TSTP Solution File: SWW258+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWW258+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 06:45:07 EDT 2024

% Result   : Theorem 13.50s 2.26s
% Output   : CNFRefutation 13.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   53 (  32 unt;   0 def)
%            Number of atoms       :  100 (  22 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   87 (  40   ~;  30   |;   6   &)
%                                         (   4 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   52 (   1 sgn  34   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_inverse__inverse__eq,axiom,
    ! [X5,X6] :
      ( class_Rings_Odivision__ring__inverse__zero(X6)
     => c_Rings_Oinverse__class_Oinverse(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).

fof(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____))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_inverse__positive__iff__positive,axiom,
    ! [X25,X6] :
      ( class_Fields_Olinordered__field__inverse__zero(X6)
     => ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Rings_Oinverse__class_Oinverse(X6,X25))
      <=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).

fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
    class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).

fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

fof(fact_real__mult__commute,axiom,
    ! [X16,X15] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).

fof(fact_real__less__def,axiom,
    ! [X21,X13] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X21)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X21)
        & X13 != X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).

fof(fact_real__mult__order,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X8)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).

fof(fact_m_I1_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I1_J) ).

fof(fact_zero__less__power,axiom,
    ! [X4,X5,X6] :
      ( class_Rings_Olinordered__semidom(X6)
     => ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
       => c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(fact__0960_A_060_061_Acmod_Aw_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_w____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_061_Acmod_Aw_096) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(fact_w0,axiom,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).

fof(fact_norm__le__zero__iff,axiom,
    ! [X13,X6] :
      ( class_RealVector_Oreal__normed__vector(X6)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).

fof(fact_real__le__refl,axiom,
    ! [X16] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X16),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(c_0_16,plain,
    ! [X351,X352] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X352)
      | c_Rings_Oinverse__class_Oinverse(X352,c_Rings_Oinverse__class_Oinverse(X352,X351)) = X351 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])])]) ).

fof(c_0_17,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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(c_0_18,plain,
    ! [X560,X561] :
      ( ( ~ c_Orderings_Oord__class_Oless(X561,c_Groups_Ozero__class_Ozero(X561),c_Rings_Oinverse__class_Oinverse(X561,X560))
        | c_Orderings_Oord__class_Oless(X561,c_Groups_Ozero__class_Ozero(X561),X560)
        | ~ class_Fields_Olinordered__field__inverse__zero(X561) )
      & ( ~ c_Orderings_Oord__class_Oless(X561,c_Groups_Ozero__class_Ozero(X561),X560)
        | c_Orderings_Oord__class_Oless(X561,c_Groups_Ozero__class_Ozero(X561),c_Rings_Oinverse__class_Oinverse(X561,X560))
        | ~ class_Fields_Olinordered__field__inverse__zero(X561) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])])]) ).

cnf(c_0_19,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]) ).

fof(c_0_21,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(fof_nnf,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)) = X1,
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).

fof(c_0_25,plain,
    ! [X692,X693] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X693),X692) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X692),X693),
    inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).

fof(c_0_26,plain,
    ! [X21,X13] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X21)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X21)
        & X13 != X21 ) ),
    inference(fof_simplification,[status(thm)],[fact_real__less__def]) ).

cnf(c_0_27,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(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,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,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_29,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_30,plain,
    ! [X836,X837] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X837)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X836)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X837),X836)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])])]) ).

fof(c_0_31,plain,
    ! [X777,X778] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X778,X777)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X778,X777) )
      & ( X778 != X777
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X778,X777) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X778,X777)
        | X778 = X777
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X778,X777) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).

cnf(c_0_32,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_33,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_34,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(split_conjunct,[status(thm)],[fact_m_I1_J]) ).

