TSTP Solution File: SWW254+1 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : SWW254+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% 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 : Mon Jun 24 18:11:24 EDT 2024

% Result   : Theorem 8.71s 1.64s
% Output   : CNFRefutation 8.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   45 (  27 unt;   0 def)
%            Number of atoms       :  161 (  18 equ)
%            Maximal formula atoms :   62 (   3 avg)
%            Number of connectives :  189 (  73   ~;  72   |;  22   &)
%                                         (   8 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   49 (   4 sgn  33   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_less__le__not__le,axiom,
    ! [X24,X7,X6] :
      ( class_Orderings_Opreorder(X6)
     => ( c_Orderings_Oord__class_Oless(X6,X7,X24)
      <=> ( c_Orderings_Oord__class_Oless__eq(X6,X7,X24)
          & ~ c_Orderings_Oord__class_Oless__eq(X6,X24,X7) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_less__le__not__le) ).

fof(fact_cq0,axiom,
    ! [X15] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X15))),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_cq0) ).

fof(conj_0,conjecture,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',conj_0) ).

fof(fact_pqc0,axiom,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_pqc0) ).

fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(fact_q_I2_J,axiom,
    ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_q_I2_J) ).

fof(fact_divide__less__eq,axiom,
    ! [X8,X33,X9,X6] :
      ( class_Fields_Olinordered__field__inverse__zero(X6)
     => ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Odivide(X6,X9,X33),X8)
      <=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X33)
           => c_Orderings_Oord__class_Oless(X6,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33)) )
          & ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X33)
           => ( ( c_Orderings_Oord__class_Oless(X6,X33,c_Groups_Ozero__class_Ozero(X6))
               => c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33),X9) )
              & ( ~ c_Orderings_Oord__class_Oless(X6,X33,c_Groups_Ozero__class_Ozero(X6))
               => c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X8) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_divide__less__eq) ).

fof(fact_zero__less__norm__iff,axiom,
    ! [X7,X6] :
      ( class_RealVector_Oreal__normed__vector(X6)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X7))
      <=> X7 != c_Groups_Ozero__class_Ozero(X6) ) ),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_zero__less__norm__iff) ).

fof(fact_real__mult__1,axiom,
    ! [X19] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X19) = X19,
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_real__mult__1) ).

fof(fact_pc0,axiom,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',fact_pc0) ).

fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(c_0_12,plain,
    ! [X24,X7,X6] :
      ( class_Orderings_Opreorder(X6)
     => ( c_Orderings_Oord__class_Oless(X6,X7,X24)
      <=> ( c_Orderings_Oord__class_Oless__eq(X6,X7,X24)
          & ~ c_Orderings_Oord__class_Oless__eq(X6,X24,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(c_0_13,plain,
    ! [X173] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X173))),
    inference(variable_rename,[status(thm)],[fact_cq0]) ).

fof(c_0_14,negated_conjecture,
    ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_15,plain,
    ! [X1311,X1312,X1313] :
      ( ( c_Orderings_Oord__class_Oless__eq(X1313,X1312,X1311)
        | ~ c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
        | ~ class_Orderings_Opreorder(X1313) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X1313,X1311,X1312)
        | ~ c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
        | ~ class_Orderings_Opreorder(X1313) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X1313,X1312,X1311)
        | c_Orderings_Oord__class_Oless__eq(X1313,X1311,X1312)
        | c_Orderings_Oord__class_Oless(X1313,X1312,X1311)
        | ~ class_Orderings_Opreorder(X1313) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).

cnf(c_0_16,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
    inference(split_conjunct,[status(thm)],[fact_pqc0]) ).

fof(c_0_18,negated_conjecture,
    ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) )
    & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).

cnf(c_0_19,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

fof(c_0_22,plain,
    ! [X182] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X182) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X182)),
    inference(variable_rename,[status(thm)],[fact_q_I2_J]) ).

fof(c_0_23,plain,
    ! [X8,X33,X9,X6] :
      ( class_Fields_Olinordered__field__inverse__zero(X6)
     => ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Odivide(X6,X9,X33),X8)
      <=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X33)
           => c_Orderings_Oord__class_Oless(X6,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33)) )
          & ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X33)
           => ( ( c_Orderings_Oord__class_Oless(X6,X33,c_Groups_Ozero__class_Ozero(X6))
               => c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X33),X9) )
              & ( ~ c_Orderings_Oord__class_Oless(X6,X33,c_Groups_Ozero__class_Ozero(X6))
               => c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X8) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).

