TSTP Solution File: SWW208+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : Wed May 31 12:44:29 EDT 2023

% Result   : Theorem 0.12s 0.40s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  110 (  32 unt;   0 def)
%            Number of atoms       :  246 (  26 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  228 (  92   ~; 101   |;   8   &)
%                                         (  17 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :   21 (  19 usr;  15 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   9 con; 0-2 aty)
%            Number of variables   :   73 (;  72   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,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(f4,axiom,
    ! [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,B_n)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [V_x] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [V_a_2,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( V_x != V_y
       => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
         => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,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(f33,axiom,
    ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f60,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(f64,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1021,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1074,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1112,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1121,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1123,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1149,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1269,conjecture,
    ( 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    & ! [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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1270,negated_conjecture,
    ~ ( 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
      & ! [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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(negated_conjecture,[status(cth)],[f1269]) ).

fof(f1274,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)],[f2]) ).

fof(f1276,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)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f1280,plain,
    ! [X0] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X0)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f1286,plain,
    ! [V_b,V_a,T_a] :
      ( ~ class_Groups_Oordered__comm__monoid__add(T_a)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f1287,plain,
    ! [T_a] :
      ( ~ class_Groups_Oordered__comm__monoid__add(T_a)
      | ! [V_a] :
          ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
          | ! [V_b] :
              ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
              | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    inference(miniscoping,[status(esa)],[f1286]) ).

fof(f1288,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0)),X1))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),X2))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2))) ),
    inference(cnf_transformation,[status(esa)],[f1287]) ).

fof(f1298,plain,
    ! [V_b,V_a,T_a] :
      ( ~ class_Groups_Oordered__comm__monoid__add(T_a)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f1299,plain,
    ! [T_a] :
      ( ~ class_Groups_Oordered__comm__monoid__add(T_a)
      | ! [V_a] :
          ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
          | ! [V_b] :
              ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
              | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    inference(miniscoping,[status(esa)],[f1298]) ).

fof(f1300,plain,
    ! [X0,X1,X2] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X0,X1),c_Groups_Ozero__class_Ozero(X0)))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),c_Groups_Ozero__class_Ozero(X0)))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)),c_Groups_Ozero__class_Ozero(X0))) ),
    inference(cnf_transformation,[status(esa)],[f1299]) ).

fof(f1307,plain,
    ! [V_a_2,T_a] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
      | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f1308,plain,
    ! [V_a_2,T_a] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
      | ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    inference(NNF_transformation,[status(esa)],[f1307]) ).

fof(f1309,plain,
    ! [T_a] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
      | ( ! [V_a_2] :
            ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
            | V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ! [V_a_2] :
            ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
            | V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    inference(miniscoping,[status(esa)],[f1308]) ).

fof(f1310,plain,
    ! [X0,X1] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oabs__class_Oabs(X0,X1)))
      | X1 != c_Groups_Ozero__class_Ozero(X0) ),
    inference(cnf_transformation,[status(esa)],[f1309]) ).

fof(f1319,plain,
    ! [V_y,V_x,T_a] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | V_x = V_y
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ),
    inference(pre_NNF_transformation,[status(esa)],[f22]) ).

fof(f1320,plain,
    ! [T_a] :
      ( ~ class_Rings_Olinordered__idom(T_a)
      | ! [V_y,V_x] :
          ( V_x = V_y
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ),
    inference(miniscoping,[status(esa)],[f1319]) ).

fof(f1321,plain,
    ! [X0,X1,X2] :
      ( ~ class_Rings_Olinordered__idom(X0)
      | X1 = X2
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X1),X2))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,X2),X1)) ),
    inference(cnf_transformation,[status(esa)],[f1320]) ).

fof(f1354,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)],[f32]) ).

fof(f1355,plain,
    ! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),X0)),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f1443,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)],[f60]) ).

fof(f1444,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)],[f1443]) ).

fof(f1445,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,X0),X1))
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f1444]) ).

fof(f1458,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f4306,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(cnf_transformation,[status(esa)],[f1021]) ).

fof(f4359,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(cnf_transformation,[status(esa)],[f1074]) ).

fof(f4397,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f1112]) ).

