TSTP Solution File: SWW261+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWW261+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% 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  : 600s
% DateTime : Thu Jul 21 00:10:25 EDT 2022

% Result   : Theorem 0.35s 2.54s
% Output   : CNFRefutation 0.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   71 (  41 unt;   0 def)
%            Number of atoms       :  122 (  32 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :   86 (  35   ~;  39   |;   1   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :   87 (   0 sgn  48   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).

fof(fact_order__trans,axiom,
    ! [X10,X4,X5,X6] :
      ( class_Orderings_Opreorder(X6)
     => ( c_Orderings_Oord__class_Oless__eq(X6,X5,X4)
       => ( c_Orderings_Oord__class_Oless__eq(X6,X4,X10)
         => c_Orderings_Oord__class_Oless__eq(X6,X5,X10) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_order__trans) ).

fof(fact_real__le__linear,axiom,
    ! [X9,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X10) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__le__linear) ).

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

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X21,X22,X6] :
      ( class_Rings_Ocomm__semiring__1(X6)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X22),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X21),X22) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_norm__of__real,axiom,
    ! [X25,X6] :
      ( class_RealVector_Oreal__normed__algebra__1(X6)
     => c_RealVector_Onorm__class_Onorm(X6,c_RealVector_Oof__real(X6,X25)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X25) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_norm__of__real) ).

fof(fact_real__norm__def,axiom,
    ! [X25] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X25) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X25),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__norm__def) ).

fof(fact_order__antisym__conv,axiom,
    ! [X8,X7,X6] :
      ( class_Orderings_Oorder(X6)
     => ( c_Orderings_Oord__class_Oless__eq(X6,X7,X8)
       => ( c_Orderings_Oord__class_Oless__eq(X6,X8,X7)
        <=> X8 = X7 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_norm__mult__ineq,axiom,
    ! [X4,X5,X6] :
      ( class_RealVector_Oreal__normed__algebra(X6)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_norm__mult__ineq) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

fof(fact_abs__of__pos,axiom,
    ! [X22,X6] :
      ( class_Groups_Oordered__ab__group__add__abs(X6)
     => ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X22)
       => c_Groups_Oabs__class_Oabs(X6,X22) = X22 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_abs__of__pos) ).

fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

fof(fact_t_I1_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_t_I1_J) ).

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

fof(fact_real__mult__commute,axiom,
    ! [X9,X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),X10),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__mult__commute) ).

fof(fact_real__mult__1,axiom,
    ! [X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10) = X10,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__mult__1) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096) ).

fof(fact_real__le__refl,axiom,
    ! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X9),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_real__le__refl) ).

fof(c_0_20,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_21,plain,
    ! [X11,X12,X13,X14] :
      ( ~ class_Orderings_Opreorder(X14)
      | ~ c_Orderings_Oord__class_Oless__eq(X14,X13,X12)
      | ~ c_Orderings_Oord__class_Oless__eq(X14,X12,X11)
      | c_Orderings_Oord__class_Oless__eq(X14,X13,X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(c_0_22,plain,
    ! [X11,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X11)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X12) ),
    inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).

fof(c_0_23,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

cnf(c_0_24,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_25,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_26,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

cnf(c_0_27,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

fof(c_0_28,plain,
    ! [X23,X24,X25] :
      ( ~ class_Rings_Ocomm__semiring__1(X25)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X24),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25),X23),X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).

fof(c_0_29,plain,
    ! [X26,X27] :
      ( ~ class_RealVector_Oreal__normed__algebra__1(X27)
      | c_RealVector_Onorm__class_Onorm(X27,c_RealVector_Oof__real(X27,X26)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X26) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])]) ).

fof(c_0_30,plain,
    ! [X26] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X26) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X26),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

fof(c_0_31,plain,
    ! [X9,X10,X11] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X11,X9,X10)
        | X9 = X10
        | ~ c_Orderings_Oord__class_Oless__eq(X11,X10,X9)
        | ~ class_Orderings_Oorder(X11) )
      & ( X9 != X10
        | c_Orderings_Oord__class_Oless__eq(X11,X9,X10)
        | ~ c_Orderings_Oord__class_Oless__eq(X11,X10,X9)
        | ~ class_Orderings_Oorder(X11) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(c_0_32,plain,
    ! [X7,X8,X9] :
      ( ~ class_RealVector_Oreal__normed__algebra(X9)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X9,X8)),c_RealVector_Onorm__class_Onorm(X9,X7))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).

