TSTP Solution File: SWW236+1 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : SWW236+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n029.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 18:11:21 EDT 2024

% Result   : Theorem 14.72s 2.56s
% Output   : CNFRefutation 14.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   38 (  28 unt;   0 def)
%            Number of atoms       :  124 (  14 equ)
%            Maximal formula atoms :   62 (   3 avg)
%            Number of connectives :  140 (  54   ~;  56   |;  16   &)
%                                         (   2 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :   43 (   0 sgn  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',conj_0) ).

fof(fact_real__norm__def,axiom,
    ! [X20] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X20) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X20),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',fact_real__norm__def) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X7,X8,X6] :
      ( class_Rings_Ocomm__semiring__1(X6)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X8),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X7),X8) ),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_divide__le__eq,axiom,
    ! [X16,X17,X15,X6] :
      ( class_Fields_Olinordered__field__inverse__zero(X6)
     => ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Odivide(X6,X15,X17),X16)
      <=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
           => c_Orderings_Oord__class_Oless__eq(X6,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17)) )
          & ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
           => ( ( c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
               => c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17),X15) )
              & ( ~ c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
               => c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X16) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',fact_divide__le__eq) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

fof(fact_norm__mult,axiom,
    ! [X4,X5,X6] :
      ( class_RealVector_Oreal__normed__div__algebra(X6)
     => c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X5)),c_RealVector_Onorm__class_Onorm(X6,X4)) ),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',fact_norm__mult) ).

fof(fact_h,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',fact_h) ).

fof(fact_real__mult__commute,axiom,
    ! [X11,X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X9),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',fact_real__mult__commute) ).

fof(fact__0960_A_060_Acmod_Ac_096,axiom,
    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_c____)),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',fact__0960_A_060_Acmod_Ac_096) ).

fof(fact_real__of__nat__zero,axiom,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',fact_real__of__nat__zero) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/tmp/tmp.YGtGxEblqT/E---3.1_15973.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

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.YGtGxEblqT/E---3.1_15973.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

fof(c_0_12,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(c_0_13,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
    inference(fof_nnf,[status(thm)],[c_0_12]) ).

fof(c_0_14,plain,
    ! [X211] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X211) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X211),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

cnf(c_0_15,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_16,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_14]) ).

fof(c_0_17,plain,
    ! [X1096,X1097,X1098] :
      ( ~ class_Rings_Ocomm__semiring__1(X1098)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1098),X1097),X1096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1098),X1096),X1097) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])]) ).

fof(c_0_18,plain,
    ! [X16,X17,X15,X6] :
      ( class_Fields_Olinordered__field__inverse__zero(X6)
     => ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Odivide(X6,X15,X17),X16)
      <=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
           => c_Orderings_Oord__class_Oless__eq(X6,X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17)) )
          & ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X17)
           => ( ( c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
               => c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X16),X17),X15) )
              & ( ~ c_Orderings_Oord__class_Oless(X6,X17,c_Groups_Ozero__class_Ozero(X6))
               => c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X16) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).

cnf(c_0_19,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),v_c____))),
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).

fof(c_0_22,plain,
    ! [X125,X126,X127] :
      ( ~ class_RealVector_Oreal__normed__div__algebra(X127)
      | c_RealVector_Onorm__class_Onorm(X127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X127),X126),X125)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X127,X126)),c_RealVector_Onorm__class_Onorm(X127,X125)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])])]) ).

fof(c_0_23,plain,
    ! [X1155,X1156,X1157,X1158] :
      ( ( ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
        | c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
        | c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
        | c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
        | c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
        | c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless(X1158,c_Groups_Ozero__class_Ozero(X1158),X1156)
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
        | c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless(X1158,X1156,c_Groups_Ozero__class_Ozero(X1158))
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X1158,c_Groups_Ozero__class_Ozero(X1158),X1155)
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156),X1157)
        | ~ c_Orderings_Oord__class_Oless__eq(X1158,X1157,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1158),X1155),X1156))
        | c_Orderings_Oord__class_Oless__eq(X1158,c_Rings_Oinverse__class_Odivide(X1158,X1157,X1156),X1155)
        | ~ class_Fields_Olinordered__field__inverse__zero(X1158) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).