fof(f4406,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f1121]) ).

fof(f4408,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f1123]) ).

fof(f4434,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f1149]) ).

fof(f4607,plain,
    ( ~ 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    | ? [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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(pre_NNF_transformation,[status(esa)],[f1270]) ).

fof(f4608,plain,
    ( ~ 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    | ~ 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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(skolemization,[status(esa)],[f4607]) ).

fof(f4609,plain,
    ( ~ 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    | ~ 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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(cnf_transformation,[status(esa)],[f4608]) ).

fof(f4646,plain,
    ( spl0_0
  <=> 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    introduced(split_symbol_definition) ).

fof(f4648,plain,
    ( ~ 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),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f4646]) ).

fof(f4649,plain,
    ( spl0_1
  <=> 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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    introduced(split_symbol_definition) ).

fof(f4651,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)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f4649]) ).

fof(f4652,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f4609,f4646,f4649]) ).

fof(f4653,plain,
    ! [X0] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X0)
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0)))) ),
    inference(destructive_equality_resolution,[status(esa)],[f1310]) ).

fof(f4830,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0),X1))
      | X0 = X1
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0)) ),
    inference(resolution,[status(thm)],[f1445,f1354]) ).

fof(f4870,plain,
    ( spl0_12
  <=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
    introduced(split_symbol_definition) ).

fof(f4872,plain,
    ( ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f4870]) ).

fof(f4921,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4651,f1276]) ).

fof(f4922,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f4921]) ).

fof(f4938,plain,
    ( spl0_26
  <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
    introduced(split_symbol_definition) ).

fof(f4940,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
    | spl0_26 ),
    inference(component_clause,[status(thm)],[f4938]) ).

fof(f4941,plain,
    ( spl0_27
  <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    introduced(split_symbol_definition) ).

fof(f4944,plain,
    ( ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f4648,f1288]) ).

fof(f4945,plain,
    ( ~ spl0_12
    | ~ spl0_26
    | ~ spl0_27
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f4944,f4870,f4938,f4941,f4646]) ).

fof(f4948,plain,
    ( $false
    | spl0_26 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4940,f1274]) ).

fof(f4949,plain,
    spl0_26,
    inference(contradiction_clause,[status(thm)],[f4948]) ).

fof(f5615,plain,
    ( spl0_111
  <=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
    introduced(split_symbol_definition) ).

fof(f5617,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
    | spl0_111 ),
    inference(component_clause,[status(thm)],[f5615]) ).

fof(f5890,plain,
    ( spl0_137
  <=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    introduced(split_symbol_definition) ).

fof(f5891,plain,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ spl0_137 ),
    inference(component_clause,[status(thm)],[f5890]) ).

fof(f5893,plain,
    ( spl0_138
  <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    introduced(split_symbol_definition) ).

fof(f5895,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
    | spl0_138 ),
    inference(component_clause,[status(thm)],[f5893]) ).

fof(f5896,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
    | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(resolution,[status(thm)],[f4653,f4830]) ).

fof(f5897,plain,
    ( ~ spl0_111
    | spl0_137
    | spl0_138 ),
    inference(split_clause,[status(thm)],[f5896,f5615,f5890,f5893]) ).

fof(f6034,plain,
    ( spl0_158
  <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    introduced(split_symbol_definition) ).

fof(f6036,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
    | spl0_158 ),
    inference(component_clause,[status(thm)],[f6034]) ).

fof(f6200,plain,
    ( spl0_176
  <=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
    introduced(split_symbol_definition) ).

fof(f6202,plain,
    ( ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
    | spl0_176 ),
    inference(component_clause,[status(thm)],[f6200]) ).

fof(f6488,plain,
    ( spl0_209
  <=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    introduced(split_symbol_definition) ).

fof(f6489,plain,
    ( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ spl0_209 ),
    inference(component_clause,[status(thm)],[f6488]) ).

fof(f6493,plain,
    ( ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
    | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | spl0_158 ),
    inference(resolution,[status(thm)],[f6036,f1321]) ).

fof(f6494,plain,
    ( ~ spl0_176
    | spl0_209
    | spl0_27
    | spl0_158 ),
    inference(split_clause,[status(thm)],[f6493,f6200,f6488,f4941,f6034]) ).

