TSTP Solution File: ALG359-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : ALG359-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n026.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 20:11:25 EDT 2024

% Result   : Unsatisfiable 46.39s 6.27s
% Output   : CNFRefutation 47.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   54 (  23 unt;   0 def)
%            Number of atoms       :   95 (  44 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   74 (  33   ~;  37   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :   43 (  43   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f35,axiom,
    ! [T_a,V_x] :
      ( ~ class_RealVector_Oreal__algebra__1(T_a)
      | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
      | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f321,axiom,
    ! [T_a,V_x] :
      ( ~ class_RealVector_Oreal__normed__vector(T_a)
      | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
      | V_x = c_HOL_Ozero__class_Ozero(T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f710,axiom,
    ! [V_n,V_x] :
      ( c_Power_Opower__class_Opower(c_NthRoot_Oroot(V_n,V_x),V_n,tc_RealDef_Oreal) = V_x
      | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f823,axiom,
    v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f825,axiom,
    ! [V_x,V_n] : c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex),V_n,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f827,axiom,
    ! [T_a,V_a,V_b,V_n] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
      | V_b = c_HOL_Ozero__class_Ozero(T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f838,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f856,axiom,
    ! [V_n] : c_NthRoot_Oroot(V_n,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f885,negated_conjecture,
    c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f996,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1006,axiom,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1018,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1082,plain,
    ! [V_x] :
      ( ! [T_a] :
          ( ~ class_RealVector_Oreal__algebra__1(T_a)
          | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(miniscoping,[status(esa)],[f35]) ).

fof(f1083,plain,
    ! [X0,X1] :
      ( ~ class_RealVector_Oreal__algebra__1(X0)
      | c_RealVector_Oof__real(X1,X0) != c_HOL_Ozero__class_Ozero(X0)
      | X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(cnf_transformation,[status(esa)],[f1082]) ).

fof(f1544,plain,
    ! [X0,X1] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_RealVector_Onorm__class_Onorm(X1,X0) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
      | X1 = c_HOL_Ozero__class_Ozero(X0) ),
    inference(cnf_transformation,[status(esa)],[f321]) ).

fof(f2169,plain,
    ! [V_n] :
      ( ! [V_x] : c_Power_Opower__class_Opower(c_NthRoot_Oroot(V_n,V_x),V_n,tc_RealDef_Oreal) = V_x
      | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ),
    inference(miniscoping,[status(esa)],[f710]) ).

fof(f2170,plain,
    ! [X0,X1] :
      ( c_Power_Opower__class_Opower(c_NthRoot_Oroot(X0,X1),X0,tc_RealDef_Oreal) = X1
      | c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) ),
    inference(cnf_transformation,[status(esa)],[f2169]) ).

fof(f2340,plain,
    v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(cnf_transformation,[status(esa)],[f823]) ).

fof(f2343,plain,
    ! [X0,X1] : c_Power_Opower__class_Opower(c_RealVector_Oof__real(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_Complex_Ocomplex),
    inference(cnf_transformation,[status(esa)],[f825]) ).

fof(f2346,plain,
    ! [T_a,V_b] :
      ( ~ class_Ring__and__Field_Ofield(T_a)
      | ! [V_a,V_n] : c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
      | V_b = c_HOL_Ozero__class_Ozero(T_a) ),
    inference(miniscoping,[status(esa)],[f827]) ).

fof(f2347,plain,
    ! [X0,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X2,X3,X0),X0)
      | X2 = c_HOL_Ozero__class_Ozero(X0) ),
    inference(cnf_transformation,[status(esa)],[f2346]) ).

fof(f2366,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(v_na____,tc_nat),
    inference(cnf_transformation,[status(esa)],[f838]) ).

fof(f2398,plain,
    ! [X0] : c_NthRoot_Oroot(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f856]) ).

fof(f2449,plain,
    c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(cnf_transformation,[status(esa)],[f885]) ).

fof(f2560,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[status(esa)],[f996]) ).

fof(f2570,plain,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[status(esa)],[f1006]) ).

fof(f2582,plain,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    inference(cnf_transformation,[status(esa)],[f1018]) ).

