TSTP Solution File: SWW194+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWW194+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n020.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  : 600s
% DateTime : Thu Jul 21 00:10:16 EDT 2022

% Result   : Theorem 0.36s 3.54s
% Output   : CNFRefutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  115 (  68 unt;   0 def)
%            Number of atoms       :  184 (  73 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  129 (  60   ~;  49   |;   6   &)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   5 con; 0-3 aty)
%            Number of variables   :  116 (   7 sgn  67   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_0,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/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).

fof(fact_Bit0__def,axiom,
    ! [X18] : c_Int_OBit0(X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X18),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Bit0__def) ).

fof(fact_Bit1__def,axiom,
    ! [X18] : c_Int_OBit1(X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18),X18),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Bit1__def) ).

fof(fact_nat__1__add__1,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__1__add__1) ).

fof(fact_add__Pls__right,axiom,
    ! [X18] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,c_Int_OPls) = X18,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__Pls__right) ).

fof(fact_one__power2,axiom,
    ! [X9] :
      ( class_Rings_Osemiring__1(X9)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Groups_Oone__class_Oone(X9)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X9) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_one__power2) ).

fof(fact_mult__2__right,axiom,
    ! [X17,X9] :
      ( class_Int_Onumber__ring(X9)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X17),c_Int_Onumber__class_Onumber__of(X9,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X9,X17,X17) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_mult__2__right) ).

fof(fact_real__mult__commute,axiom,
    ! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X17),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__mult__commute) ).

fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).

fof(fact_real__mult__1,axiom,
    ! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X17) = X17,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__mult__1) ).

fof(fact_power2__abs,axiom,
    ! [X8,X9] :
      ( class_Rings_Olinordered__idom(X9)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Groups_Oabs__class_Oabs(X9,X8)),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(X9),X8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_power2__abs) ).

fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).

fof(fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096,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/sandbox2/solver/bin/../tmp/theBenchmark.p',fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) ).

fof(fact_less__one__imp__sqr__less__one,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_less__one__imp__sqr__less__one) ).

fof(fact_real__sqrt__pow2,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X5 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__sqrt__pow2) ).

fof(fact_norm__ge__zero,axiom,
    ! [X5,X9] :
      ( class_RealVector_Oreal__normed__vector(X9)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X9,X5)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_norm__ge__zero) ).

fof(fact_real__norm__def,axiom,
    ! [X50] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X50) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X50),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__norm__def) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

fof(fact_less__eq__real__def,axiom,
    ! [X26,X25] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X26)
    <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,X26)
        | X25 = X26 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_less__eq__real__def) ).

fof(fact_real__sqrt__le__1__iff,axiom,
    ! [X25] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X25),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__sqrt__le__1__iff) ).

fof(fact_real__sqrt__eq__1__iff,axiom,
    ! [X25] :
      ( c_NthRoot_Osqrt(X25) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    <=> X25 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__sqrt__eq__1__iff) ).

fof(fact_real__le__refl,axiom,
    ! [X6] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X6),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__le__refl) ).

fof(fact_real__sqrt__ge__0__iff,axiom,
    ! [X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X26))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X26) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__sqrt__ge__0__iff) ).

fof(fact_real__sqrt__abs2,axiom,
    ! [X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X5)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__sqrt__abs2) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [X26,X25,X9] :
      ( class_Orderings_Olinorder(X9)
     => ( c_Orderings_Oord__class_Oless__eq(X9,X25,X26)
       => ( ~ c_Orderings_Oord__class_Oless(X9,X25,X26)
        <=> X25 = X26 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_real__mult__assoc,axiom,
    ! [X21,X22,X23] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),X22)),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X22),X21)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__mult__assoc) ).

fof(fact_abs__mult__self,axiom,
    ! [X8,X9] :
      ( class_Rings_Olinordered__idom(X9)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Oabs__class_Oabs(X9,X8)),c_Groups_Oabs__class_Oabs(X9,X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X8) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_abs__mult__self) ).

fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

fof(c_0_29,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(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_30,plain,
    ! [X19] : c_Int_OBit0(X19) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,X19),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(c_0_31,plain,
    ! [X19] : c_Int_OBit1(X19) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X19),X19),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(c_0_32,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(fof_simplification,[status(thm)],[c_0_29]) ).

