TSTP Solution File: SWW224+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWW224+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n032.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 00:10:20 EDT 2022

% Result   : Theorem 0.40s 23.58s
% Output   : CNFRefutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  171 (  71 unt;   0 def)
%            Number of atoms       :  385 (  87 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  388 ( 174   ~; 154   |;  13   &)
%                                         (   8 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  271 (   6 sgn 160   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_order__le__less__trans,axiom,
    ! [X13,X14,X12,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X12,X14)
       => ( c_Orderings_Oord__class_Oless(X7,X14,X13)
         => c_Orderings_Oord__class_Oless(X7,X12,X13) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_order__le__less__trans) ).

fof(fact_order__less__le__trans,axiom,
    ! [X13,X14,X12,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X12,X14)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X14,X13)
         => c_Orderings_Oord__class_Oless(X7,X12,X13) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_order__less__le__trans) ).

fof(conj_0,hypothesis,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_0) ).

fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(fact_order__less__irrefl,axiom,
    ! [X12,X7] :
      ( class_Orderings_Opreorder(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,X12,X12) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_order__less__irrefl) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [X18,X5,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X5,X18)
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X5,X18),c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_less__iff__diff__less__0) ).

fof(fact_leI,axiom,
    ! [X14,X12,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X12,X14)
       => c_Orderings_Oord__class_Oless__eq(X7,X14,X12) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_leI) ).

fof(fact_positive__add,axiom,
    ! [X14,X12] :
      ( c_RealDef_Opositive(X12)
     => ( c_RealDef_Opositive(X14)
       => c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X14)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_positive__add) ).

fof(fact_double__zero__sym,axiom,
    ! [X5,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Groups_Ozero__class_Ozero(X7) = c_Groups_Oplus__class_Oplus(X7,X5,X5)
      <=> X5 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_double__zero__sym) ).

fof(fact_positive__zero,axiom,
    ~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_positive__zero) ).

fof(fact_less__real__def,axiom,
    ! [X16,X6] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X16)
    <=> c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X16,X6)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_less__real__def) ).

fof(conj_1,hypothesis,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_1) ).

fof(fact_real__norm__def,axiom,
    ! [X31] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X31) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X31),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_real__norm__def) ).

fof(fact_abs__minus__commute,axiom,
    ! [X8,X9,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X9,X8)) = c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X8,X9)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_abs__minus__commute) ).

fof(fact_order__less__asym,axiom,
    ! [X14,X12,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X12,X14)
       => ~ c_Orderings_Oord__class_Oless(X7,X14,X12) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_order__less__asym) ).

fof(fact_less__eq__real__def,axiom,
    ! [X16,X6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X16)
    <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X16)
        | X6 = X16 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_less__eq__real__def) ).

fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

fof(conj_2,conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_2) ).

fof(fact_abs__of__nonneg,axiom,
    ! [X9,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
       => c_Groups_Oabs__class_Oabs(X7,X9) = X9 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_abs__of__nonneg) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Orderings_Olinorder) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).

fof(fact_abs__of__pos,axiom,
    ! [X9,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X9)
       => c_Groups_Oabs__class_Oabs(X7,X9) = X9 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_abs__of__pos) ).

fof(fact_add__right__cancel,axiom,
    ! [X17,X5,X18,X7] :
      ( class_Groups_Ocancel__semigroup__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X18,X5) = c_Groups_Oplus__class_Oplus(X7,X17,X5)
      <=> X18 = X17 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__right__cancel) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X9,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X9) = X9 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_diff__add__cancel,axiom,
    ! [X8,X9,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X9,X8),X8) = X9 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_diff__add__cancel) ).

fof(fact_add__diff__cancel,axiom,
    ! [X8,X9,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X9,X8),X8) = X9 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__diff__cancel) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X11,X9,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X9,X11) = c_Groups_Oplus__class_Oplus(X7,X11,X9) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_norm__minus__commute,axiom,
    ! [X8,X9,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X9,X8)) = c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X8,X9)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_norm__minus__commute) ).

fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Ogroup__add) ).

fof(fact_add__0__iff,axiom,
    ! [X5,X18,X7] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
     => ( X18 = c_Groups_Oplus__class_Oplus(X7,X18,X5)
      <=> X5 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__0__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.mepo_128.in',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X14,X12,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( X12 != X14
       => ( ~ c_Orderings_Oord__class_Oless(X7,X12,X14)
         => c_Orderings_Oord__class_Oless(X7,X14,X12) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_linorder__neqE__linordered__idom) ).

fof(fact_less__le__not__le,axiom,
    ! [X16,X6,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X16)
      <=> ( c_Orderings_Oord__class_Oless__eq(X7,X6,X16)
          & ~ c_Orderings_Oord__class_Oless__eq(X7,X16,X6) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_less__le__not__le) ).

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.mepo_128.in',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X8,X11,X9,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X9,X11),c_Groups_Oplus__class_Oplus(X7,X8,X11))
       => c_Orderings_Oord__class_Oless__eq(X7,X9,X8) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__le__imp__le__right) ).

fof(fact_norm__not__less__zero,axiom,
    ! [X12,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_norm__not__less__zero) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

fof(fact_abs__diff__less__iff,axiom,
    ! [X4,X5,X6,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)),X4)
      <=> ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X5,X4),X6)
          & c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Oplus__class_Oplus(X7,X5,X4)) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_abs__diff__less__iff) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X11,X8,X9,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
       => ( c_Orderings_Oord__class_Oless(X7,X8,X11)
         => c_Orderings_Oord__class_Oless(X7,X8,c_Groups_Oplus__class_Oplus(X7,X9,X11)) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_add__strict__increasing2) ).

fof(fact_norm__ge__zero,axiom,
    ! [X12,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X12)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_norm__ge__zero) ).

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.mepo_128.in',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

fof(c_0_45,plain,
    ! [X15,X16,X17,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_Orderings_Oord__class_Oless__eq(X18,X17,X16)
      | ~ c_Orderings_Oord__class_Oless(X18,X16,X15)
      | c_Orderings_Oord__class_Oless(X18,X17,X15) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(c_0_46,plain,
    ! [X15,X16,X17,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_Orderings_Oord__class_Oless(X18,X17,X16)
      | ~ c_Orderings_Oord__class_Oless__eq(X18,X16,X15)
      | c_Orderings_Oord__class_Oless(X18,X17,X15) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

cnf(c_0_47,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_48,hypothesis,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x),
    inference(split_conjunct,[status(thm)],[conj_0]) ).

cnf(c_0_49,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

fof(c_0_50,plain,
    ! [X13,X14] :
      ( ~ class_Orderings_Opreorder(X14)
      | ~ c_Orderings_Oord__class_Oless(X14,X13,X13) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__irrefl])])]) ).

cnf(c_0_51,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

fof(c_0_52,plain,
    ! [X19,X20,X21] :
      ( ( ~ c_Orderings_Oord__class_Oless(X21,X20,X19)
        | c_Orderings_Oord__class_Oless(X21,c_Groups_Ominus__class_Ominus(X21,X20,X19),c_Groups_Ozero__class_Ozero(X21))
        | ~ class_Groups_Oordered__ab__group__add(X21) )
      & ( ~ c_Orderings_Oord__class_Oless(X21,c_Groups_Ominus__class_Ominus(X21,X20,X19),c_Groups_Ozero__class_Ozero(X21))
        | c_Orderings_Oord__class_Oless(X21,X20,X19)
        | ~ class_Groups_Oordered__ab__group__add(X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).

fof(c_0_53,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Olinorder(X17)
      | c_Orderings_Oord__class_Oless(X17,X16,X15)
      | c_Orderings_Oord__class_Oless__eq(X17,X15,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_leI])])]) ).

fof(c_0_54,plain,
    ! [X15,X16] :
      ( ~ c_RealDef_Opositive(X16)
      | ~ c_RealDef_Opositive(X15)
      | c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X16,X15)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_positive__add])]) ).

