TSTP Solution File: SWW207+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWW207+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 20:49:50 EDT 2024

% Result   : Theorem 0.19s 0.55s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   84 (  19 unt;   0 def)
%            Number of atoms       :  198 (  39 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  195 (  81   ~;  92   |;  11   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   6 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-2 aty)
%            Number of variables   :   87 (  84   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
        & V_x_2 != V_y_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
        | V_x_2 = V_y_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f56,axiom,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
       => V_z = V_w ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f57,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f58,axiom,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f84,axiom,
    ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f133,axiom,
    ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f203,axiom,
    hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f570,axiom,
    ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1269,conjecture,
    ? [B_K] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
      & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1270,negated_conjecture,
    ~ ? [B_K] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
        & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K)) ),
    inference(negated_conjecture,[status(cth)],[f1269]) ).

fof(f1276,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f1302,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),v_r)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f1303,plain,
    ! [V_y_2,V_x_2] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
        | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
          & V_x_2 != V_y_2 ) )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
        | V_x_2 = V_y_2 ) ),
    inference(NNF_transformation,[status(esa)],[f13]) ).

fof(f1304,plain,
    ( ! [V_y_2,V_x_2] :
        ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
        | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
          & V_x_2 != V_y_2 ) )
    & ! [V_y_2,V_x_2] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
        | V_x_2 = V_y_2 ) ),
    inference(miniscoping,[status(esa)],[f1303]) ).

fof(f1305,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1)) ),
    inference(cnf_transformation,[status(esa)],[f1304]) ).

fof(f1306,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f1304]) ).

fof(f1307,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f1304]) ).

fof(f1308,plain,
    ! [V_y_2,V_x_2] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
        | V_x_2 = V_y_2 )
      & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
        | ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
          & V_x_2 != V_y_2 ) ) ),
    inference(NNF_transformation,[status(esa)],[f14]) ).

fof(f1309,plain,
    ( ! [V_y_2,V_x_2] :
        ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
        | V_x_2 = V_y_2 )
    & ! [V_y_2,V_x_2] :
        ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
        | ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
          & V_x_2 != V_y_2 ) ) ),
    inference(miniscoping,[status(esa)],[f1308]) ).

fof(f1312,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f1309]) ).

fof(f1452,plain,
    ! [V_w,V_z] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
      | V_z = V_w ),
    inference(pre_NNF_transformation,[status(esa)],[f56]) ).

fof(f1453,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f1452]) ).

fof(f1454,plain,
    ! [V_k,V_j,V_i] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ),
    inference(pre_NNF_transformation,[status(esa)],[f57]) ).

fof(f1455,plain,
    ! [V_j,V_i] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
      | ! [V_k] :
          ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ),
    inference(miniscoping,[status(esa)],[f1454]) ).

fof(f1456,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X2)) ),
    inference(cnf_transformation,[status(esa)],[f1455]) ).

fof(f1457,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f1549,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0))),
    inference(cnf_transformation,[status(esa)],[f84]) ).

fof(f1713,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)))),
    inference(cnf_transformation,[status(esa)],[f133]) ).

fof(f1907,plain,
    hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f203]) ).

fof(f3033,plain,
    ! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0)) = c_RealDef_Oreal(tc_Nat_Onat,X0),
    inference(cnf_transformation,[status(esa)],[f570]) ).

fof(f4607,plain,
    ! [B_K] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
      | ? [B_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K)) ),
    inference(pre_NNF_transformation,[status(esa)],[f1270]) ).

fof(f4608,plain,
    ! [B_K] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(B_K))))))),B_K)) ),
    inference(skolemization,[status(esa)],[f4607]) ).

fof(f4609,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))),X0)) ),
    inference(cnf_transformation,[status(esa)],[f4608]) ).

fof(f4648,plain,
    ! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X0)),
    inference(destructive_equality_resolution,[status(esa)],[f1306]) ).

fof(f4649,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)),
    inference(destructive_equality_resolution,[status(esa)],[f1312]) ).

fof(f4779,plain,
    ( spl0_0
  <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
    introduced(split_symbol_definition) ).

fof(f4780,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f4779]) ).

fof(f4782,plain,
    ( spl0_1
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ),
    introduced(split_symbol_definition) ).

fof(f4783,plain,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f4782]) ).

fof(f4785,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
    | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ),
    inference(resolution,[status(thm)],[f1276,f1307]) ).

fof(f4786,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f4785,f4779,f4782]) ).

fof(f4809,plain,
    ( hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = v_r
    | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f4783,f1907]) ).