cnf(c_0_33,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).

cnf(c_0_34,plain,
    c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_35,plain,
    c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_36,plain,
    ! [X19] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,c_Int_OPls) = X19,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

fof(c_0_37,plain,
    ! [X10] :
      ( ~ class_Rings_Osemiring__1(X10)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Oone__class_Oone(X10)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X10) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).

cnf(c_0_38,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(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_39,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_35]) ).

cnf(c_0_40,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_41,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

fof(c_0_42,plain,
    ! [X18,X19] :
      ( ~ class_Int_Onumber__ring(X19)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19),X18),c_Int_Onumber__class_Onumber__of(X19,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X19,X18,X18) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).

cnf(c_0_43,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_34]),c_0_34]),c_0_34]),c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).

cnf(c_0_44,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_40]),c_0_40]),c_0_40]) ).

fof(c_0_45,plain,
    ! [X18,X19] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X19),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X19),
    inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).

cnf(c_0_46,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_34]),c_0_35]),c_0_35]) ).

cnf(c_0_47,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_48,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_x____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_44]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_44]) ).

cnf(c_0_49,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_50,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_44]) ).

cnf(c_0_51,plain,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]) ).

fof(c_0_52,plain,
    ! [X18] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X18) = X18,
    inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).

cnf(c_0_53,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_34]),c_0_35]),c_0_35]) ).

fof(c_0_54,plain,
    ! [X10,X11] :
      ( ~ class_Rings_Olinordered__idom(X11)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X11),c_Groups_Oabs__class_Oabs(X11,X10)),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(X11),X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__abs])]) ).

cnf(c_0_55,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),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(rw,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_56,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_57,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_58,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_40]),c_0_40]),c_0_40]),c_0_40]) ).

cnf(c_0_59,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).

cnf(c_0_60,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),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(X1),X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_61,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(split_conjunct,[status(thm)],[fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096]) ).

cnf(c_0_62,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),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rw,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_63,plain,
    c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).

cnf(c_0_64,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_34]),c_0_34]),c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).

fof(c_0_65,plain,
    ! [X6] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X6),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__one__imp__sqr__less__one])]) ).

fof(c_0_66,plain,
    ! [X6] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X6 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2])]) ).

fof(c_0_67,plain,
    ! [X10,X11] :
      ( ~ class_RealVector_Oreal__normed__vector(X11)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X11,X10)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).

fof(c_0_68,plain,
    ! [X51] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X51) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X51),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

cnf(c_0_69,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_34]),c_0_35]),c_0_35]) ).

cnf(c_0_70,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),v_x____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rw,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_71,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_44]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_44]) ).

cnf(c_0_72,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).

fof(c_0_73,plain,
    ! [X27,X28,X27,X28] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X28,X27)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X28,X27)
        | X28 = X27 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X28,X27)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X28,X27) )
      & ( X28 != X27
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X28,X27) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])])])]) ).

cnf(c_0_74,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

fof(c_0_75,plain,
    ! [X26,X26] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X26),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X26),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__1__iff])])])]) ).

fof(c_0_76,plain,
    ! [X26,X26] :
      ( ( c_NthRoot_Osqrt(X26) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | X26 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
      & ( X26 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | c_NthRoot_Osqrt(X26) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__1__iff])])])]) ).

fof(c_0_77,plain,
    ! [X7] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X7),
    inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).

cnf(c_0_78,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

fof(c_0_79,plain,
    ! [X27,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X27))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X27) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X27)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X27)) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__0__iff])])])]) ).

fof(c_0_80,plain,
    ! [X6] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X6)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),
    inference(variable_rename,[status(thm)],[fact_real__sqrt__abs2]) ).

cnf(c_0_81,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_82,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_83,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).

cnf(c_0_84,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_40]),c_0_40]),c_0_40]),c_0_40]) ).

cnf(c_0_85,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).

cnf(c_0_86,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_73]) ).

cnf(c_0_87,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_34]),c_0_35]),c_0_35]) ).