fof(c_0_55,plain,
    ! [X8,X9] :
      ( ( c_Groups_Ozero__class_Ozero(X9) != c_Groups_Oplus__class_Oplus(X9,X8,X8)
        | X8 = c_Groups_Ozero__class_Ozero(X9)
        | ~ class_Groups_Olinordered__ab__group__add(X9) )
      & ( X8 != c_Groups_Ozero__class_Ozero(X9)
        | c_Groups_Ozero__class_Ozero(X9) = c_Groups_Oplus__class_Oplus(X9,X8,X8)
        | ~ class_Groups_Olinordered__ab__group__add(X9) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(c_0_56,plain,
    ~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(fof_simplification,[status(thm)],[fact_positive__zero]) ).

fof(c_0_57,plain,
    ! [X17,X18,X17,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
        | c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X17,X18)) )
      & ( ~ c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X17,X18))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__real__def])])])]) ).

cnf(c_0_58,hypothesis,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).

cnf(c_0_59,hypothesis,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
    inference(split_conjunct,[status(thm)],[conj_1]) ).

cnf(c_0_60,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X2)
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_61,hypothesis,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_x)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_m) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_48]),c_0_49])]) ).

cnf(c_0_62,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_63,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

fof(c_0_64,plain,
    ! [X32] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X32) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X32),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

fof(c_0_65,plain,
    ! [X10,X11,X12] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X12)
      | c_Groups_Oabs__class_Oabs(X12,c_Groups_Ominus__class_Ominus(X12,X11,X10)) = c_Groups_Oabs__class_Oabs(X12,c_Groups_Ominus__class_Ominus(X12,X10,X11)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).

fof(c_0_66,plain,
    ! [X15,X16,X17] :
      ( ~ class_Orderings_Opreorder(X17)
      | ~ c_Orderings_Oord__class_Oless(X17,X16,X15)
      | ~ c_Orderings_Oord__class_Oless(X17,X15,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__asym])])]) ).

fof(c_0_67,plain,
    ! [X17,X18,X17,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
        | X18 = X17 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17) )
      & ( X18 != X17
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17) ) ),
    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_68,plain,
    ( c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
    | ~ c_RealDef_Opositive(X2)
    | ~ c_RealDef_Opositive(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_69,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_70,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).

cnf(c_0_71,plain,
    ~ c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_72,plain,
    ( c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_73,hypothesis,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

fof(c_0_74,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
    inference(assume_negation,[status(cth)],[conj_2]) ).

fof(c_0_75,plain,
    ! [X10,X11] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X11)
      | ~ c_Orderings_Oord__class_Oless__eq(X11,c_Groups_Ozero__class_Ozero(X11),X10)
      | c_Groups_Oabs__class_Oabs(X11,X10) = X10 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).

cnf(c_0_76,hypothesis,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_49])]) ).

cnf(c_0_77,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3))
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_78,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]) ).

cnf(c_0_79,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).

cnf(c_0_80,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_64]) ).

cnf(c_0_81,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_82,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).

cnf(c_0_83,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_84,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_85,plain,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_RealDef_Opositive(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]),c_0_71]) ).

cnf(c_0_86,hypothesis,
    c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m)),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

fof(c_0_87,plain,
    ! [X10,X11] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X11)
      | ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Ozero__class_Ozero(X11),X10)
      | c_Groups_Oabs__class_Oabs(X11,X10) = X10 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).

fof(c_0_88,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_89,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Groups_Oplus__class_Oplus(X22,X21,X20) != c_Groups_Oplus__class_Oplus(X22,X19,X20)
        | X21 = X19
        | ~ class_Groups_Ocancel__semigroup__add(X22) )
      & ( X21 != X19
        | c_Groups_Oplus__class_Oplus(X22,X21,X20) = c_Groups_Oplus__class_Oplus(X22,X19,X20)
        | ~ class_Groups_Ocancel__semigroup__add(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(c_0_90,plain,
    ! [X10,X11] :
      ( ~ class_Rings_Ocomm__semiring__1(X11)
      | c_Groups_Oplus__class_Oplus(X11,c_Groups_Ozero__class_Ozero(X11),X10) = X10 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(c_0_91,plain,
    ! [X10,X11,X12] :
      ( ~ class_Groups_Ogroup__add(X12)
      | c_Groups_Oplus__class_Oplus(X12,c_Groups_Ominus__class_Ominus(X12,X11,X10),X10) = X11 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).