fof(f6495,plain,
    ( $false
    | ~ spl0_209 ),
    inference(forward_subsumption_resolution,[status(thm)],[f6489,f1458]) ).

fof(f6496,plain,
    ~ spl0_209,
    inference(contradiction_clause,[status(thm)],[f6495]) ).

fof(f7143,plain,
    ( $false
    | spl0_111 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4406,f5617]) ).

fof(f7144,plain,
    spl0_111,
    inference(contradiction_clause,[status(thm)],[f7143]) ).

fof(f7630,plain,
    ( ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(resolution,[status(thm)],[f1280,f1300]) ).

fof(f7631,plain,
    ( ~ spl0_12
    | ~ spl0_138
    | ~ spl0_158 ),
    inference(split_clause,[status(thm)],[f7630,f4870,f5893,f6034]) ).

fof(f7718,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4408,f4872]) ).

fof(f7719,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f7718]) ).

fof(f8103,plain,
    ( $false
    | spl0_176 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4434,f6202]) ).

fof(f8104,plain,
    spl0_176,
    inference(contradiction_clause,[status(thm)],[f8103]) ).

fof(f8195,plain,
    ( spl0_336
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
    introduced(split_symbol_definition) ).

fof(f8197,plain,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)
    | spl0_336 ),
    inference(component_clause,[status(thm)],[f8195]) ).

fof(f8231,plain,
    ( spl0_342
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
    introduced(split_symbol_definition) ).

fof(f8233,plain,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
    | spl0_342 ),
    inference(component_clause,[status(thm)],[f8231]) ).

fof(f8259,plain,
    ( spl0_348
  <=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
    introduced(split_symbol_definition) ).

fof(f8261,plain,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint)
    | spl0_348 ),
    inference(component_clause,[status(thm)],[f8259]) ).

fof(f8340,plain,
    ( $false
    | spl0_348 ),
    inference(forward_subsumption_resolution,[status(thm)],[f8261,f4306]) ).

fof(f8341,plain,
    spl0_348,
    inference(contradiction_clause,[status(thm)],[f8340]) ).

fof(f8342,plain,
    ( $false
    | spl0_342 ),
    inference(forward_subsumption_resolution,[status(thm)],[f8233,f4397]) ).

fof(f8343,plain,
    spl0_342,
    inference(contradiction_clause,[status(thm)],[f8342]) ).

fof(f8344,plain,
    ( $false
    | spl0_336 ),
    inference(forward_subsumption_resolution,[status(thm)],[f8197,f4359]) ).

fof(f8345,plain,
    spl0_336,
    inference(contradiction_clause,[status(thm)],[f8344]) ).

fof(f8359,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
    | ~ spl0_137
    | spl0_138 ),
    inference(forward_demodulation,[status(thm)],[f5891,f5895]) ).

fof(f8360,plain,
    ( $false
    | ~ spl0_137
    | spl0_138 ),
    inference(forward_subsumption_resolution,[status(thm)],[f8359,f1355]) ).

fof(f8361,plain,
    ( ~ spl0_137
    | spl0_138 ),
    inference(contradiction_clause,[status(thm)],[f8360]) ).

fof(f8362,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f4652,f4922,f4945,f4949,f5897,f6494,f6496,f7144,f7631,f7719,f8104,f8341,f8343,f8345,f8361]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem  : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.28  % Computer : n014.cluster.edu
% 0.07/0.28  % Model    : x86_64 x86_64
% 0.07/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28  % Memory   : 8042.1875MB
% 0.07/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28  % CPULimit : 300
% 0.07/0.28  % WCLimit  : 300
% 0.07/0.28  % DateTime : Tue May 30 10:51:03 EDT 2023
% 0.07/0.28  % CPUTime  : 
% 0.12/0.33  % Drodi V3.5.1
% 0.12/0.40  % Refutation found
% 0.12/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45  % Elapsed time: 0.167320 seconds
% 0.12/0.45  % CPU time: 0.626536 seconds
% 0.12/0.45  % Memory used: 126.685 MB
%------------------------------------------------------------------------------