cnf(c_0_88,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

cnf(c_0_89,plain,
    ( c_NthRoot_Osqrt(X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_90,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_91,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_34]),c_0_35]),c_0_35]) ).

cnf(c_0_92,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_79]) ).

cnf(c_0_93,plain,
    c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_94,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).

fof(c_0_95,plain,
    ! [X27,X28,X29] :
      ( ( c_Orderings_Oord__class_Oless(X29,X28,X27)
        | X28 = X27
        | ~ c_Orderings_Oord__class_Oless__eq(X29,X28,X27)
        | ~ class_Orderings_Olinorder(X29) )
      & ( X28 != X27
        | ~ c_Orderings_Oord__class_Oless(X29,X28,X27)
        | ~ c_Orderings_Oord__class_Oless__eq(X29,X28,X27)
        | ~ class_Orderings_Olinorder(X29) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2])])])]) ).

cnf(c_0_96,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),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rw,[status(thm)],[c_0_84,c_0_49]) ).

cnf(c_0_97,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_98,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_44]) ).

cnf(c_0_99,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).

cnf(c_0_100,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_44]) ).

cnf(c_0_101,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]) ).

fof(c_0_102,plain,
    ! [X24,X25,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X25)),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X24)),
    inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).

fof(c_0_103,plain,
    ! [X10,X11] :
      ( ~ class_Rings_Olinordered__idom(X11)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),c_Groups_Oabs__class_Oabs(X11,X10)),c_Groups_Oabs__class_Oabs(X11,X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11),X10),X10) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).

cnf(c_0_104,plain,
    ( X2 = X3
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_95]) ).

cnf(c_0_105,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),v_x____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rw,[status(thm)],[c_0_96,c_0_63]) ).

cnf(c_0_106,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).

cnf(c_0_107,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_108,negated_conjecture,
    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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(spm,[status(thm)],[c_0_70,c_0_99]) ).

cnf(c_0_109,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_93]),c_0_101])]) ).

cnf(c_0_110,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
    inference(split_conjunct,[status(thm)],[c_0_102]) ).

cnf(c_0_111,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_103]) ).

cnf(c_0_112,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106])]),c_0_107]) ).

cnf(c_0_113,negated_conjecture,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109]),c_0_110]) ).