cnf(c_0_92,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

cnf(c_0_93,hypothesis,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79])]) ).

cnf(c_0_94,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_80]),c_0_82])]) ).

cnf(c_0_95,hypothesis,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_73]),c_0_49])]) ).

cnf(c_0_96,plain,
    ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_84]),c_0_78])]) ).

cnf(c_0_97,hypothesis,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_98,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = X2
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

fof(c_0_99,plain,
    ! [X10,X11,X12] :
      ( ~ class_Groups_Ogroup__add(X12)
      | c_Groups_Ominus__class_Ominus(X12,c_Groups_Oplus__class_Oplus(X12,X11,X10),X10) = X11 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).

fof(c_0_100,plain,
    ! [X12,X13,X14] :
      ( ~ class_Rings_Ocomm__semiring__1(X14)
      | c_Groups_Oplus__class_Oplus(X14,X13,X12) = c_Groups_Oplus__class_Oplus(X14,X12,X13) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

cnf(c_0_101,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
    inference(split_conjunct,[status(thm)],[c_0_88]) ).

fof(c_0_102,plain,
    ! [X10,X11,X12] :
      ( ~ class_RealVector_Oreal__normed__vector(X12)
      | c_RealVector_Onorm__class_Onorm(X12,c_Groups_Ominus__class_Ominus(X12,X11,X10)) = c_RealVector_Onorm__class_Onorm(X12,c_Groups_Ominus__class_Ominus(X12,X10,X11)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).

cnf(c_0_103,plain,
    ( X2 = X3
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_104,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_90]) ).

cnf(c_0_105,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_91]) ).

cnf(c_0_106,hypothesis,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_x)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_80]),c_0_94]),c_0_82])]) ).

cnf(c_0_107,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).

fof(c_0_108,plain,
    ! [X19,X20,X21] :
      ( ( X20 != c_Groups_Oplus__class_Oplus(X21,X20,X19)
        | X19 = c_Groups_Ozero__class_Ozero(X21)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21) )
      & ( X19 != c_Groups_Ozero__class_Ozero(X21)
        | X20 = c_Groups_Oplus__class_Oplus(X21,X20,X19)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

cnf(c_0_109,hypothesis,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).

cnf(c_0_110,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = X2
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(spm,[status(thm)],[c_0_98,c_0_63]) ).

cnf(c_0_111,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_99]) ).

cnf(c_0_112,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_100]) ).

cnf(c_0_113,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e),
    inference(rw,[status(thm)],[c_0_101,c_0_80]) ).

cnf(c_0_114,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_102]) ).

cnf(c_0_115,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).

cnf(c_0_116,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Oplus__class_Oplus(X2,X1,X3) != X3
    | ~ class_Rings_Ocomm__semiring__1(X2)
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(spm,[status(thm)],[c_0_103,c_0_104]) ).

cnf(c_0_117,hypothesis,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_x)),v_m) = v_x,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]) ).

cnf(c_0_118,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).

cnf(c_0_119,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).

fof(c_0_120,plain,
    ! [X15,X16,X17] :
      ( ~ class_Rings_Olinordered__idom(X17)
      | X16 = X15
      | c_Orderings_Oord__class_Oless(X17,X16,X15)
      | c_Orderings_Oord__class_Oless(X17,X15,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom])])]) ).

