TSTP Solution File: SWW179+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWW179+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n024.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 00:10:14 EDT 2022

% Result   : Theorem 0.34s 1.53s
% Output   : CNFRefutation 0.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   63 (  36 unt;   0 def)
%            Number of atoms       :  130 (  42 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  121 (  54   ~;  45   |;   8   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    7 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-3 aty)
%            Number of variables   :   78 (   3 sgn  45   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X19,X16,X17,X8] :
      ( class_Groups_Oab__semigroup__add(X8)
     => c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X17,X16),X19) = c_Groups_Oplus__class_Oplus(X8,X17,c_Groups_Oplus__class_Oplus(X8,X16,X19)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

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

fof(fact_add__0__iff,axiom,
    ! [X21,X20,X8] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
     => ( X20 = c_Groups_Oplus__class_Oplus(X8,X20,X21)
      <=> X21 = c_Groups_Ozero__class_Ozero(X8) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__0__iff) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X19,X16,X17,X8] :
      ( class_Groups_Oordered__comm__monoid__add(X8)
     => ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X17)
       => ( c_Orderings_Oord__class_Oless(X8,X16,X19)
         => c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Oplus__class_Oplus(X8,X17,X19)) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_real__of__nat__ge__zero,axiom,
    ! [X34] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X34)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__of__nat__ge__zero) ).

fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(fact_abs__add__one__gt__zero,axiom,
    ! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4))),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_abs__add__one__gt__zero) ).

fof(fact_abs__real__def,axiom,
    ! [X17] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X17) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X17) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X17) = X17 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_abs__real__def) ).

fof(fact_less__le__not__le,axiom,
    ! [X10,X9,X8] :
      ( class_Orderings_Opreorder(X8)
     => ( c_Orderings_Oord__class_Oless(X8,X9,X10)
      <=> ( c_Orderings_Oord__class_Oless__eq(X8,X9,X10)
          & ~ c_Orderings_Oord__class_Oless__eq(X8,X10,X9) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_less__le__not__le) ).

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

fof(fact_real__of__nat__1,axiom,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__of__nat__1) ).

fof(fact__0960_A_060_061_Acmod_Ac_096,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact__0960_A_060_061_Acmod_Ac_096) ).

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

fof(fact_norm__eq__zero,axiom,
    ! [X9,X8] :
      ( class_RealVector_Oreal__normed__vector(X8)
     => ( c_RealVector_Onorm__class_Onorm(X8,X9) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      <=> X9 = c_Groups_Ozero__class_Ozero(X8) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_norm__eq__zero) ).

fof(fact_real__norm__def,axiom,
    ! [X7] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X7) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__norm__def) ).

fof(fact_zero__less__norm__iff,axiom,
    ! [X9,X8] :
      ( class_RealVector_Oreal__normed__vector(X8)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X9))
      <=> X9 != c_Groups_Ozero__class_Ozero(X8) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_zero__less__norm__iff) ).

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(c_0_18,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_19,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Groups_Oab__semigroup__add(X23)
      | c_Groups_Oplus__class_Oplus(X23,c_Groups_Oplus__class_Oplus(X23,X22,X21),X20) = c_Groups_Oplus__class_Oplus(X23,X22,c_Groups_Oplus__class_Oplus(X23,X21,X20)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(c_0_20,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

cnf(c_0_21,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).

fof(c_0_23,plain,
    ! [X22,X23,X24] :
      ( ( X23 != c_Groups_Oplus__class_Oplus(X24,X23,X22)
        | X22 = c_Groups_Ozero__class_Ozero(X24)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X24) )
      & ( X22 != c_Groups_Ozero__class_Ozero(X24)
        | X23 = c_Groups_Oplus__class_Oplus(X24,X23,X22)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(c_0_24,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Ozero__class_Ozero(X23),X22)
      | ~ c_Orderings_Oord__class_Oless(X23,X21,X20)
      | c_Orderings_Oord__class_Oless(X23,X21,c_Groups_Oplus__class_Oplus(X23,X22,X20)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(c_0_25,plain,
    ! [X35] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X35)),
    inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).