fof(f2590,plain,
    ! [X0] : c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,X0),v_na____,tc_RealDef_Oreal) = X0,
    inference(resolution,[status(thm)],[f2170,f2366]) ).

fof(f2591,plain,
    c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_na____,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(paramodulation,[status(thm)],[f2398,f2590]) ).

fof(f2698,plain,
    ( spl0_13
  <=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    introduced(split_symbol_definition) ).

fof(f2700,plain,
    ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f2698]) ).

fof(f11389,plain,
    ( $false
    | spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2560,f2700]) ).

fof(f11390,plain,
    spl0_13,
    inference(contradiction_clause,[status(thm)],[f11389]) ).

fof(f24699,plain,
    ! [X0,X1,X2] :
      ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
      | X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(resolution,[status(thm)],[f2582,f2347]) ).

fof(f24896,plain,
    ! [X0,X1,X2] :
      ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Power_Opower__class_Opower(X1,X2,tc_RealDef_Oreal),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
      | c_RealVector_Oof__real(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(paramodulation,[status(thm)],[f2343,f24699]) ).

fof(f25121,plain,
    ! [X0,X1] :
      ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
      | c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(paramodulation,[status(thm)],[f2590,f24896]) ).

fof(f30771,plain,
    c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(resolution,[status(thm)],[f25121,f2449]) ).

fof(f30833,plain,
    ( spl0_3877
  <=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
    introduced(split_symbol_definition) ).

fof(f30835,plain,
    ( ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
    | spl0_3877 ),
    inference(component_clause,[status(thm)],[f30833]) ).

fof(f30836,plain,
    ( spl0_3878
  <=> c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    introduced(split_symbol_definition) ).

fof(f30837,plain,
    ( c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ spl0_3878 ),
    inference(component_clause,[status(thm)],[f30836]) ).

fof(f30839,plain,
    ( ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
    | c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[f30771,f1083]) ).

fof(f30840,plain,
    ( ~ spl0_3877
    | spl0_3878 ),
    inference(split_clause,[status(thm)],[f30839,f30833,f30836]) ).

fof(f30860,plain,
    ( $false
    | spl0_3877 ),
    inference(forward_subsumption_resolution,[status(thm)],[f30835,f2570]) ).

fof(f30861,plain,
    spl0_3877,
    inference(contradiction_clause,[status(thm)],[f30860]) ).

fof(f33362,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_na____,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)
    | ~ spl0_3878 ),
    inference(paramodulation,[status(thm)],[f30837,f2590]) ).

fof(f33363,plain,
    ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)
    | ~ spl0_3878 ),
    inference(forward_demodulation,[status(thm)],[f2591,f33362]) ).

fof(f33378,plain,
    ( spl0_4193
  <=> v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    introduced(split_symbol_definition) ).

fof(f33379,plain,
    ( v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | ~ spl0_4193 ),
    inference(component_clause,[status(thm)],[f33378]) ).

fof(f33381,plain,
    ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | v_b = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | ~ spl0_3878 ),
    inference(resolution,[status(thm)],[f33363,f1544]) ).

fof(f33382,plain,
    ( ~ spl0_13
    | spl0_4193
    | ~ spl0_3878 ),
    inference(split_clause,[status(thm)],[f33381,f2698,f33378,f30836]) ).

fof(f33388,plain,
    ( $false
    | ~ spl0_4193 ),
    inference(forward_subsumption_resolution,[status(thm)],[f33379,f2340]) ).

fof(f33389,plain,
    ~ spl0_4193,
    inference(contradiction_clause,[status(thm)],[f33388]) ).

fof(f33390,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f11390,f30840,f30861,f33382,f33389]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG359-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 23:50:34 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.19/0.40  % Drodi V3.6.0
% 46.39/6.27  % Refutation found
% 46.39/6.27  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 46.39/6.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 47.45/6.41  % Elapsed time: 6.043851 seconds
% 47.45/6.41  % CPU time: 47.270570 seconds
% 47.45/6.41  % Total memory used: 791.735 MB
% 47.45/6.41  % Net memory used: 782.215 MB
%------------------------------------------------------------------------------