TSTP Solution File: SWW261+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SWW261+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 06:42:01 EDT 2024

% Result   : Theorem 8.57s 1.63s
% Output   : CNFRefutation 8.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   82 (  45 unt;   0 def)
%            Number of atoms       :  164 (  52 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  139 (  57   ~;  54   |;   8   &)
%                                         (   6 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   1 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   :   95 (   0 sgn  62   !;   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/sandbox/benchmark/theBenchmark.p',conj_0) ).

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/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).

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/sandbox/benchmark/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/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).

fof(fact_less__eq__real__def,axiom,
    ! [X7,X8] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X7)
    <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8,X7)
        | X8 = X7 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

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/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).

fof(fact_xt1_I6_J,axiom,
    ! [X10,X5,X4,X6] :
      ( class_Orderings_Oorder(X6)
     => ( c_Orderings_Oord__class_Oless__eq(X6,X4,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X6,X10,X4)
         => c_Orderings_Oord__class_Oless__eq(X6,X10,X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_abs__of__nonneg,axiom,
    ! [X22,X6] :
      ( class_Groups_Oordered__ab__group__add__abs(X6)
     => ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X22)
       => c_Groups_Oabs__class_Oabs(X6,X22) = X22 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

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/sandbox/benchmark/theBenchmark.p',fact_t_I1_J) ).

fof(fact_real__le__antisym,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)
       => X10 = X9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).

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/sandbox/benchmark/theBenchmark.p',fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096) ).

fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

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/sandbox/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).

fof(fact_real__mult__right__cancel,axiom,
    ! [X17,X18,X19] :
      ( X19 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X19)
      <=> X18 = X17 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(fact_less__le__not__le,axiom,
    ! [X7,X8,X6] :
      ( class_Orderings_Opreorder(X6)
     => ( c_Orderings_Oord__class_Oless(X6,X8,X7)
      <=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X7)
          & ~ c_Orderings_Oord__class_Oless__eq(X6,X7,X8) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).

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

fof(fact_norm__le__zero__iff,axiom,
    ! [X8,X6] :
      ( class_RealVector_Oreal__normed__vector(X6)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X8),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> X8 = c_Groups_Ozero__class_Ozero(X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).

fof(fact_real__le__refl,axiom,
    ! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).

fof(fact_t_I2_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_t_I2_J) ).

fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

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

fof(c_0_24,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)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(c_0_25,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_nnf,[status(thm)],[c_0_24]) ).

fof(c_0_26,plain,
    ! [X105,X106] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X106,X105)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X105,X106) ),
    inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).

fof(c_0_27,plain,
    ! [X1995,X1996] :
      ( ~ class_RealVector_Oreal__normed__algebra__1(X1996)
      | c_RealVector_Onorm__class_Onorm(X1996,c_RealVector_Oof__real(X1996,X1995)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1995) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])])]) ).

fof(c_0_28,plain,
    ! [X1925] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1925) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1925),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

fof(c_0_29,plain,
    ! [X294,X295] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X295,X294)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X295,X294)
        | X295 = X294 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X295,X294)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X295,X294) )
      & ( X295 != X294
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X295,X294) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])])]) ).

fof(c_0_30,plain,
    ! [X127] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X127) = X127,
    inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).

fof(c_0_31,plain,
    ! [X315,X316,X317,X318] :
      ( ~ class_Orderings_Oorder(X318)
      | ~ c_Orderings_Oord__class_Oless__eq(X318,X317,X316)
      | ~ c_Orderings_Oord__class_Oless__eq(X318,X315,X317)
      | c_Orderings_Oord__class_Oless__eq(X318,X315,X316) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])])]) ).

cnf(c_0_32,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_25]) ).

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,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_34,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_27]) ).

cnf(c_0_35,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_28]) ).

fof(c_0_36,plain,
    ! [X1947,X1948] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X1948)
      | ~ c_Orderings_Oord__class_Oless__eq(X1948,c_Groups_Ozero__class_Ozero(X1948),X1947)
      | c_Groups_Oabs__class_Oabs(X1948,X1947) = X1947 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])])]) ).

cnf(c_0_37,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_38,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]) ).

fof(c_0_39,plain,
    ! [X110,X111] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X111,X110)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X110,X111)
      | X111 = X110 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])])]) ).

cnf(c_0_40,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_41,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_30]) ).

cnf(c_0_42,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_43,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_32,c_0_33]) ).

cnf(c_0_44,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).

fof(c_0_45,plain,
    ! [X90,X91,X92] :
      ( ~ class_RealVector_Oreal__normed__algebra(X92)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X92,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X92),X91),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X92,X91)),c_RealVector_Onorm__class_Onorm(X92,X90))) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])])]) ).

cnf(c_0_46,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_34,c_0_35]) ).