cnf(c_0_33,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).

cnf(c_0_34,negated_conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),
    inference(spm,[status(thm)],[c_0_27,c_0_25]) ).

cnf(c_0_35,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_28]) ).

cnf(c_0_36,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).

cnf(c_0_37,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2)
    | ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_38,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_30]) ).

fof(c_0_39,plain,
    ! [X23,X24] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | c_Groups_Oabs__class_Oabs(X24,X23) = X23 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).

cnf(c_0_40,plain,
    ( X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_41,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_42,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).

cnf(c_0_43,negated_conjecture,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_44,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_45,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2)
    | ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
    inference(rw,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_46,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).

cnf(c_0_47,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = X2
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_48,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
    inference(split_conjunct,[status(thm)],[fact_t_I1_J]) ).

cnf(c_0_49,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).

fof(c_0_50,plain,
    ! [X11,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X12),
    inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).

fof(c_0_51,plain,
    ! [X11] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X11) = X11,
    inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).

cnf(c_0_52,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)) = c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).

cnf(c_0_53,negated_conjecture,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))))
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),X1) ),
    inference(rw,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_54,plain,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_55,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____) = v_t____,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_38]),c_0_49])]) ).

cnf(c_0_56,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).

cnf(c_0_57,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_50]) ).

cnf(c_0_58,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
    inference(split_conjunct,[status(thm)],[fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096]) ).

cnf(c_0_59,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_51]) ).

cnf(c_0_60,negated_conjecture,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]),c_0_54]),c_0_55]),c_0_56])]),c_0_57]),c_0_57]) ).

cnf(c_0_61,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(rw,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_62,negated_conjecture,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_26])]) ).

cnf(c_0_63,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(rw,[status(thm)],[c_0_27,c_0_44]) ).

cnf(c_0_64,negated_conjecture,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_60]),c_0_42]),c_0_61])]) ).

fof(c_0_65,plain,
    ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X10),
    inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).

cnf(c_0_66,negated_conjecture,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
    inference(rw,[status(thm)],[c_0_62,c_0_44]) ).

cnf(c_0_67,negated_conjecture,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_61])]) ).

cnf(c_0_68,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_69,negated_conjecture,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_66]),c_0_54]),c_0_55]),c_0_56]),c_0_54]),c_0_55])]),c_0_57]),c_0_67]),c_0_57]),c_0_67]),c_0_68])]) ).

