TSTP Solution File: SWW194+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWW194+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 20:49:48 EDT 2024

% Result   : Theorem 29.26s 4.16s
% Output   : CNFRefutation 29.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   80 (  43 unt;   0 def)
%            Number of atoms       :  126 (  50 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   84 (  38   ~;  35   |;   2   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   4 con; 0-2 aty)
%            Number of variables   :   53 (  53   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
     => ( 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(f34,axiom,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f35,axiom,
    ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f127,axiom,
    ! [V_n,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f225,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f230,axiom,
    ! [V_k,V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_k)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),V_k),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f231,axiom,
    ! [V_xa_2] :
      ( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    <=> V_xa_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f272,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f288,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f359,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f371,axiom,
    ! [V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1103,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1140,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1199,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1200,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(negated_conjecture,[status(cth)],[f1199]) ).

fof(f1204,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f1242,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f1271,plain,
    ! [V_w,V_z] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
      | V_z = V_w ),
    inference(pre_NNF_transformation,[status(esa)],[f32]) ).

fof(f1272,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f1271]) ).

fof(f1276,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f1277,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f1279,plain,
    ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X0),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f1547,plain,
    ! [V_n,T_a] :
      ( ~ class_Groups_Omonoid__mult(T_a)
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
    inference(pre_NNF_transformation,[status(esa)],[f127]) ).

fof(f1548,plain,
    ! [T_a] :
      ( ~ class_Groups_Omonoid__mult(T_a)
      | ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
    inference(miniscoping,[status(esa)],[f1547]) ).

fof(f1549,plain,
    ! [X0,X1] :
      ( ~ class_Groups_Omonoid__mult(X0)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X0),c_Groups_Oone__class_Oone(X0)),X1) = c_Groups_Oone__class_Oone(X0) ),
    inference(cnf_transformation,[status(esa)],[f1548]) ).

fof(f1781,plain,
    ! [V_y,V_x] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ),
    inference(pre_NNF_transformation,[status(esa)],[f225]) ).

fof(f1782,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X0),c_NthRoot_Osqrt(X1)) ),
    inference(cnf_transformation,[status(esa)],[f1781]) ).

fof(f1796,plain,
    ! [X0,X1] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X0),X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0)),X1),
    inference(cnf_transformation,[status(esa)],[f230]) ).

fof(f1797,plain,
    ! [V_xa_2] :
      ( ( c_NthRoot_Osqrt(V_xa_2) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | V_xa_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
      & ( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | V_xa_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
    inference(NNF_transformation,[status(esa)],[f231]) ).

fof(f1798,plain,
    ( ! [V_xa_2] :
        ( c_NthRoot_Osqrt(V_xa_2) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | V_xa_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
    & ! [V_xa_2] :
        ( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | V_xa_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
    inference(miniscoping,[status(esa)],[f1797]) ).

fof(f1800,plain,
    ! [X0] :
      ( c_NthRoot_Osqrt(X0) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
      | X0 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(cnf_transformation,[status(esa)],[f1798]) ).

fof(f1906,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(cnf_transformation,[status(esa)],[f272]) ).

fof(f1949,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(cnf_transformation,[status(esa)],[f288]) ).

fof(f2145,plain,
    ! [V_a,T_a] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
      | c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
    inference(pre_NNF_transformation,[status(esa)],[f359]) ).

fof(f2146,plain,
    ! [T_a] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
      | ! [V_a] : c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
    inference(miniscoping,[status(esa)],[f2145]) ).

fof(f2147,plain,
    ! [X0,X1] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X0)
      | c_Groups_Oabs__class_Oabs(X0,c_Groups_Oabs__class_Oabs(X0,X1)) = c_Groups_Oabs__class_Oabs(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2146]) ).

fof(f2180,plain,
    ! [X0] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
    inference(cnf_transformation,[status(esa)],[f371]) ).

fof(f4371,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f1103]) ).

fof(f4408,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(cnf_transformation,[status(esa)],[f1140]) ).

fof(f4467,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(cnf_transformation,[status(esa)],[f1200]) ).