cnf(c_0_24,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    inference(split_conjunct,[status(thm)],[fact_h]) ).

fof(c_0_25,plain,
    ! [X142,X143] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X143),X142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X142),X143),
    inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).

cnf(c_0_26,plain,
    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_c____)),
    inference(split_conjunct,[status(thm)],[fact__0960_A_060_Acmod_Ac_096]) ).

cnf(c_0_27,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]) ).

cnf(c_0_28,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_c____),v_z____))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_29,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))
    | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).

cnf(c_0_31,plain,
    ( c_Orderings_Oord__class_Oless__eq(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__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_32,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
    inference(rw,[status(thm)],[c_0_24,c_0_16]) ).

cnf(c_0_33,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]) ).

cnf(c_0_34,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_35,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_36,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_da____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).

cnf(c_0_37,plain,
    $false,
    inference(sr,[status(thm)],[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_31,c_0_32]),c_0_33]),c_0_27]),c_0_34]),c_0_35])]),c_0_36]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWW236+1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.13  % Command    : run_E %s %d THM
% 0.11/0.34  % Computer : n029.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit   : 300
% 0.11/0.34  % WCLimit    : 300
% 0.11/0.34  % DateTime   : Wed Jun 19 07:42:09 EDT 2024
% 0.11/0.35  % CPUTime    : 
% 0.47/0.63  Running first-order theorem proving
% 0.47/0.63  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.YGtGxEblqT/E---3.1_15973.p
% 14.72/2.56  # Version: 3.2.0
% 14.72/2.56  # Preprocessing class: FMLMSMSMSSSNFFN.
% 14.72/2.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.72/2.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.72/2.56  # Starting new_bool_3 with 300s (1) cores
% 14.72/2.56  # Starting new_bool_1 with 300s (1) cores
% 14.72/2.56  # Starting sh5l with 300s (1) cores
% 14.72/2.56  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 16052 completed with status 0
% 14.72/2.56  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.72/2.56  # Preprocessing class: FMLMSMSMSSSNFFN.
% 14.72/2.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.72/2.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.72/2.56  # No SInE strategy applied
% 14.72/2.56  # Search class: FGHSM-SMLM32-DFFFFFNN
% 14.72/2.56  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.72/2.56  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 14.72/2.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.72/2.56  # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 14.72/2.56  # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 14.72/2.56  # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 113s (1) cores
% 14.72/2.56  # G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 16062 completed with status 0
% 14.72/2.56  # Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 14.72/2.56  # Preprocessing class: FMLMSMSMSSSNFFN.
% 14.72/2.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.72/2.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.72/2.56  # No SInE strategy applied
% 14.72/2.56  # Search class: FGHSM-SMLM32-DFFFFFNN
% 14.72/2.56  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.72/2.56  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 14.72/2.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.72/2.56  # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 14.72/2.56  # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 14.72/2.56  # Preprocessing time       : 0.021 s
% 14.72/2.56  # Presaturation interreduction done
% 14.72/2.56  