cnf(c_0_26,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(X1,X2,X3)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

fof(c_0_30,plain,
    ! [X5] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5))),
    inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).

fof(c_0_31,plain,
    ! [X18,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) = X18 ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__real__def])])])])]) ).

fof(c_0_32,plain,
    ! [X11,X12,X13] :
      ( ( c_Orderings_Oord__class_Oless__eq(X13,X12,X11)
        | ~ c_Orderings_Oord__class_Oless(X13,X12,X11)
        | ~ class_Orderings_Opreorder(X13) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X13,X11,X12)
        | ~ c_Orderings_Oord__class_Oless(X13,X12,X11)
        | ~ class_Orderings_Opreorder(X13) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X13,X12,X11)
        | c_Orderings_Oord__class_Oless__eq(X13,X11,X12)
        | c_Orderings_Oord__class_Oless(X13,X12,X11)
        | ~ class_Orderings_Opreorder(X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__le__not__le])])])]) ).

cnf(c_0_33,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).

cnf(c_0_35,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_36,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_real__of__nat__1]) ).

cnf(c_0_37,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))),
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_38,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = X1
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_39,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_40,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_41,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_42,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
    inference(split_conjunct,[status(thm)],[fact__0960_A_060_061_Acmod_Ac_096]) ).

cnf(c_0_43,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

fof(c_0_44,plain,
    ! [X10,X11] :
      ( ( c_RealVector_Onorm__class_Onorm(X11,X10) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X10 = c_Groups_Ozero__class_Ozero(X11)
        | ~ class_RealVector_Oreal__normed__vector(X11) )
      & ( X10 != c_Groups_Ozero__class_Ozero(X11)
        | c_RealVector_Onorm__class_Onorm(X11,X10) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ class_RealVector_Oreal__normed__vector(X11) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).

fof(c_0_45,plain,
    ! [X8] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X8) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X8),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

cnf(c_0_46,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_47,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

fof(c_0_48,plain,
    ! [X10,X11] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X11,X10))
        | X10 != c_Groups_Ozero__class_Ozero(X11)
        | ~ class_RealVector_Oreal__normed__vector(X11) )
      & ( X10 = c_Groups_Ozero__class_Ozero(X11)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X11,X10))
        | ~ class_RealVector_Oreal__normed__vector(X11) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).

cnf(c_0_49,negated_conjecture,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_50,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_51,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).

cnf(c_0_52,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_53,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).

cnf(c_0_54,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_45]) ).

cnf(c_0_55,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_46]),c_0_47])]) ).

cnf(c_0_56,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_57,negated_conjecture,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).

cnf(c_0_58,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).

cnf(c_0_59,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_46]),c_0_42])]) ).

cnf(c_0_60,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless(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_56,c_0_54]),c_0_53])]) ).