fof(c_0_35,plain,
    ! [X515,X516,X517] :
      ( ~ class_Rings_Olinordered__semidom(X517)
      | ~ c_Orderings_Oord__class_Oless(X517,c_Groups_Ozero__class_Ozero(X517),X516)
      | c_Orderings_Oord__class_Oless(X517,c_Groups_Ozero__class_Ozero(X517),hAPP(hAPP(c_Power_Opower__class_Opower(X517),X516),X515)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])])]) ).

cnf(c_0_36,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_31]) ).

cnf(c_0_37,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_w____)),
    inference(split_conjunct,[status(thm)],[fact__0960_A_060_061_Acmod_Aw_096]) ).

cnf(c_0_38,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(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)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

cnf(c_0_39,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_40,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).

fof(c_0_41,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_simplification,[status(thm)],[fact_w0]) ).

fof(c_0_42,plain,
    ! [X319,X320] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X320,X319),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | X319 = c_Groups_Ozero__class_Ozero(X320)
        | ~ class_RealVector_Oreal__normed__vector(X320) )
      & ( X319 != c_Groups_Ozero__class_Ozero(X320)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X320,X319),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ class_RealVector_Oreal__normed__vector(X320) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])])]) ).

cnf(c_0_43,plain,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = 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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_44,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).

fof(c_0_45,plain,
    ! [X691] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X691,X691),
    inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).

fof(c_0_46,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[c_0_41]) ).

cnf(c_0_47,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(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_42]) ).

cnf(c_0_48,plain,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(sr,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_49,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).