fof(c_0_121,plain,
    ! [X17,X18,X19] :
      ( ( c_Orderings_Oord__class_Oless__eq(X19,X18,X17)
        | ~ c_Orderings_Oord__class_Oless(X19,X18,X17)
        | ~ class_Orderings_Opreorder(X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X19,X17,X18)
        | ~ c_Orderings_Oord__class_Oless(X19,X18,X17)
        | ~ class_Orderings_Opreorder(X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X19,X18,X17)
        | c_Orderings_Oord__class_Oless__eq(X19,X17,X18)
        | c_Orderings_Oord__class_Oless(X19,X18,X17)
        | ~ class_Orderings_Opreorder(X19) ) ),
    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_122,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_108]) ).

cnf(c_0_123,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_124,plain,
    ! [X12,X13,X14,X15] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X15)
      | ~ c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Oplus__class_Oplus(X15,X14,X13),c_Groups_Oplus__class_Oplus(X15,X12,X13))
      | c_Orderings_Oord__class_Oless__eq(X15,X14,X12) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(c_0_125,plain,
    ! [X13,X14] :
      ( ~ class_RealVector_Oreal__normed__vector(X14)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X14,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero])])]) ).

cnf(c_0_126,hypothesis,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_m) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_80]),c_0_79]),c_0_82])]),c_0_94]) ).

cnf(c_0_127,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = X3
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_128,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_x)),v_e),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115])]) ).

cnf(c_0_129,hypothesis,
    ( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,v_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | v_x != v_m ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_119])]) ).

cnf(c_0_130,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | X3 = X2
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_120]) ).

cnf(c_0_131,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).

cnf(c_0_132,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_121]) ).

cnf(c_0_133,hypothesis,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
    | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_e ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_122]),c_0_123])]) ).

cnf(c_0_134,hypothesis,
    c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x)),
    inference(spm,[status(thm)],[c_0_72,c_0_59]) ).

fof(c_0_135,plain,
    ! [X8,X9,X10,X11] :
      ( ( c_Orderings_Oord__class_Oless(X11,c_Groups_Ominus__class_Ominus(X11,X9,X8),X10)
        | ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Oabs__class_Oabs(X11,c_Groups_Ominus__class_Ominus(X11,X10,X9)),X8)
        | ~ class_Rings_Olinordered__idom(X11) )
      & ( c_Orderings_Oord__class_Oless(X11,X10,c_Groups_Oplus__class_Oplus(X11,X9,X8))
        | ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Oabs__class_Oabs(X11,c_Groups_Ominus__class_Ominus(X11,X10,X9)),X8)
        | ~ class_Rings_Olinordered__idom(X11) )
      & ( ~ c_Orderings_Oord__class_Oless(X11,c_Groups_Ominus__class_Ominus(X11,X9,X8),X10)
        | ~ c_Orderings_Oord__class_Oless(X11,X10,c_Groups_Oplus__class_Oplus(X11,X9,X8))
        | c_Orderings_Oord__class_Oless(X11,c_Groups_Oabs__class_Oabs(X11,c_Groups_Ominus__class_Ominus(X11,X10,X9)),X8)
        | ~ class_Rings_Olinordered__idom(X11) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])]) ).

cnf(c_0_136,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

cnf(c_0_137,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_67]) ).

cnf(c_0_138,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_125]) ).

cnf(c_0_139,hypothesis,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))) = v_e,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_118]),c_0_107])]) ).

cnf(c_0_140,negated_conjecture,
    ( v_x != v_m
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e) ),
    inference(spm,[status(thm)],[c_0_128,c_0_129]) ).

cnf(c_0_141,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(spm,[status(thm)],[c_0_130,c_0_131]) ).

cnf(c_0_142,hypothesis,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != v_e,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_49]),c_0_48])]) ).

cnf(c_0_143,hypothesis,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_59]),c_0_49])]) ).

cnf(c_0_144,hypothesis,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(spm,[status(thm)],[c_0_85,c_0_134]) ).

cnf(c_0_145,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_135]) ).

cnf(c_0_146,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_Groups_Ogroup__add(X1)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(spm,[status(thm)],[c_0_136,c_0_105]) ).

cnf(c_0_147,hypothesis,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
    inference(spm,[status(thm)],[c_0_137,c_0_59]) ).