cnf(c_0_61,negated_conjecture,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_62,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWW179+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n024.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 17:15:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.34/1.53  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.34/1.53  # Preprocessing time       : 0.129 s
% 0.34/1.53  
% 0.34/1.53  # Proof found!
% 0.34/1.53  # SZS status Theorem
% 0.34/1.53  # SZS output start CNFRefutation
% See solution above
% 0.34/1.53  # Proof object total steps             : 63
% 0.34/1.53  # Proof object clause steps            : 33
% 0.34/1.53  # Proof object formula steps           : 30
% 0.34/1.53  # Proof object conjectures             : 11
% 0.34/1.53  # Proof object clause conjectures      : 8
% 0.34/1.53  # Proof object formula conjectures     : 3
% 0.34/1.53  # Proof object initial clauses used    : 18
% 0.34/1.53  # Proof object initial formulas used   : 18
% 0.34/1.53  # Proof object generating inferences   : 14
% 0.34/1.53  # Proof object simplifying inferences  : 12
% 0.34/1.53  # Training examples: 0 positive, 0 negative
% 0.34/1.53  # Parsed axioms                        : 1275
% 0.34/1.53  # Removed by relevancy pruning/SinE    : 0
% 0.34/1.53  # Initial clauses                      : 1761
% 0.34/1.53  # Removed in clause preprocessing      : 50
% 0.34/1.53  # Initial clauses in saturation        : 1711
% 0.34/1.53  # Processed clauses                    : 2321
% 0.34/1.53  # ...of these trivial                  : 41
% 0.34/1.53  # ...subsumed                          : 599
% 0.34/1.53  # ...remaining for further processing  : 1681
% 0.34/1.53  # Other redundant clauses eliminated   : 215
% 0.34/1.53  # Clauses deleted for lack of memory   : 0
% 0.34/1.53  # Backward-subsumed                    : 19
% 0.34/1.53  # Backward-rewritten                   : 17
% 0.34/1.53  # Generated clauses                    : 49375
% 0.34/1.53  # ...of the previous two non-trivial   : 45875
% 0.34/1.53  # Contextual simplify-reflections      : 47
% 0.34/1.53  # Paramodulations                      : 49109
% 0.34/1.53  # Factorizations                       : 10
% 0.34/1.53  # Equation resolutions                 : 256
% 0.34/1.53  # Current number of processed clauses  : 1608
% 0.34/1.53  #    Positive orientable unit clauses  : 329
% 0.34/1.53  #    Positive unorientable unit clauses: 11
% 0.34/1.53  #    Negative unit clauses             : 60
% 0.34/1.53  #    Non-unit-clauses                  : 1208
% 0.34/1.53  # Current number of unprocessed clauses: 44716
% 0.34/1.53  # ...number of literals in the above   : 145530
% 0.34/1.53  # Current number of archived formulas  : 0
% 0.34/1.53  # Current number of archived clauses   : 37
% 0.34/1.53  # Clause-clause subsumption calls (NU) : 128841
% 0.34/1.53  # Rec. Clause-clause subsumption calls : 85049
% 0.34/1.53  # Non-unit clause-clause subsumptions  : 296
% 0.34/1.53  # Unit Clause-clause subsumption calls : 4736
% 0.34/1.53  # Rewrite failures with RHS unbound    : 0
% 0.34/1.53  # BW rewrite match attempts            : 1233
% 0.34/1.53  # BW rewrite match successes           : 125
% 0.34/1.53  # Condensation attempts                : 0
% 0.34/1.53  # Condensation successes               : 0
% 0.34/1.53  # Termbank termtop insertions          : 1248665
% 0.34/1.53  
% 0.34/1.53  # -------------------------------------------------
% 0.34/1.53  # User time                : 0.729 s
% 0.34/1.53  # System time              : 0.029 s
% 0.34/1.53  # Total time               : 0.758 s
% 0.34/1.53  # Maximum resident set size: 51064 pages
% 0.34/23.52  eprover: CPU time limit exceeded, terminating
% 0.34/23.53  eprover: CPU time limit exceeded, terminating
% 0.34/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.54  eprover: No such file or directory
% 0.34/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.54  eprover: No such file or directory
% 0.34/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.55  eprover: No such file or directory
% 0.34/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.55  eprover: No such file or directory
% 0.34/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.56  eprover: No such file or directory
% 0.34/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.57  eprover: No such file or directory
% 0.34/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.57  eprover: No such file or directory
% 0.34/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.57  eprover: No such file or directory
% 0.34/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.58  eprover: No such file or directory
% 0.34/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.58  eprover: No such file or directory
% 0.34/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.58  eprover: No such file or directory
% 0.34/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.58  eprover: No such file or directory
% 0.34/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.58  eprover: No such file or directory
% 0.34/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.59  eprover: No such file or directory
% 0.34/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.59  eprover: No such file or directory
% 0.34/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.59  eprover: No such file or directory
% 0.34/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.34/23.59  eprover: No such file or directory
% 0.34/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.60  eprover: No such file or directory
% 0.34/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.60  eprover: No such file or directory
% 0.34/23.61  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.61  eprover: No such file or directory
% 0.34/23.61  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.61  eprover: No such file or directory
% 0.34/23.62  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.34/23.62  eprover: No such file or directory
%------------------------------------------------------------------------------