 = c_0 ),
    inference(paramodulation,[status(thm)],[f237,f39]) ).

fof(f260,plain,
    ! [X0,X1] :
      ( X0 = c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X0,t_a),t_a)
      | X1 = c_0 ),
    inference(forward_demodulation,[status(thm)],[f37,f259]) ).

fof(f282,plain,
    ( spl0_7
  <=> v_c = c_0 ),
    introduced(split_symbol_definition) ).

fof(f283,plain,
    ( v_c = c_0
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f282]) ).

fof(f292,plain,
    ( spl0_9
  <=> c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a) ),
    introduced(split_symbol_definition) ).

fof(f294,plain,
    ( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f292]) ).

fof(f295,plain,
    ( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
    | v_c = c_0 ),
    inference(paramodulation,[status(thm)],[f260,f49]) ).

fof(f296,plain,
    ( ~ spl0_9
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f295,f292,f282]) ).

fof(f317,plain,
    ( $false
    | spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f294,f36]) ).

fof(f318,plain,
    spl0_9,
    inference(contradiction_clause,[status(thm)],[f317]) ).

fof(f319,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f283,f14]) ).

fof(f320,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f319]) ).

fof(f321,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f296,f318,f320]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ANA014-2 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n007.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 09:49:02 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.18/0.36  % Refutation found
% 0.18/0.36  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.38  % Elapsed time: 0.039091 seconds
% 0.18/0.38  % CPU time: 0.165170 seconds
% 0.18/0.38  % Memory used: 17.869 MB
%------------------------------------------------------------------------------