cnf(c_0_47,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_48,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_49,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_50,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_51,plain,
    ! [X17,X18,X19] :
      ( X19 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X19)
      <=> X18 = X17 ) ),
    inference(fof_simplification,[status(thm)],[fact_real__mult__right__cancel]) ).

cnf(c_0_52,plain,
    ( X1 = X2
    | ~ 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_39]) ).

cnf(c_0_53,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_40,c_0_41]) ).

cnf(c_0_54,negated_conjecture,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),X1)
    | ~ 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____)),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).

cnf(c_0_55,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_45]) ).

cnf(c_0_56,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_46,c_0_47]) ).

cnf(c_0_57,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_48,c_0_49]),c_0_35]),c_0_50])]) ).

cnf(c_0_58,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).

fof(c_0_59,plain,
    ! [X142,X143,X144] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X143),X144) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X142),X144)
        | X143 = X142
        | X144 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X143 != X142
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X143),X144) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X142),X144)
        | X144 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])]) ).

cnf(c_0_60,plain,
    ( 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____)
    | ~ 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(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_61,negated_conjecture,
    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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]),c_0_58])]) ).

fof(c_0_62,plain,
    ! [X7,X8,X6] :
      ( class_Orderings_Opreorder(X6)
     => ( c_Orderings_Oord__class_Oless(X6,X8,X7)
      <=> ( c_Orderings_Oord__class_Oless__eq(X6,X8,X7)
          & ~ c_Orderings_Oord__class_Oless__eq(X6,X7,X8) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

cnf(c_0_63,plain,
    ( X1 = X3
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_64,plain,
    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)],[c_0_60,c_0_61])]) ).

fof(c_0_65,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_simplification,[status(thm)],[fact_w0]) ).

fof(c_0_66,plain,
    ! [X271,X272,X273] :
      ( ( c_Orderings_Oord__class_Oless__eq(X273,X272,X271)
        | ~ c_Orderings_Oord__class_Oless(X273,X272,X271)
        | ~ class_Orderings_Opreorder(X273) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X273,X271,X272)
        | ~ c_Orderings_Oord__class_Oless(X273,X272,X271)
        | ~ class_Orderings_Opreorder(X273) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X273,X272,X271)
        | c_Orderings_Oord__class_Oless__eq(X273,X271,X272)
        | c_Orderings_Oord__class_Oless(X273,X272,X271)
        | ~ class_Orderings_Opreorder(X273) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).

fof(c_0_67,plain,
    ! [X298,X299] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X299,X298),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | X298 = c_Groups_Ozero__class_Ozero(X299)
        | ~ class_RealVector_Oreal__normed__vector(X299) )
      & ( X298 != c_Groups_Ozero__class_Ozero(X299)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X299,X298),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ class_RealVector_Oreal__normed__vector(X299) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])])]) ).

cnf(c_0_68,plain,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | v_t____ = X1
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

fof(c_0_69,plain,
    ! [X104] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X104,X104),
    inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).

fof(c_0_70,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[c_0_65]) ).

cnf(c_0_71,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_66]) ).

cnf(c_0_72,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[fact_t_I2_J]) ).

cnf(c_0_73,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

cnf(c_0_74,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_75,plain,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | v_t____ = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[c_0_68,c_0_41]) ).

cnf(c_0_76,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).

cnf(c_0_77,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_78,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

cnf(c_0_79,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_t____),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).

cnf(c_0_80,plain,
    v_t____ = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_77])]),c_0_78]) ).