cnf(c_0_70,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_69]),c_0_68])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW261+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13  % Command  : run_ET %s %d
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun  5 23:38:34 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.35/2.54  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.35/2.54  # Preprocessing time       : 0.117 s
% 0.35/2.54  
% 0.35/2.54  # Proof found!
% 0.35/2.54  # SZS status Theorem
% 0.35/2.54  # SZS output start CNFRefutation
% See solution above
% 0.35/2.54  # Proof object total steps             : 71
% 0.35/2.54  # Proof object clause steps            : 38
% 0.35/2.54  # Proof object formula steps           : 33
% 0.35/2.54  # Proof object conjectures             : 15
% 0.35/2.54  # Proof object clause conjectures      : 12
% 0.35/2.54  # Proof object formula conjectures     : 3
% 0.35/2.54  # Proof object initial clauses used    : 20
% 0.35/2.54  # Proof object initial formulas used   : 20
% 0.35/2.54  # Proof object generating inferences   : 12
% 0.35/2.54  # Proof object simplifying inferences  : 42
% 0.35/2.54  # Training examples: 0 positive, 0 negative
% 0.35/2.54  # Parsed axioms                        : 1288
% 0.35/2.54  # Removed by relevancy pruning/SinE    : 0
% 0.35/2.54  # Initial clauses                      : 1648
% 0.35/2.54  # Removed in clause preprocessing      : 46
% 0.35/2.54  # Initial clauses in saturation        : 1602
% 0.35/2.54  # Processed clauses                    : 7668
% 0.35/2.54  # ...of these trivial                  : 286
% 0.35/2.54  # ...subsumed                          : 4335
% 0.35/2.54  # ...remaining for further processing  : 3047
% 0.35/2.54  # Other redundant clauses eliminated   : 178
% 0.35/2.54  # Clauses deleted for lack of memory   : 0
% 0.35/2.54  # Backward-subsumed                    : 9
% 0.35/2.54  # Backward-rewritten                   : 211
% 0.35/2.54  # Generated clauses                    : 61651
% 0.35/2.54  # ...of the previous two non-trivial   : 56173
% 0.35/2.54  # Contextual simplify-reflections      : 305
% 0.35/2.54  # Paramodulations                      : 61392
% 0.35/2.54  # Factorizations                       : 10
% 0.35/2.54  # Equation resolutions                 : 249
% 0.35/2.54  # Current number of processed clauses  : 2793
% 0.35/2.54  #    Positive orientable unit clauses  : 598
% 0.35/2.54  #    Positive unorientable unit clauses: 11
% 0.35/2.54  #    Negative unit clauses             : 280
% 0.35/2.54  #    Non-unit-clauses                  : 1904
% 0.35/2.54  # Current number of unprocessed clauses: 47547
% 0.35/2.54  # ...number of literals in the above   : 137020
% 0.35/2.54  # Current number of archived formulas  : 0
% 0.35/2.54  # Current number of archived clauses   : 220
% 0.35/2.54  # Clause-clause subsumption calls (NU) : 715675
% 0.35/2.54  # Rec. Clause-clause subsumption calls : 511513
% 0.35/2.54  # Non-unit clause-clause subsumptions  : 1763
% 0.35/2.54  # Unit Clause-clause subsumption calls : 56307
% 0.35/2.54  # Rewrite failures with RHS unbound    : 0
% 0.35/2.54  # BW rewrite match attempts            : 4271
% 0.35/2.54  # BW rewrite match successes           : 213
% 0.35/2.54  # Condensation attempts                : 0
% 0.35/2.54  # Condensation successes               : 0
% 0.35/2.54  # Termbank termtop insertions          : 1424273
% 0.35/2.54  
% 0.35/2.54  # -------------------------------------------------
% 0.35/2.54  # User time                : 1.111 s
% 0.35/2.54  # System time              : 0.026 s
% 0.35/2.54  # Total time               : 1.137 s
% 0.35/2.54  # Maximum resident set size: 55616 pages
% 0.35/23.53  eprover: CPU time limit exceeded, terminating
% 0.35/23.53  eprover: CPU time limit exceeded, terminating
% 0.35/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.54  eprover: No such file or directory
% 0.35/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.55  eprover: No such file or directory
% 0.35/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.55  eprover: No such file or directory
% 0.35/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.55  eprover: No such file or directory
% 0.35/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.56  eprover: No such file or directory
% 0.35/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.56  eprover: No such file or directory
% 0.35/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.56  eprover: No such file or directory
% 0.35/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.57  eprover: No such file or directory
% 0.35/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.57  eprover: No such file or directory
% 0.35/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.57  eprover: No such file or directory
% 0.35/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.57  eprover: No such file or directory
% 0.35/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.58  eprover: No such file or directory
% 0.35/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.58  eprover: No such file or directory
% 0.35/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.58  eprover: No such file or directory
% 0.35/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.58  eprover: No such file or directory
% 0.35/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.59  eprover: No such file or directory
% 0.35/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.59  eprover: No such file or directory
% 0.35/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.59  eprover: No such file or directory
% 0.35/23.59  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.59  eprover: No such file or directory
% 0.35/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.60  eprover: No such file or directory
% 0.35/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.35/23.60  eprover: No such file or directory
% 0.35/23.60  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.35/23.60  eprover: No such file or directory
%------------------------------------------------------------------------------