cnf(c_0_50,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_51,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_52,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50])]),c_0_51]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWW258+1 : TPTP v8.2.0. Released v5.2.0.
% 0.12/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n017.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    : 300
% 0.13/0.34  % DateTime   : Sat May 18 19:04:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  Running first-order model finding
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.50/2.26  # Version: 3.1.0
% 13.50/2.26  # Preprocessing class: FMLMSMSMSSSNFFN.
% 13.50/2.26  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.50/2.26  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.50/2.26  # Starting new_bool_3 with 300s (1) cores
% 13.50/2.26  # Starting new_bool_1 with 300s (1) cores
% 13.50/2.26  # Starting sh5l with 300s (1) cores
% 13.50/2.26  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 20221 completed with status 0
% 13.50/2.26  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 13.50/2.26  # Preprocessing class: FMLMSMSMSSSNFFN.
% 13.50/2.26  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.50/2.26  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.50/2.26  # No SInE strategy applied
% 13.50/2.26  # Search class: FGHSM-SSLM32-DFFFFFNN
% 13.50/2.26  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 13.50/2.26  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 13.50/2.26  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.50/2.26  # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 13.50/2.26  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 13.50/2.26  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 13.50/2.26  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 20229 completed with status 0
% 13.50/2.26  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 13.50/2.26  # Preprocessing class: FMLMSMSMSSSNFFN.
% 13.50/2.26  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.50/2.26  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.50/2.26  # No SInE strategy applied
% 13.50/2.26  # Search class: FGHSM-SSLM32-DFFFFFNN
% 13.50/2.26  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 13.50/2.26  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 13.50/2.26  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.50/2.26  # Preprocessing time       : 0.024 s
% 13.50/2.26  # Presaturation interreduction done
% 13.50/2.26  
% 13.50/2.26  # Proof found!
% 13.50/2.26  # SZS status Theorem
% 13.50/2.26  # SZS output start CNFRefutation
% See solution above
% 13.50/2.26  # Parsed axioms                        : 1272
% 13.50/2.26  # Removed by relevancy pruning/SinE    : 0
% 13.50/2.26  # Initial clauses                      : 1673
% 13.50/2.26  # Removed in clause preprocessing      : 71
% 13.50/2.26  # Initial clauses in saturation        : 1602
% 13.50/2.26  # Processed clauses                    : 12609
% 13.50/2.26  # ...of these trivial                  : 491
% 13.50/2.26  # ...subsumed                          : 7480
% 13.50/2.26  # ...remaining for further processing  : 4638
% 13.50/2.26  # Other redundant clauses eliminated   : 802
% 13.50/2.26  # Clauses deleted for lack of memory   : 0
% 13.50/2.26  # Backward-subsumed                    : 98
% 13.50/2.26  # Backward-rewritten                   : 75
% 13.50/2.26  # Generated clauses                    : 87176
% 13.50/2.26  # ...of the previous two non-redundant : 76533
% 13.50/2.26  # ...aggressively subsumed             : 0
% 13.50/2.26  # Contextual simplify-reflections      : 19
% 13.50/2.26  # Paramodulations                      : 86331
% 13.50/2.26  # Factorizations                       : 13
% 13.50/2.26  # NegExts                              : 0
% 13.50/2.26  # Equation resolutions                 : 847
% 13.50/2.26  # Disequality decompositions           : 0
% 13.50/2.26  # Total rewrite steps                  : 70448
% 13.50/2.26  # ...of those cached                   : 65603
% 13.50/2.26  # Propositional unsat checks           : 0
% 13.50/2.26  #    Propositional check models        : 0
% 13.50/2.26  #    Propositional check unsatisfiable : 0
% 13.50/2.26  #    Propositional clauses             : 0
% 13.50/2.26  #    Propositional clauses after purity: 0
% 13.50/2.26  #    Propositional unsat core size     : 0
% 13.50/2.26  #    Propositional preprocessing time  : 0.000
% 13.50/2.26  #    Propositional encoding time       : 0.000
% 13.50/2.26  #    Propositional solver time         : 0.000
% 13.50/2.26  #    Success case prop preproc time    : 0.000
% 13.50/2.26  #    Success case prop encoding time   : 0.000
% 13.50/2.26  #    Success case prop solver time     : 0.000
% 13.50/2.26  # Current number of processed clauses  : 3023
% 13.50/2.26  #    Positive orientable unit clauses  : 668
% 13.50/2.26  #    Positive unorientable unit clauses: 13
% 13.50/2.26  #    Negative unit clauses             : 367
% 13.50/2.26  #    Non-unit-clauses                  : 1975
% 13.50/2.26  # Current number of unprocessed clauses: 66615
% 13.50/2.26  # ...number of literals in the above   : 177301
% 13.50/2.26  # Current number of archived formulas  : 0
% 13.50/2.26  # Current number of archived clauses   : 1474
% 13.50/2.26  # Clause-clause subsumption calls (NU) : 287481
% 13.50/2.26  # Rec. Clause-clause subsumption calls : 204697
% 13.50/2.26  # Non-unit clause-clause subsumptions  : 2953
% 13.50/2.26  # Unit Clause-clause subsumption calls : 15841
% 13.50/2.26  # Rewrite failures with RHS unbound    : 0
% 13.50/2.26  # BW rewrite match attempts            : 9439
% 13.50/2.26  # BW rewrite match successes           : 326
% 13.50/2.26  # Condensation attempts                : 0
% 13.50/2.26  # Condensation successes               : 0
% 13.50/2.26  # Termbank termtop insertions          : 1906168
% 13.50/2.26  # Search garbage collected termcells   : 19825
% 13.50/2.26  
% 13.50/2.26  # -------------------------------------------------
% 13.50/2.26  # User time                : 1.626 s
% 13.50/2.26  # System time              : 0.058 s
% 13.50/2.26  # Total time               : 1.684 s
% 13.50/2.26  # Maximum resident set size: 8272 pages
% 13.50/2.26  
% 13.50/2.26  # -------------------------------------------------
% 13.50/2.26  # User time                : 7.954 s
% 13.50/2.26  # System time              : 0.304 s
% 13.50/2.26  # Total time               : 8.259 s
% 13.50/2.26  # Maximum resident set size: 3096 pages
% 13.50/2.26  % E---3.1 exiting
%------------------------------------------------------------------------------