cnf(c_0_148,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(c_0_149,plain,
    ! [X12,X13,X14,X15] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X15)
      | ~ c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Ozero__class_Ozero(X15),X14)
      | ~ c_Orderings_Oord__class_Oless(X15,X13,X12)
      | c_Orderings_Oord__class_Oless(X15,X13,c_Groups_Oplus__class_Oplus(X15,X14,X12)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(c_0_150,plain,
    ! [X13,X14] :
      ( ~ class_RealVector_Oreal__normed__vector(X14)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X14,X13)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).

cnf(c_0_151,hypothesis,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_115])]) ).

cnf(c_0_152,negated_conjecture,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | v_x != v_m ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]) ).

cnf(c_0_153,hypothesis,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_96]),c_0_144]) ).

cnf(c_0_154,plain,
    ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = X3
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X1)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_84]),c_0_80]),c_0_131])]) ).

cnf(c_0_155,hypothesis,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_e),v_m),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_107]),c_0_148])]) ).

cnf(c_0_156,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_149]) ).

cnf(c_0_157,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_150]) ).

cnf(c_0_158,hypothesis,
    ( v_x = v_m
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,v_x) ),
    inference(spm,[status(thm)],[c_0_76,c_0_141]) ).

cnf(c_0_159,negated_conjecture,
    v_x != v_m,
    inference(spm,[status(thm)],[c_0_151,c_0_152]) ).

cnf(c_0_160,hypothesis,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_110]),c_0_80]),c_0_79]),c_0_82])]),c_0_94]) ).

cnf(c_0_161,negated_conjecture,
    ( c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_e) = v_m
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x,v_e)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_154]),c_0_155])]) ).

cnf(c_0_162,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_156,c_0_112]) ).

cnf(c_0_163,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_164,hypothesis,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_139]),c_0_115])]) ).

cnf(c_0_165,hypothesis,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m,v_x),
    inference(sr,[status(thm)],[c_0_158,c_0_159]) ).

cnf(c_0_166,hypothesis,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))),v_x) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_160]),c_0_107])]) ).

cnf(c_0_167,hypothesis,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(rw,[status(thm)],[c_0_144,c_0_160]) ).

cnf(c_0_168,negated_conjecture,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_e) = v_m,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]),c_0_118]),c_0_164]),c_0_165])]) ).

cnf(c_0_169,hypothesis,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e) != v_x,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_166]),c_0_118]),c_0_119])]),c_0_167]) ).