cnf(c_0_24,negated_conjecture,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_25,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_26,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_27,plain,
    ! [X7,X6] :
      ( class_RealVector_Oreal__normed__vector(X6)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X7))
      <=> X7 != c_Groups_Ozero__class_Ozero(X6) ) ),
    inference(fof_simplification,[status(thm)],[fact_zero__less__norm__iff]) ).

fof(c_0_28,plain,
    ! [X1072,X1073,X1074,X1075] :
      ( ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
        | ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
        | c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
        | c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | ~ c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
        | c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
        | c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
        | ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
        | c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1073)
        | ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
        | c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,X1073,c_Groups_Ozero__class_Ozero(X1075))
        | ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
        | ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) )
      & ( ~ c_Orderings_Oord__class_Oless(X1075,c_Groups_Ozero__class_Ozero(X1075),X1072)
        | ~ c_Orderings_Oord__class_Oless(X1075,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073),X1074)
        | ~ c_Orderings_Oord__class_Oless(X1075,X1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1075),X1072),X1073))
        | c_Orderings_Oord__class_Oless(X1075,c_Rings_Oinverse__class_Odivide(X1075,X1074,X1073),X1072)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1075) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).

cnf(c_0_29,negated_conjecture,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17]),c_0_17]) ).

cnf(c_0_30,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

fof(c_0_31,plain,
    ! [X1377] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1377) = X1377,
    inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).

fof(c_0_32,plain,
    ! [X102,X103] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X103,X102))
        | X102 != c_Groups_Ozero__class_Ozero(X103)
        | ~ class_RealVector_Oreal__normed__vector(X103) )
      & ( X102 = c_Groups_Ozero__class_Ozero(X103)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X103,X102))
        | ~ class_RealVector_Oreal__normed__vector(X103) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).

fof(c_0_33,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_simplification,[status(thm)],[fact_pc0]) ).

cnf(c_0_34,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(sr,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_36,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_37,plain,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).

cnf(c_0_38,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_39,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).

fof(c_0_40,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[c_0_33]) ).

cnf(c_0_41,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,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]),c_0_30]) ).

