TSTP Solution File: SWW208+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 20:08:48 EDT 2023

% Result   : Theorem 4.94s 1.41s
% Output   : CNFRefutation 4.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   59 (  31 unt;   0 def)
%            Number of atoms       :  110 (  25 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   93 (  42   ~;  34   |;   8   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-2 aty)
%            Number of variables   :   70 (   5 sgn;  43   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_less__le__not__le,axiom,
    ! [X21,X13,X6] :
      ( class_Orderings_Opreorder(X6)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X13),X21))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X13),X21))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X21),X13)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_less__le__not__le) ).

fof(fact_real__le__trans,axiom,
    ! [X17,X18,X19] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X18))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),X17))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X17)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_real__le__trans) ).

fof(fact_rp,axiom,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_rp) ).

fof(conj_0,conjecture,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    & ! [X4] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X4)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',conj_0) ).

fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(fact_real__le__linear,axiom,
    ! [X12,X11] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11),X12))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),X11)) ),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_real__le__linear) ).

fof(fact_less__add__one,axiom,
    ! [X8,X6] :
      ( class_Rings_Olinordered__semidom(X6)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X8),c_Groups_Oone__class_Oone(X6)))) ),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_less__add__one) ).

fof(fact_real__norm__def,axiom,
    ! [X23] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X23) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_real__norm__def) ).

fof(fact_th,axiom,
    ! [X4] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X4)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_th) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X29] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X29),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_Zero__neq__Suc) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X25] : c_Nat_OSuc(X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_Suc__eq__plus1) ).

fof(fact_natfloor__add__one,axiom,
    ! [X5] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X5))
     => c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X5)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_natfloor__add__one) ).

fof(fact_nat__add__commute,axiom,
    ! [X25,X29] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X29),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_nat__add__commute) ).

fof(fact_less__eq__real__def,axiom,
    ! [X21,X13] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13),X21))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13),X21))
        | X13 = X21 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_less__eq__real__def) ).

fof(fact_natfloor__zero,axiom,
    c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_natfloor__zero) ).

fof(c_0_16,plain,
    ! [X21,X13,X6] :
      ( class_Orderings_Opreorder(X6)
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X13),X21))
      <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X13),X21))
          & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X21),X13)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(c_0_17,plain,
    ! [X180,X181,X182] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X182),X181))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X181),X180))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X182),X180)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).

fof(c_0_18,plain,
    ! [X503,X504,X505] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X504),X503))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
        | ~ class_Orderings_Opreorder(X505) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X503),X504))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
        | ~ class_Orderings_Opreorder(X505) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X504),X503))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X503),X504))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
        | ~ class_Orderings_Opreorder(X505) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

cnf(c_0_19,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_20,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    inference(split_conjunct,[status(thm)],[fact_rp]) ).

fof(c_0_21,negated_conjecture,
    ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
      & ! [X4] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X4)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

cnf(c_0_22,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

fof(c_0_25,plain,
    ! [X183,X184] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X184),X183))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X183),X184)) ),
    inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).

fof(c_0_26,plain,
    ! [X326,X327] :
      ( ~ class_Rings_Olinordered__semidom(X327)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X327,X326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X327),X326),c_Groups_Oone__class_Oone(X327)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(c_0_27,negated_conjecture,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).

fof(c_0_28,plain,
    ! [X361] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X361) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X361),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

fof(c_0_29,plain,
    ! [X113] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X113)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    inference(variable_rename,[status(thm)],[fact_th]) ).

cnf(c_0_30,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_31,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).

cnf(c_0_34,negated_conjecture,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    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]) ).

cnf(c_0_36,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_37,plain,
    ! [X1557] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1557),
    inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(c_0_38,plain,
    ! [X1623] : c_Nat_OSuc(X1623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1623),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(c_0_39,plain,
    ! [X1393] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1393))
      | c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1393),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1393)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add__one])]) ).

fof(c_0_40,plain,
    ! [X1198,X1199] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1199),X1198) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1198),X1199),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(c_0_41,plain,
    ! [X266,X267] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X267),X266))
        | X267 = X266 )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X267),X266))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266)) )
      & ( X267 != X266
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).

cnf(c_0_42,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),X1)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_43,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_44,negated_conjecture,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_45,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    inference(rw,[status(thm)],[c_0_36,c_0_35]) ).

cnf(c_0_46,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_47,plain,
    c_Nat_OSuc(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_48,plain,
    ( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_49,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_50,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_51,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_52,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).

cnf(c_0_53,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_54,plain,
    ( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
    inference(rw,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_55,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).

cnf(c_0_56,plain,
    c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_natfloor__zero]) ).

cnf(c_0_57,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(spm,[status(thm)],[c_0_53,c_0_49]) ).