cnf(c_0_170,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_168]),c_0_107])]),c_0_169]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SWW224+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.10  % Command  : run_ET %s %d
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Sat Jun  4 10:19:32 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.40/23.42  eprover: CPU time limit exceeded, terminating
% 0.40/23.43  eprover: CPU time limit exceeded, terminating
% 0.40/23.43  eprover: CPU time limit exceeded, terminating
% 0.40/23.58  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.40/23.58  # Preprocessing time       : 0.094 s
% 0.40/23.58  
% 0.40/23.58  # Proof found!
% 0.40/23.58  # SZS status Theorem
% 0.40/23.58  # SZS output start CNFRefutation
% See solution above
% 0.40/23.58  # Proof object total steps             : 171
% 0.40/23.58  # Proof object clause steps            : 95
% 0.40/23.58  # Proof object formula steps           : 76
% 0.40/23.58  # Proof object conjectures             : 12
% 0.40/23.58  # Proof object clause conjectures      : 9
% 0.40/23.58  # Proof object formula conjectures     : 3
% 0.40/23.58  # Proof object initial clauses used    : 46
% 0.40/23.58  # Proof object initial formulas used   : 45
% 0.40/23.58  # Proof object generating inferences   : 46
% 0.40/23.58  # Proof object simplifying inferences  : 82
% 0.40/23.58  # Training examples: 0 positive, 0 negative
% 0.40/23.58  # Parsed axioms                        : 1188
% 0.40/23.58  # Removed by relevancy pruning/SinE    : 0
% 0.40/23.58  # Initial clauses                      : 1702
% 0.40/23.58  # Removed in clause preprocessing      : 44
% 0.40/23.58  # Initial clauses in saturation        : 1658
% 0.40/23.58  # Processed clauses                    : 33328
% 0.40/23.58  # ...of these trivial                  : 935
% 0.40/23.58  # ...subsumed                          : 21490
% 0.40/23.58  # ...remaining for further processing  : 10903
% 0.40/23.58  # Other redundant clauses eliminated   : 1145
% 0.40/23.58  # Clauses deleted for lack of memory   : 753966
% 0.40/23.58  # Backward-subsumed                    : 318
% 0.40/23.58  # Backward-rewritten                   : 1263
% 0.40/23.58  # Generated clauses                    : 1064088
% 0.40/23.58  # ...of the previous two non-trivial   : 989595
% 0.40/23.58  # Contextual simplify-reflections      : 6470
% 0.40/23.58  # Paramodulations                      : 1062566
% 0.40/23.58  # Factorizations                       : 13
% 0.40/23.58  # Equation resolutions                 : 1290
% 0.40/23.58  # Current number of processed clauses  : 9184
% 0.40/23.58  #    Positive orientable unit clauses  : 720
% 0.40/23.58  #    Positive unorientable unit clauses: 62
% 0.40/23.58  #    Negative unit clauses             : 380
% 0.40/23.58  #    Non-unit-clauses                  : 8022
% 0.40/23.58  # Current number of unprocessed clauses: 127778
% 0.40/23.58  # ...number of literals in the above   : 428145
% 0.40/23.58  # Current number of archived formulas  : 0
% 0.40/23.58  # Current number of archived clauses   : 1608
% 0.40/23.58  # Clause-clause subsumption calls (NU) : 15503889
% 0.40/23.58  # Rec. Clause-clause subsumption calls : 11095901
% 0.40/23.58  # Non-unit clause-clause subsumptions  : 19190
% 0.40/23.58  # Unit Clause-clause subsumption calls : 294170
% 0.40/23.58  # Rewrite failures with RHS unbound    : 0
% 0.40/23.58  # BW rewrite match attempts            : 14302
% 0.40/23.58  # BW rewrite match successes           : 533
% 0.40/23.58  # Condensation attempts                : 0
% 0.40/23.58  # Condensation successes               : 0
% 0.40/23.58  # Termbank termtop insertions          : 24183119
% 0.40/23.58  
% 0.40/23.58  # -------------------------------------------------
% 0.40/23.58  # User time                : 22.353 s
% 0.40/23.58  # System time              : 0.151 s
% 0.40/23.58  # Total time               : 22.504 s
% 0.40/23.58  # Maximum resident set size: 155584 pages
% 0.40/46.45  eprover: eprover: CPU time limit exceeded, terminatingCPU time limit exceeded, terminating
% 0.40/46.45  
% 0.40/46.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.46  eprover: No such file or directory
% 0.40/46.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.46  eprover: No such file or directory
% 0.40/46.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.47  eprover: No such file or directory
% 0.40/46.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.47  eprover: No such file or directory
% 0.40/46.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.47  eprover: No such file or directory
% 0.40/46.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.47  eprover: No such file or directory
% 0.40/46.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.48  eprover: No such file or directory
% 0.40/46.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.48  eprover: No such file or directory
% 0.40/46.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.48  eprover: No such file or directory
% 0.40/46.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.48  eprover: No such file or directory
% 0.40/46.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.49  eprover: No such file or directory
% 0.40/46.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.49  eprover: No such file or directory
% 0.40/46.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.49  eprover: No such file or directory
% 0.40/46.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.49  eprover: No such file or directory
% 0.40/46.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.49  eprover: No such file or directory
% 0.40/46.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.50  eprover: No such file or directory
% 0.40/46.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.50  eprover: No such file or directory
% 0.40/46.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.50  eprover: No such file or directory
% 0.40/46.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.50  eprover: No such file or directory
% 0.40/46.51  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.40/46.51  eprover: No such file or directory
%------------------------------------------------------------------------------