fof(f4812,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),X0))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))),X0))
      | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f4783,f4609]) ).

fof(f4818,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0)) ),
    inference(resolution,[status(thm)],[f1457,f4609]) ).

fof(f4819,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X0))
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f1457,f1307]) ).

fof(f4823,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f4818,f4780]) ).

fof(f4824,plain,
    ( spl0_6
  <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))),v_r)) ),
    introduced(split_symbol_definition) ).

fof(f4826,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))),v_r))
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f4824]) ).

fof(f4827,plain,
    ( spl0_7
  <=> v_r = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r)))))) ),
    introduced(split_symbol_definition) ).

fof(f4828,plain,
    ( v_r = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f4827]) ).

fof(f4830,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))),v_r))
    | v_r = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(v_r))))))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f4823,f1453]) ).

fof(f4831,plain,
    ( ~ spl0_6
    | spl0_7
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f4830,f4824,f4827,f4779]) ).

fof(f4845,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0)),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,X0))),X1)) ),
    inference(resolution,[status(thm)],[f1549,f1456]) ).

fof(f4908,plain,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f1907,f4809]) ).

fof(f4910,plain,
    ! [X0] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),X0))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))))
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f4812,f1457]) ).

fof(f4972,plain,
    ( spl0_26
  <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),v_r)) ),
    introduced(split_symbol_definition) ).

fof(f4974,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),v_r))
    | spl0_26 ),
    inference(component_clause,[status(thm)],[f4972]) ).

fof(f4975,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),v_r))
    | ~ spl0_7 ),
    inference(paramodulation,[status(thm)],[f4828,f4609]) ).

fof(f4976,plain,
    ( ~ spl0_0
    | ~ spl0_26
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f4975,f4779,f4972,f4827]) ).

fof(f4985,plain,
    ( $false
    | spl0_26 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4974,f4649]) ).

fof(f4986,plain,
    spl0_26,
    inference(contradiction_clause,[status(thm)],[f4985]) ).

fof(f5021,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
      | v_r = X0
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))))
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f4819,f4910]) ).

fof(f5066,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))))
      | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f4908,f1713]) ).

fof(f5068,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))))
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f5066,f1305]) ).

fof(f5069,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X0))))
      | ~ spl0_1 ),
    inference(paramodulation,[status(thm)],[f3033,f5066]) ).

fof(f5099,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
      | v_r = X0
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0))))))),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f5021,f1456]) ).

fof(f5102,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
      | v_r = X0
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0)))))))
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f5099,f1549]) ).

fof(f5110,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
      | v_r = X0
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sk0_73(X0)))))),X1))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X1))
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f5102,f1456]) ).

fof(f5158,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X0))))
      | ~ spl0_1 ),
    inference(paramodulation,[status(thm)],[f3033,f5068]) ).

fof(f5670,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
      | v_r = X0
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f1302,f5110]) ).

fof(f5671,plain,
    ! [X0] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r))
      | v_r = X0
      | ~ spl0_1 ),
    inference(duplicate_literals_removal,[status(esa)],[f5670]) ).

fof(f5672,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X0)))),v_r)),
    inference(resolution,[status(thm)],[f1302,f4845]) ).

fof(f5685,plain,
    ! [X0] :
      ( v_r = X0
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),X0))
      | X0 = v_r
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f5671,f1453]) ).

fof(f5686,plain,
    ! [X0] :
      ( v_r = X0
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),X0))
      | ~ spl0_1 ),
    inference(duplicate_literals_removal,[status(esa)],[f5685]) ).

fof(f5691,plain,
    ! [X0] :
      ( v_r = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X0))
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f5686,f5158]) ).

fof(f5713,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),v_r))
    | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f5691,f5069]) ).

fof(f5714,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f5713,f4648]) ).

fof(f5715,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f5714]) ).

fof(f5945,plain,
    ( $false
    | spl0_6 ),
    inference(backward_subsumption_resolution,[status(thm)],[f4826,f5672]) ).

fof(f5946,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f5945]) ).

fof(f5947,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f4786,f4831,f4976,f4986,f5715,f5946]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SWW207+1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n008.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 : Mon Apr 29 23:09:42 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.19/0.43  % Drodi V3.6.0
% 0.19/0.55  % Refutation found
% 0.19/0.55  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.55  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.58  % Elapsed time: 0.236212 seconds
% 0.19/0.58  % CPU time: 1.075763 seconds
% 0.19/0.58  % Total memory used: 174.297 MB
% 0.19/0.58  % Net memory used: 173.345 MB
%------------------------------------------------------------------------------