cnf(c_0_58,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[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_20])]),c_0_57]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.22/0.22  % Problem    : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% 0.22/0.23  % Command    : run_E %s %d THM
% 0.22/0.44  % Computer : n004.cluster.edu
% 0.22/0.44  % Model    : x86_64 x86_64
% 0.22/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.44  % Memory   : 8042.1875MB
% 0.22/0.44  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.22/0.44  % CPULimit   : 2400
% 0.22/0.44  % WCLimit    : 300
% 0.22/0.44  % DateTime   : Mon Oct  2 22:09:00 EDT 2023
% 0.22/0.44  % CPUTime    : 
% 0.41/0.67  Running first-order theorem proving
% 0.41/0.67  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p
% 4.94/1.41  # Version: 3.1pre001
% 4.94/1.41  # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.94/1.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.94/1.41  # Starting new_bool_3 with 300s (1) cores
% 4.94/1.41  # Starting new_bool_1 with 300s (1) cores
% 4.94/1.41  # Starting sh5l with 300s (1) cores
% 4.94/1.41  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 17334 completed with status 0
% 4.94/1.41  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 4.94/1.41  # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.94/1.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.94/1.41  # No SInE strategy applied
% 4.94/1.41  # Search class: FGHSM-SSLM32-DFFFFFNN
% 4.94/1.41  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.94/1.41  # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 4.94/1.41  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 4.94/1.41  # G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 17345 completed with status 0
% 4.94/1.41  # Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 4.94/1.41  # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.94/1.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.94/1.41  # No SInE strategy applied
% 4.94/1.41  # Search class: FGHSM-SSLM32-DFFFFFNN
% 4.94/1.41  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.94/1.41  # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 4.94/1.41  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 4.94/1.41  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 4.94/1.41  # Preprocessing time       : 0.023 s
% 4.94/1.41  # Presaturation interreduction done
% 4.94/1.41  
% 4.94/1.41  # Proof found!
% 4.94/1.41  # SZS status Theorem
% 4.94/1.41  # SZS output start CNFRefutation
% See solution above
% 4.94/1.41  # Parsed axioms                        : 1269
% 4.94/1.41  # Removed by relevancy pruning/SinE    : 0
% 4.94/1.41  # Initial clauses                      : 1712
% 4.94/1.41  # Removed in clause preprocessing      : 48
% 4.94/1.41  # Initial clauses in saturation        : 1664
% 4.94/1.41  # Processed clauses                    : 5171
% 4.94/1.41  # ...of these trivial                  : 86
% 4.94/1.41  # ...subsumed                          : 2050
% 4.94/1.41  # ...remaining for further processing  : 3035
% 4.94/1.41  # Other redundant clauses eliminated   : 223
% 4.94/1.41  # Clauses deleted for lack of memory   : 0
% 4.94/1.41  # Backward-subsumed                    : 25
% 4.94/1.41  # Backward-rewritten                   : 41
% 4.94/1.41  # Generated clauses                    : 10855
% 4.94/1.41  # ...of the previous two non-redundant : 9246
% 4.94/1.41  # ...aggressively subsumed             : 0
% 4.94/1.41  # Contextual simplify-reflections      : 5
% 4.94/1.41  # Paramodulations                      : 10629
% 4.94/1.41  # Factorizations                       : 6
% 4.94/1.41  # NegExts                              : 0
% 4.94/1.41  # Equation resolutions                 : 236
% 4.94/1.41  # Total rewrite steps                  : 7716
% 4.94/1.41  # Propositional unsat checks           : 0
% 4.94/1.41  #    Propositional check models        : 0
% 4.94/1.41  #    Propositional check unsatisfiable : 0
% 4.94/1.41  #    Propositional clauses             : 0
% 4.94/1.41  #    Propositional clauses after purity: 0
% 4.94/1.41  #    Propositional unsat core size     : 0
% 4.94/1.41  #    Propositional preprocessing time  : 0.000
% 4.94/1.41  #    Propositional encoding time       : 0.000
% 4.94/1.41  #    Propositional solver time         : 0.000
% 4.94/1.41  #    Success case prop preproc time    : 0.000
% 4.94/1.41  #    Success case prop encoding time   : 0.000
% 4.94/1.41  #    Success case prop solver time     : 0.000
% 4.94/1.41  # Current number of processed clauses  : 1453
% 4.94/1.41  #    Positive orientable unit clauses  : 545
% 4.94/1.41  #    Positive unorientable unit clauses: 23
% 4.94/1.41  #    Negative unit clauses             : 235
% 4.94/1.41  #    Non-unit-clauses                  : 650
% 4.94/1.41  # Current number of unprocessed clauses: 7099
% 4.94/1.41  # ...number of literals in the above   : 13241
% 4.94/1.41  # Current number of archived formulas  : 0
% 4.94/1.41  # Current number of archived clauses   : 1454
% 4.94/1.41  # Clause-clause subsumption calls (NU) : 178148
% 4.94/1.41  # Rec. Clause-clause subsumption calls : 105018
% 4.94/1.41  # Non-unit clause-clause subsumptions  : 693
% 4.94/1.41  # Unit Clause-clause subsumption calls : 9149
% 4.94/1.41  # Rewrite failures with RHS unbound    : 1776
% 4.94/1.41  # BW rewrite match attempts            : 4255
% 4.94/1.41  # BW rewrite match successes           : 551
% 4.94/1.41  # Condensation attempts                : 0
% 4.94/1.41  # Condensation successes               : 0
% 4.94/1.41  # Termbank termtop insertions          : 428223
% 4.94/1.41  
% 4.94/1.41  # -------------------------------------------------
% 4.94/1.41  # User time                : 0.624 s
% 4.94/1.41  # System time              : 0.031 s
% 4.94/1.41  # Total time               : 0.655 s
% 4.94/1.41  # Maximum resident set size: 8696 pages
% 4.94/1.41  
% 4.94/1.41  # -------------------------------------------------
% 4.94/1.41  # User time                : 2.779 s
% 4.94/1.41  # System time              : 0.112 s
% 4.94/1.41  # Total time               : 2.892 s
% 4.94/1.41  # Maximum resident set size: 3236 pages
% 4.94/1.41  % E---3.1 exiting
% 5.47/1.41  % E---3.1 exiting
%------------------------------------------------------------------------------