fof(f4616,plain,
    c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(destructive_equality_resolution,[status(esa)],[f1800]) ).

fof(f4627,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(forward_demodulation,[status(thm)],[f1242,f1906]) ).

fof(f4630,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(forward_demodulation,[status(thm)],[f4627,f1949]) ).

fof(f4670,plain,
    ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
    inference(forward_demodulation,[status(thm)],[f1796,f2180]) ).

fof(f4671,plain,
    ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
    inference(forward_demodulation,[status(thm)],[f4630,f4670]) ).

fof(f4953,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(forward_demodulation,[status(thm)],[f1279,f4467]) ).

fof(f4954,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(forward_demodulation,[status(thm)],[f4630,f4953]) ).

fof(f4955,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(forward_demodulation,[status(thm)],[f4630,f4954]) ).

fof(f5046,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(resolution,[status(thm)],[f1276,f4955]) ).

fof(f5069,plain,
    ( spl0_4
  <=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    introduced(split_symbol_definition) ).

fof(f5070,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f5069]) ).

fof(f5071,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f5069]) ).

fof(f5098,plain,
    ( spl0_11
  <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))) ),
    introduced(split_symbol_definition) ).

fof(f5100,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)))
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f5098]) ).

fof(f5101,plain,
    ( spl0_12
  <=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    introduced(split_symbol_definition) ).

fof(f5102,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f5101]) ).

fof(f5104,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)))
    | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[f1272,f1204]) ).

fof(f5105,plain,
    ( ~ spl0_11
    | spl0_12 ),
    inference(split_clause,[status(thm)],[f5104,f5098,f5101]) ).

fof(f5108,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | spl0_11 ),
    inference(forward_demodulation,[status(thm)],[f1279,f5100]) ).

fof(f5150,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | ~ spl0_12 ),
    inference(forward_demodulation,[status(thm)],[f1279,f5102]) ).

fof(f5860,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ spl0_4 ),
    inference(backward_demodulation,[status(thm)],[f5070,f4955]) ).

fof(f5861,plain,
    ( $false
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f5860,f1277]) ).

fof(f5862,plain,
    ~ spl0_4,
    inference(contradiction_clause,[status(thm)],[f5861]) ).

fof(f9261,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ spl0_12
    | spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f5150,f5071]) ).

fof(f9262,plain,
    ( $false
    | ~ spl0_12
    | spl0_4 ),
    inference(trivial_equality_resolution,[status(esa)],[f9261]) ).

fof(f9263,plain,
    ( ~ spl0_12
    | spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f9262]) ).

fof(f9787,plain,
    ! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
    inference(resolution,[status(thm)],[f2147,f4371]) ).

fof(f14433,plain,
    ! [X0] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(resolution,[status(thm)],[f1549,f4408]) ).

fof(f14464,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(backward_demodulation,[status(thm)],[f14433,f5046]) ).

fof(f23264,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    inference(resolution,[status(thm)],[f1782,f14464]) ).

fof(f23265,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    inference(forward_demodulation,[status(thm)],[f4616,f23264]) ).

fof(f23266,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(forward_demodulation,[status(thm)],[f1796,f23265]) ).

fof(f23267,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(forward_demodulation,[status(thm)],[f4671,f23266]) ).

fof(f23268,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
    inference(forward_demodulation,[status(thm)],[f9787,f23267]) ).

fof(f23269,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f23268,f5108]) ).

fof(f23270,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f23269]) ).

fof(f23271,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f5105,f5862,f9263,f23270]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SWW194+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 22:47:50 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.44  % Drodi V3.6.0
% 29.26/4.16  % Refutation found
% 29.26/4.16  % SZS status Theorem for theBenchmark: Theorem is valid
% 29.26/4.16  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 29.64/4.23  % Elapsed time: 3.870838 seconds
% 29.64/4.23  % CPU time: 29.946641 seconds
% 29.64/4.23  % Total memory used: 445.173 MB
% 29.64/4.23  % Net memory used: 438.998 MB
%------------------------------------------------------------------------------