TSTP Solution File: SWW258+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SWW258+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.S79va378Mo true

% 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  : 300s
% DateTime : Fri Sep  1 01:41:20 EDT 2023

% Result   : Theorem 90.74s 13.84s
% Output   : Refutation 90.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   84 (  35 unt;  24 typ;   0 def)
%            Number of atoms       :  106 (  19 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  598 (  36   ~;  28   |;   3   &; 516   @)
%                                         (   4 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;   7 con; 0-3 aty)
%            Number of variables   :   51 (   0   ^;  51   !;   0   ?;  51   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_w_____type,type,
    v_w____: $i ).

thf(tc_RealDef_Oreal_type,type,
    tc_RealDef_Oreal: $i ).

thf(c_Power_Opower__class_Opower_type,type,
    c_Power_Opower__class_Opower: $i > $i ).

thf(class_Orderings_Opreorder_type,type,
    class_Orderings_Opreorder: $i > $o ).

thf(class_RealVector_Oreal__normed__algebra__1_type,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

thf(hAPP_type,type,
    hAPP: $i > $i > $i ).

thf(v_m_____type,type,
    v_m____: $i ).

thf(c_Groups_Ozero__class_Ozero_type,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

thf(class_RealVector_Oreal__normed__vector_type,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

thf(v_k_____type,type,
    v_k____: $i ).

thf(c_Nat_OSuc_type,type,
    c_Nat_OSuc: $i > $i ).

thf(c_Orderings_Oord__class_Oless__eq_type,type,
    c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).

thf(c_Groups_Oplus__class_Oplus_type,type,
    c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).

thf(c_Rings_Oinverse__class_Oinverse_type,type,
    c_Rings_Oinverse__class_Oinverse: $i > $i > $i ).

thf(c_Groups_Otimes__class_Otimes_type,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

thf(c_Groups_Oone__class_Oone_type,type,
    c_Groups_Oone__class_Oone: $i > $i ).

thf(class_Rings_Olinordered__ring__strict_type,type,
    class_Rings_Olinordered__ring__strict: $i > $o ).

thf(class_Fields_Olinordered__field__inverse__zero_type,type,
    class_Fields_Olinordered__field__inverse__zero: $i > $o ).

thf(tc_Nat_Onat_type,type,
    tc_Nat_Onat: $i ).

thf(c_RealVector_Onorm__class_Onorm_type,type,
    c_RealVector_Onorm__class_Onorm: $i > $i > $i ).

thf(tc_Complex_Ocomplex_type,type,
    tc_Complex_Ocomplex: $i ).

thf(c_Orderings_Oord__class_Oless_type,type,
    c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).

thf(class_Rings_Oring__1__no__zero__divisors_type,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

thf(class_Orderings_Olinorder_type,type,
    class_Orderings_Olinorder: $i > $o ).

thf(fact_norm__power__ineq,axiom,
    ! [V_n: $i,V_x: $i,T_a: $i] :
      ( ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ T_a @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ T_a ) @ V_x ) @ V_n ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ T_a @ V_x ) ) @ V_n ) ) ) ).

thf(zip_derived_cl104,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ X0 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ X0 ) @ X1 ) @ X2 ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ X0 @ X1 ) ) @ X2 ) )
      | ~ ( class_RealVector_Oreal__normed__algebra__1 @ X0 ) ),
    inference(cnf,[status(esa)],[fact_norm__power__ineq]) ).

thf(fact_not__leE,axiom,
    ! [V_x: $i,V_y: $i,T_a: $i] :
      ( ( class_Orderings_Olinorder @ T_a )
     => ( ~ ( c_Orderings_Oord__class_Oless__eq @ T_a @ V_y @ V_x )
       => ( c_Orderings_Oord__class_Oless @ T_a @ V_x @ V_y ) ) ) ).

thf(zip_derived_cl1028,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ X0 @ X1 @ X2 )
      | ( c_Orderings_Oord__class_Oless @ X0 @ X2 @ X1 )
      | ~ ( class_Orderings_Olinorder @ X0 ) ),
    inference(cnf,[status(esa)],[fact_not__leE]) ).

thf(conj_0,conjecture,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_k____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ v_m____ ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_k____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ v_m____ ) ) ),
    inference('cnf.neg',[status(esa)],[conj_0]) ).

thf(zip_derived_cl1671,plain,
    ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_k____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) @ v_m____ ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(fact_Suc__eq__plus1,axiom,
    ! [V_n: $i] :
      ( ( c_Nat_OSuc @ V_n )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ).

thf(zip_derived_cl1316,plain,
    ! [X0: $i] :
      ( ( c_Nat_OSuc @ X0 )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X0 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(cnf,[status(esa)],[fact_Suc__eq__plus1]) ).

thf(zip_derived_cl14219,plain,
    ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) ) @ v_m____ ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1671,zip_derived_cl1316]) ).

thf(zip_derived_cl14220,plain,
    ( ~ ( class_Orderings_Olinorder @ tc_RealDef_Oreal )
    | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) ) @ v_m____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1028,zip_derived_cl14219]) ).

thf(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder @ tc_RealDef_Oreal ).