cnf(c_0_81,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_77])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWW261+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat May 18 20:38:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  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/benchmark/theBenchmark.p
% 8.57/1.63  # Version: 3.1.0
% 8.57/1.63  # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.57/1.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.57/1.63  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.57/1.63  # Starting new_bool_3 with 300s (1) cores
% 8.57/1.63  # Starting new_bool_1 with 300s (1) cores
% 8.57/1.63  # Starting sh5l with 300s (1) cores
% 8.57/1.63  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 13257 completed with status 0
% 8.57/1.63  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.57/1.63  # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.57/1.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.57/1.63  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.57/1.63  # No SInE strategy applied
% 8.57/1.63  # Search class: FGHSM-SSLM31-DFFFFFNN
% 8.57/1.63  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 8.57/1.63  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 811s (1) cores
% 8.57/1.63  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.57/1.63  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 136s (1) cores
% 8.57/1.63  # Starting G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 8.57/1.63  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 8.57/1.63  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 13289 completed with status 0
% 8.57/1.63  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 8.57/1.63  # Preprocessing class: FMLMSMSMSSSNFFN.
% 8.57/1.63  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.57/1.63  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.57/1.63  # No SInE strategy applied
% 8.57/1.63  # Search class: FGHSM-SSLM31-DFFFFFNN
% 8.57/1.63  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 8.57/1.63  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 811s (1) cores
% 8.57/1.63  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.57/1.63  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 136s (1) cores
% 8.57/1.63  # Preprocessing time       : 0.022 s
% 8.57/1.63  # Presaturation interreduction done
% 8.57/1.63  
% 8.57/1.63  # Proof found!
% 8.57/1.63  # SZS status Theorem
% 8.57/1.63  # SZS output start CNFRefutation
% See solution above
% 8.57/1.63  # Parsed axioms                        : 1288
% 8.57/1.63  # Removed by relevancy pruning/SinE    : 0
% 8.57/1.63  # Initial clauses                      : 1648
% 8.57/1.63  # Removed in clause preprocessing      : 46
% 8.57/1.63  # Initial clauses in saturation        : 1602
% 8.57/1.63  # Processed clauses                    : 3956
% 8.57/1.63  # ...of these trivial                  : 82
% 8.57/1.63  # ...subsumed                          : 614
% 8.57/1.63  # ...remaining for further processing  : 3260
% 8.57/1.63  # Other redundant clauses eliminated   : 297
% 8.57/1.63  # Clauses deleted for lack of memory   : 0
% 8.57/1.63  # Backward-subsumed                    : 21
% 8.57/1.63  # Backward-rewritten                   : 130
% 8.57/1.63  # Generated clauses                    : 32869
% 8.57/1.63  # ...of the previous two non-redundant : 29306
% 8.57/1.63  # ...aggressively subsumed             : 0
% 8.57/1.63  # Contextual simplify-reflections      : 5
% 8.57/1.63  # Paramodulations                      : 32561
% 8.57/1.63  # Factorizations                       : 10
% 8.57/1.63  # NegExts                              : 0
% 8.57/1.63  # Equation resolutions                 : 309
% 8.57/1.63  # Disequality decompositions           : 0
% 8.57/1.63  # Total rewrite steps                  : 24390
% 8.57/1.63  # ...of those cached                   : 22252
% 8.57/1.63  # Propositional unsat checks           : 0
% 8.57/1.63  #    Propositional check models        : 0
% 8.57/1.63  #    Propositional check unsatisfiable : 0
% 8.57/1.63  #    Propositional clauses             : 0
% 8.57/1.63  #    Propositional clauses after purity: 0
% 8.57/1.63  #    Propositional unsat core size     : 0
% 8.57/1.63  #    Propositional preprocessing time  : 0.000
% 8.57/1.63  #    Propositional encoding time       : 0.000
% 8.57/1.63  #    Propositional solver time         : 0.000
% 8.57/1.63  #    Success case prop preproc time    : 0.000
% 8.57/1.63  #    Success case prop encoding time   : 0.000
% 8.57/1.63  #    Success case prop solver time     : 0.000
% 8.57/1.63  # Current number of processed clauses  : 1612
% 8.57/1.63  #    Positive orientable unit clauses  : 483
% 8.57/1.63  #    Positive unorientable unit clauses: 8
% 8.57/1.63  #    Negative unit clauses             : 77
% 8.57/1.63  #    Non-unit-clauses                  : 1044
% 8.57/1.63  # Current number of unprocessed clauses: 28260
% 8.57/1.63  # ...number of literals in the above   : 82785
% 8.57/1.63  # Current number of archived formulas  : 0
% 8.57/1.63  # Current number of archived clauses   : 1529
% 8.57/1.63  # Clause-clause subsumption calls (NU) : 500637
% 8.57/1.63  # Rec. Clause-clause subsumption calls : 229823
% 8.57/1.63  # Non-unit clause-clause subsumptions  : 380
% 8.57/1.63  # Unit Clause-clause subsumption calls : 3355
% 8.57/1.63  # Rewrite failures with RHS unbound    : 0
% 8.57/1.63  # BW rewrite match attempts            : 1800
% 8.57/1.63  # BW rewrite match successes           : 167
% 8.57/1.63  # Condensation attempts                : 0
% 8.57/1.63  # Condensation successes               : 0
% 8.57/1.63  # Termbank termtop insertions          : 863329
% 8.57/1.63  # Search garbage collected termcells   : 19014
% 8.57/1.63  
% 8.57/1.63  # -------------------------------------------------
% 8.57/1.63  # User time                : 1.032 s
% 8.57/1.63  # System time              : 0.039 s
% 8.57/1.63  # Total time               : 1.071 s
% 8.57/1.63  # Maximum resident set size: 8176 pages
% 8.57/1.63  
% 8.57/1.63  # -------------------------------------------------
% 8.57/1.63  # User time                : 4.895 s
% 8.57/1.63  # System time              : 0.171 s
% 8.57/1.63  # Total time               : 5.066 s
% 8.57/1.63  # Maximum resident set size: 3116 pages
% 8.57/1.63  % E---3.1 exiting
% 8.57/1.63  % E exiting
%------------------------------------------------------------------------------