cnf(c_0_42,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_43,plain,
    hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SWW254+1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.09  % Command    : run_E %s %d THM
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit   : 300
% 0.09/0.28  % WCLimit    : 300
% 0.09/0.28  % DateTime   : Wed Jun 19 07:04:53 EDT 2024
% 0.13/0.28  % CPUTime    : 
% 0.14/0.47  Running first-order theorem proving
% 0.14/0.47  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.DIUXeBFOEP/E---3.1_923.p
% 8.71/1.64  # Version: 3.2.0
% 8.71/1.64  # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.71/1.64  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.71/1.64  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.71/1.64  # Starting new_bool_3 with 300s (1) cores
% 8.71/1.64  # Starting new_bool_1 with 300s (1) cores
% 8.71/1.64  # Starting sh5l with 300s (1) cores
% 8.71/1.64  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1055 completed with status 0
% 8.71/1.64  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.71/1.64  # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.71/1.64  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.71/1.64  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.71/1.64  # No SInE strategy applied
% 8.71/1.64  # Search class: FGHSM-SMLM32-DFFFFFNN
% 8.71/1.64  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.71/1.64  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 8.71/1.64  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.71/1.64  # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 8.71/1.64  # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 8.71/1.64  # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 113s (1) cores
% 8.71/1.64  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with pid 1067 completed with status 0
% 8.71/1.64  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 8.71/1.64  # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.71/1.64  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.71/1.64  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.71/1.64  # No SInE strategy applied
% 8.71/1.64  # Search class: FGHSM-SMLM32-DFFFFFNN
% 8.71/1.64  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.71/1.64  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 8.71/1.64  # Preprocessing time       : 0.024 s
% 8.71/1.64  # Presaturation interreduction done
% 8.71/1.64  
% 8.71/1.64  # Proof found!
% 8.71/1.64  # SZS status Theorem
% 8.71/1.64  # SZS output start CNFRefutation
% See solution above
% 8.71/1.64  # Parsed axioms                        : 1245
% 8.71/1.64  # Removed by relevancy pruning/SinE    : 0
% 8.71/1.64  # Initial clauses                      : 1805
% 8.71/1.64  # Removed in clause preprocessing      : 83
% 8.71/1.64  # Initial clauses in saturation        : 1722
% 8.71/1.64  # Processed clauses                    : 4809
% 8.71/1.64  # ...of these trivial                  : 132
% 8.71/1.64  # ...subsumed                          : 1242
% 8.71/1.64  # ...remaining for further processing  : 3435
% 8.71/1.64  # Other redundant clauses eliminated   : 479
% 8.71/1.64  # Clauses deleted for lack of memory   : 0
% 8.71/1.64  # Backward-subsumed                    : 9
% 8.71/1.64  # Backward-rewritten                   : 30
% 8.71/1.64  # Generated clauses                    : 42395
% 8.71/1.64  # ...of the previous two non-redundant : 37943
% 8.71/1.64  # ...aggressively subsumed             : 0
% 8.71/1.64  # Contextual simplify-reflections      : 2
% 8.71/1.64  # Paramodulations                      : 41901
% 8.71/1.64  # Factorizations                       : 11
% 8.71/1.64  # NegExts                              : 0
% 8.71/1.64  # Equation resolutions                 : 498
% 8.71/1.64  # Disequality decompositions           : 0
% 8.71/1.64  # Total rewrite steps                  : 29914
% 8.71/1.64  # ...of those cached                   : 27470
% 8.71/1.64  # Propositional unsat checks           : 0
% 8.71/1.64  #    Propositional check models        : 0
% 8.71/1.64  #    Propositional check unsatisfiable : 0
% 8.71/1.64  #    Propositional clauses             : 0
% 8.71/1.64  #    Propositional clauses after purity: 0
% 8.71/1.64  #    Propositional unsat core size     : 0
% 8.71/1.64  #    Propositional preprocessing time  : 0.000
% 8.71/1.64  #    Propositional encoding time       : 0.000
% 8.71/1.64  #    Propositional solver time         : 0.000
% 8.71/1.64  #    Success case prop preproc time    : 0.000
% 8.71/1.64  #    Success case prop encoding time   : 0.000
% 8.71/1.64  #    Success case prop solver time     : 0.000
% 8.71/1.64  # Current number of processed clauses  : 1775
% 8.71/1.64  #    Positive orientable unit clauses  : 384
% 8.71/1.64  #    Positive unorientable unit clauses: 8
% 8.71/1.64  #    Negative unit clauses             : 66
% 8.71/1.64  #    Non-unit-clauses                  : 1317
% 8.71/1.64  # Current number of unprocessed clauses: 36305
% 8.71/1.64  # ...number of literals in the above   : 127553
% 8.71/1.64  # Current number of archived formulas  : 0
% 8.71/1.64  # Current number of archived clauses   : 1521
% 8.71/1.64  # Clause-clause subsumption calls (NU) : 378701
% 8.71/1.64  # Rec. Clause-clause subsumption calls : 174500
% 8.71/1.64  # Non-unit clause-clause subsumptions  : 465
% 8.71/1.64  # Unit Clause-clause subsumption calls : 18152
% 8.71/1.64  # Rewrite failures with RHS unbound    : 0
% 8.71/1.64  # BW rewrite match attempts            : 1735
% 8.71/1.64  # BW rewrite match successes           : 175
% 8.71/1.64  # Condensation attempts                : 0
% 8.71/1.64  # Condensation successes               : 0
% 8.71/1.64  # Termbank termtop insertions          : 1107681
% 8.71/1.64  # Search garbage collected termcells   : 22950
% 8.71/1.64  
% 8.71/1.64  # -------------------------------------------------
% 8.71/1.64  # User time                : 1.040 s
% 8.71/1.64  # System time              : 0.049 s
% 8.71/1.64  # Total time               : 1.088 s
% 8.71/1.64  # Maximum resident set size: 8612 pages
% 8.71/1.64  
% 8.71/1.64  # -------------------------------------------------
% 8.71/1.64  # User time                : 4.909 s
% 8.71/1.64  # System time              : 0.184 s
% 8.71/1.64  # Total time               : 5.093 s
% 8.71/1.64  # Maximum resident set size: 3140 pages
% 8.71/1.64  % E---3.1 exiting
% 8.71/1.64  % E exiting
%------------------------------------------------------------------------------