thf(zip_derived_cl1550,plain,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    inference(cnf,[status(esa)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).

thf(zip_derived_cl14222,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) ) @ v_m____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ),
    inference(demod,[status(thm)],[zip_derived_cl14220,zip_derived_cl1550]) ).

thf(fact_real__mult__commute,axiom,
    ! [V_w: $i,V_z: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ V_z ) @ V_w )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ V_w ) @ V_z ) ) ).

thf(zip_derived_cl272,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ X1 ) @ X0 )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[fact_real__mult__commute]) ).

thf(zip_derived_cl39680,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_m____ ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ),
    inference(demod,[status(thm)],[zip_derived_cl14222,zip_derived_cl272]) ).

thf(fact_inverse__nonpositive__iff__nonpositive,axiom,
    ! [V_aa_2: $i,T_a: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ T_a )
     => ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( c_Rings_Oinverse__class_Oinverse @ T_a @ V_aa_2 ) @ ( c_Groups_Ozero__class_Ozero @ T_a ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ T_a @ V_aa_2 @ ( c_Groups_Ozero__class_Ozero @ T_a ) ) ) ) ).

thf(zip_derived_cl69,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ X0 @ ( c_Rings_Oinverse__class_Oinverse @ X0 @ X1 ) @ ( c_Groups_Ozero__class_Ozero @ X0 ) )
      | ( c_Orderings_Oord__class_Oless__eq @ X0 @ X1 @ ( c_Groups_Ozero__class_Ozero @ X0 ) )
      | ~ ( class_Fields_Olinordered__field__inverse__zero @ X0 ) ),
    inference(cnf,[status(esa)],[fact_inverse__nonpositive__iff__nonpositive]) ).

thf(zip_derived_cl39712,plain,
    ( ~ ( class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal )
    | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_m____ ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39680,zip_derived_cl69]) ).

thf(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
    class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal ).

thf(zip_derived_cl1510,plain,
    class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
    inference(cnf,[status(esa)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).

thf(zip_derived_cl39750,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_m____ ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ),
    inference(demod,[status(thm)],[zip_derived_cl39712,zip_derived_cl1510]) ).

thf(fact_mult__le__0__iff,axiom,
    ! [V_b_2: $i,V_aa_2: $i,T_a: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ T_a )
     => ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_aa_2 ) @ V_b_2 ) @ ( c_Groups_Ozero__class_Ozero @ T_a ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( c_Groups_Ozero__class_Ozero @ T_a ) @ V_aa_2 )
            & ( c_Orderings_Oord__class_Oless__eq @ T_a @ V_b_2 @ ( c_Groups_Ozero__class_Ozero @ T_a ) ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ V_aa_2 @ ( c_Groups_Ozero__class_Ozero @ T_a ) )
            & ( c_Orderings_Oord__class_Oless__eq @ T_a @ ( c_Groups_Ozero__class_Ozero @ T_a ) @ V_b_2 ) ) ) ) ) ).

thf(zip_derived_cl55,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ X0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) @ ( c_Groups_Ozero__class_Ozero @ X0 ) )
      | ( c_Orderings_Oord__class_Oless__eq @ X0 @ X2 @ ( c_Groups_Ozero__class_Ozero @ X0 ) )
      | ( c_Orderings_Oord__class_Oless__eq @ X0 @ X1 @ ( c_Groups_Ozero__class_Ozero @ X0 ) )
      | ~ ( class_Rings_Olinordered__ring__strict @ X0 ) ),
    inference(cnf,[status(esa)],[fact_mult__le__0__iff]) ).

thf(zip_derived_cl40542,plain,
    ( ~ ( class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal )
    | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_m____ @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39750,zip_derived_cl55]) ).

thf(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
    class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal ).

thf(zip_derived_cl1524,plain,
    class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
    inference(cnf,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).

thf(fact_m_I1_J,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_m____ ).

thf(zip_derived_cl1,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_m____,
    inference(cnf,[status(esa)],[fact_m_I1_J]) ).

thf(fact_less__le__not__le,axiom,
    ! [V_y_2: $i,V_x_2: $i,T_a: $i] :
      ( ( class_Orderings_Opreorder @ T_a )
     => ( ( c_Orderings_Oord__class_Oless @ T_a @ V_x_2 @ V_y_2 )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ T_a @ V_x_2 @ V_y_2 )
          & ~ ( c_Orderings_Oord__class_Oless__eq @ T_a @ V_y_2 @ V_x_2 ) ) ) ) ).

thf(zip_derived_cl1034,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ X0 @ X1 @ X2 )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ X0 @ X2 @ X1 )
      | ~ ( class_Orderings_Opreorder @ X0 ) ),
    inference(cnf,[status(esa)],[fact_less__le__not__le]) ).

thf(zip_derived_cl3969,plain,
    ( ~ ( class_Orderings_Opreorder @ tc_RealDef_Oreal )
    | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_m____ @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl1034]) ).

thf(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder @ tc_RealDef_Oreal ).

thf(zip_derived_cl1549,plain,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    inference(cnf,[status(esa)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

thf(zip_derived_cl3986,plain,
    ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_m____ @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(demod,[status(thm)],[zip_derived_cl3969,zip_derived_cl1549]) ).