cnf(c_0_114,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_57]),c_0_110]),c_0_72])]),c_0_113]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW194+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n020.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  : 600
% 0.13/0.34  % DateTime : Sat Jun  4 07:30:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.36/3.54  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.36/3.54  # Preprocessing time       : 0.159 s
% 0.36/3.54  
% 0.36/3.54  # Proof found!
% 0.36/3.54  # SZS status Theorem
% 0.36/3.54  # SZS output start CNFRefutation
% See solution above
% 0.36/3.54  # Proof object total steps             : 115
% 0.36/3.54  # Proof object clause steps            : 63
% 0.36/3.54  # Proof object formula steps           : 52
% 0.36/3.54  # Proof object conjectures             : 14
% 0.36/3.54  # Proof object clause conjectures      : 11
% 0.36/3.54  # Proof object formula conjectures     : 3
% 0.36/3.54  # Proof object initial clauses used    : 29
% 0.36/3.54  # Proof object initial formulas used   : 29
% 0.36/3.54  # Proof object generating inferences   : 12
% 0.36/3.54  # Proof object simplifying inferences  : 111
% 0.36/3.54  # Training examples: 0 positive, 0 negative
% 0.36/3.54  # Parsed axioms                        : 1199
% 0.36/3.54  # Removed by relevancy pruning/SinE    : 0
% 0.36/3.54  # Initial clauses                      : 1727
% 0.36/3.54  # Removed in clause preprocessing      : 89
% 0.36/3.54  # Initial clauses in saturation        : 1638
% 0.36/3.54  # Processed clauses                    : 9043
% 0.36/3.54  # ...of these trivial                  : 238
% 0.36/3.54  # ...subsumed                          : 6013
% 0.36/3.54  # ...remaining for further processing  : 2792
% 0.36/3.54  # Other redundant clauses eliminated   : 153
% 0.36/3.54  # Clauses deleted for lack of memory   : 0
% 0.36/3.54  # Backward-subsumed                    : 64
% 0.36/3.54  # Backward-rewritten                   : 213
% 0.36/3.54  # Generated clauses                    : 104710
% 0.36/3.54  # ...of the previous two non-trivial   : 95728
% 0.36/3.54  # Contextual simplify-reflections      : 793
% 0.36/3.54  # Paramodulations                      : 104453
% 0.36/3.54  # Factorizations                       : 14
% 0.36/3.54  # Equation resolutions                 : 242
% 0.36/3.54  # Current number of processed clauses  : 2479
% 0.36/3.54  #    Positive orientable unit clauses  : 448
% 0.36/3.54  #    Positive unorientable unit clauses: 18
% 0.36/3.54  #    Negative unit clauses             : 233
% 0.36/3.54  #    Non-unit-clauses                  : 1780
% 0.36/3.54  # Current number of unprocessed clauses: 83141
% 0.36/3.54  # ...number of literals in the above   : 265162
% 0.36/3.54  # Current number of archived formulas  : 0
% 0.36/3.54  # Current number of archived clauses   : 281
% 0.36/3.54  # Clause-clause subsumption calls (NU) : 728728
% 0.36/3.54  # Rec. Clause-clause subsumption calls : 440972
% 0.36/3.54  # Non-unit clause-clause subsumptions  : 3167
% 0.36/3.54  # Unit Clause-clause subsumption calls : 20367
% 0.36/3.54  # Rewrite failures with RHS unbound    : 0
% 0.36/3.54  # BW rewrite match attempts            : 5764
% 0.36/3.54  # BW rewrite match successes           : 1668
% 0.36/3.54  # Condensation attempts                : 0
% 0.36/3.54  # Condensation successes               : 0
% 0.36/3.54  # Termbank termtop insertions          : 7217285
% 0.36/3.54  
% 0.36/3.54  # -------------------------------------------------
% 0.36/3.54  # User time                : 2.319 s
% 0.36/3.54  # System time              : 0.055 s
% 0.36/3.54  # Total time               : 2.374 s
% 0.36/3.54  # Maximum resident set size: 87652 pages
% 0.36/23.52  eprover: CPU time limit exceeded, terminating
% 0.36/23.52  eprover: CPU time limit exceeded, terminating
% 0.36/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.54  eprover: No such file or directory
% 0.36/23.54  eprover: CPU time limit exceeded, terminating
% 0.36/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.54  eprover: No such file or directory
% 0.36/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.54  eprover: No such file or directory
% 0.36/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.55  eprover: No such file or directory
% 0.36/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.55  eprover: No such file or directory
% 0.36/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.55  eprover: No such file or directory
% 0.36/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56  eprover: No such file or directory
% 0.36/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56  eprover: No such file or directory
% 0.36/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.56  eprover: No such file or directory
% 0.36/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56  eprover: No such file or directory
% 0.36/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56  eprover: No such file or directory
% 0.36/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56  eprover: No such file or directory
% 0.36/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.57  eprover: No such file or directory
% 0.36/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.57  eprover: No such file or directory
% 0.36/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.57  eprover: No such file or directory
% 0.36/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.57  eprover: No such file or directory
% 0.36/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.57  eprover: No such file or directory
% 0.36/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.57  eprover: No such file or directory
% 0.36/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.58  eprover: No such file or directory
% 0.36/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.58  eprover: No such file or directory
% 0.36/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.58  eprover: No such file or directory
% 0.36/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.58  eprover: No such file or directory
% 0.36/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.58  eprover: No such file or directory
% 0.36/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.58  eprover: No such file or directory
% 0.36/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.59  eprover: No such file or directory
% 0.36/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.59  eprover: No such file or directory
% 0.36/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.59  eprover: No such file or directory
% 0.36/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.59  eprover: No such file or directory
% 0.36/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.60  eprover: No such file or directory
% 0.36/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.60  eprover: No such file or directory
% 0.36/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.60  eprover: No such file or directory
% 0.36/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.60  eprover: No such file or directory
% 0.36/23.61  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.36/23.61  eprover: No such file or directory
%------------------------------------------------------------------------------