% 14.72/2.56  # Proof found!
% 14.72/2.56  # SZS status Theorem
% 14.72/2.56  # SZS output start CNFRefutation
% See solution above
% 14.72/2.56  # Parsed axioms                        : 1266
% 14.72/2.56  # Removed by relevancy pruning/SinE    : 0
% 14.72/2.56  # Initial clauses                      : 1785
% 14.72/2.56  # Removed in clause preprocessing      : 59
% 14.72/2.56  # Initial clauses in saturation        : 1726
% 14.72/2.56  # Processed clauses                    : 10368
% 14.72/2.56  # ...of these trivial                  : 214
% 14.72/2.56  # ...subsumed                          : 5959
% 14.72/2.56  # ...remaining for further processing  : 4195
% 14.72/2.56  # Other redundant clauses eliminated   : 721
% 14.72/2.56  # Clauses deleted for lack of memory   : 0
% 14.72/2.56  # Backward-subsumed                    : 43
% 14.72/2.56  # Backward-rewritten                   : 117
% 14.72/2.56  # Generated clauses                    : 94096
% 14.72/2.56  # ...of the previous two non-redundant : 84271
% 14.72/2.56  # ...aggressively subsumed             : 0
% 14.72/2.56  # Contextual simplify-reflections      : 4
% 14.72/2.56  # Paramodulations                      : 93367
% 14.72/2.56  # Factorizations                       : 10
% 14.72/2.56  # NegExts                              : 0
% 14.72/2.56  # Equation resolutions                 : 740
% 14.72/2.56  # Disequality decompositions           : 0
% 14.72/2.56  # Total rewrite steps                  : 76487
% 14.72/2.56  # ...of those cached                   : 73531
% 14.72/2.56  # Propositional unsat checks           : 0
% 14.72/2.56  #    Propositional check models        : 0
% 14.72/2.56  #    Propositional check unsatisfiable : 0
% 14.72/2.56  #    Propositional clauses             : 0
% 14.72/2.56  #    Propositional clauses after purity: 0
% 14.72/2.56  #    Propositional unsat core size     : 0
% 14.72/2.56  #    Propositional preprocessing time  : 0.000
% 14.72/2.56  #    Propositional encoding time       : 0.000
% 14.72/2.56  #    Propositional solver time         : 0.000
% 14.72/2.56  #    Success case prop preproc time    : 0.000
% 14.72/2.56  #    Success case prop encoding time   : 0.000
% 14.72/2.56  #    Success case prop solver time     : 0.000
% 14.72/2.56  # Current number of processed clauses  : 2454
% 14.72/2.56  #    Positive orientable unit clauses  : 583
% 14.72/2.56  #    Positive unorientable unit clauses: 22
% 14.72/2.56  #    Negative unit clauses             : 311
% 14.72/2.56  #    Non-unit-clauses                  : 1538
% 14.72/2.56  # Current number of unprocessed clauses: 76869
% 14.72/2.56  # ...number of literals in the above   : 186410
% 14.72/2.56  # Current number of archived formulas  : 0
% 14.72/2.56  # Current number of archived clauses   : 1599
% 14.72/2.56  # Clause-clause subsumption calls (NU) : 509243
% 14.72/2.56  # Rec. Clause-clause subsumption calls : 371991
% 14.72/2.56  # Non-unit clause-clause subsumptions  : 2769
% 14.72/2.56  # Unit Clause-clause subsumption calls : 67313
% 14.72/2.56  # Rewrite failures with RHS unbound    : 0
% 14.72/2.56  # BW rewrite match attempts            : 22418
% 14.72/2.56  # BW rewrite match successes           : 303
% 14.72/2.56  # Condensation attempts                : 0
% 14.72/2.56  # Condensation successes               : 0
% 14.72/2.56  # Termbank termtop insertions          : 1936705
% 14.72/2.56  # Search garbage collected termcells   : 21900
% 14.72/2.56  
% 14.72/2.56  # -------------------------------------------------
% 14.72/2.56  # User time                : 1.760 s
% 14.72/2.56  # System time              : 0.071 s
% 14.72/2.56  # Total time               : 1.831 s
% 14.72/2.56  # Maximum resident set size: 8552 pages
% 14.72/2.56  
% 14.72/2.56  # -------------------------------------------------
% 14.72/2.56  # User time                : 8.457 s
% 14.72/2.56  # System time              : 0.360 s
% 14.72/2.56  # Total time               : 8.817 s
% 14.72/2.56  # Maximum resident set size: 3156 pages
% 14.72/2.56  % E---3.1 exiting
% 14.72/2.56  % E exiting
%------------------------------------------------------------------------------