thf(zip_derived_cl40583,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ),
    inference(demod,[status(thm)],[zip_derived_cl40542,zip_derived_cl1524,zip_derived_cl3986]) ).

thf(fact_real__le__trans,axiom,
    ! [V_k: $i,V_j: $i,V_i: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ V_i @ V_j )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ V_j @ V_k )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ V_i @ V_k ) ) ) ).

thf(zip_derived_cl267,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ X0 @ X1 )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ X2 @ X0 )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[fact_real__le__trans]) ).

thf(zip_derived_cl40618,plain,
    ! [X0: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ X0 @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ X0 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) ) @ ( c_Nat_OSuc @ v_k____ ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40583,zip_derived_cl267]) ).

thf(zip_derived_cl43858,plain,
    ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex )
    | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ ( c_Nat_OSuc @ v_k____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl40618]) ).

thf(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex ).

thf(zip_derived_cl1576,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    inference(cnf,[status(esa)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).

thf(zip_derived_cl43862,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ ( c_Nat_OSuc @ v_k____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ),
    inference(demod,[status(thm)],[zip_derived_cl43858,zip_derived_cl1576]) ).

thf(fact_norm__le__zero__iff,axiom,
    ! [V_x_2: $i,T_a: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ T_a )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ T_a @ V_x_2 ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      <=> ( V_x_2
          = ( c_Groups_Ozero__class_Ozero @ T_a ) ) ) ) ).

thf(zip_derived_cl101,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ X0 @ X1 ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( X1
        = ( c_Groups_Ozero__class_Ozero @ X0 ) )
      | ~ ( class_RealVector_Oreal__normed__vector @ X0 ) ),
    inference(cnf,[status(esa)],[fact_norm__le__zero__iff]) ).

thf(zip_derived_cl46212,plain,
    ( ~ ( class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex )
    | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ ( c_Nat_OSuc @ v_k____ ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl43862,zip_derived_cl101]) ).

thf(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex ).

thf(zip_derived_cl1580,plain,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    inference(cnf,[status(esa)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).

thf(zip_derived_cl46253,plain,
    ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ v_w____ ) @ ( c_Nat_OSuc @ v_k____ ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(demod,[status(thm)],[zip_derived_cl46212,zip_derived_cl1580]) ).

thf(fact_field__power__not__zero,axiom,
    ! [V_n: $i,V_a: $i,T_a: $i] :
      ( ( class_Rings_Oring__1__no__zero__divisors @ T_a )
     => ( ( V_a
         != ( c_Groups_Ozero__class_Ozero @ T_a ) )
       => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ T_a ) @ V_a ) @ V_n )
         != ( c_Groups_Ozero__class_Ozero @ T_a ) ) ) ) ).

thf(zip_derived_cl138,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1
        = ( c_Groups_Ozero__class_Ozero @ X0 ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ X0 ) @ X1 ) @ X2 )
       != ( c_Groups_Ozero__class_Ozero @ X0 ) )
      | ~ ( class_Rings_Oring__1__no__zero__divisors @ X0 ) ),
    inference(cnf,[status(esa)],[fact_field__power__not__zero]) ).

thf(zip_derived_cl46269,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
     != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
    | ~ ( class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex )
    | ( v_w____
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl46253,zip_derived_cl138]) ).

thf(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
    class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex ).

thf(zip_derived_cl1579,plain,
    class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors]) ).

thf(zip_derived_cl46291,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
     != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
    | ( v_w____
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl46269,zip_derived_cl1579]) ).

thf(zip_derived_cl46292,plain,
    ( v_w____
    = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(simplify,[status(thm)],[zip_derived_cl46291]) ).

thf(fact_w0,axiom,
    ( v_w____
   != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ).

thf(zip_derived_cl2,plain,
    ( v_w____
   != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(cnf,[status(esa)],[fact_w0]) ).

thf(zip_derived_cl46293,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl46292,zip_derived_cl2]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SWW258+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.09  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.S79va378Mo true
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Sun Aug 27 17:53:30 EDT 2023
% 0.08/0.28  % CPUTime  : 
% 0.08/0.28  % Running portfolio for 300 s
% 0.08/0.28  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.28  % Number of cores: 8
% 0.08/0.28  % Python version: Python 3.6.8
% 0.08/0.28  % Running in FO mode
% 0.12/0.51  % Total configuration time : 435
% 0.12/0.51  % Estimated wc time : 1092
% 0.12/0.51  % Estimated cpu time (7 cpus) : 156.0
% 0.12/0.62  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.12/0.62  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.12/0.62  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.12/0.63  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.12/0.64  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.12/0.65  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.12/0.66  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 90.74/13.84  % Solved by fo/fo5.sh.
% 90.74/13.84  % done 3621 iterations in 13.164s
% 90.74/13.84  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 90.74/13.84  % SZS output start Refutation
% See solution above
% 90.74/13.84  
% 90.74/13.84  
% 90.74/13.84  % Terminating...
% 91.92/13.96  % Runner terminated.
% 91.92/13.98  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------