TSTP Solution File: SWW208+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWW208+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Mar  6 15:02:38 EST 2011

% Result   : Theorem 9.42s
% Output   : CNFRefutation 9.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   82 (  29 unt;   0 def)
%            Number of atoms       :  194 (  38 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  208 (  96   ~;  81   |;  17   &)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   9 con; 0-2 aty)
%            Number of variables   :  105 (   2 sgn  69   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(37,axiom,
    ! [X25,X8] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8),X25))
    <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8),X25))
        | X8 = X25 ) ),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_less__eq__real__def) ).

fof(58,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))))
    & ! [X29] : 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____,X29)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',conj_0) ).

fof(223,axiom,
    hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_complex__Re__i) ).

fof(274,axiom,
    ! [X29] : 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,X29)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_th) ).

fof(310,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(356,axiom,
    ! [X3,X4] :
      ( class_Rings_Olinordered__semidom(X4)
     => hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X3),c_Groups_Oone__class_Oone(X4)))) ),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_less__add__one) ).

fof(381,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_real__zero__not__eq__one) ).

fof(457,axiom,
    ! [X22,X21,X20] :
      ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20),X21))
     => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21),X22))
       => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20),X22)) ) ),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_real__le__trans) ).

fof(635,axiom,
    ! [X25,X8,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X8),X25))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X25),X8)) ) ),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_linorder__not__less) ).

fof(668,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(685,axiom,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_rp) ).

fof(936,axiom,
    ! [X25,X8,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X8),X25))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X25),X8)) ) ),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_linorder__not__le) ).

fof(1114,axiom,
    ! [X15,X14,X4] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
     => ( X14 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X14),X15)
      <=> X15 = c_Groups_Ozero__class_Ozero(X4) ) ),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_add__0__iff) ).

fof(1146,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',arity_RealDef__Oreal__Orderings_Olinorder) ).

fof(1259,axiom,
    hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/tmp/tmpodmhmL/sel_SWW208+1.p_1',fact_complex__Im__i) ).

fof(1270,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))))
      & ! [X29] : 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____,X29)))))),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)],[58]) ).

fof(1297,plain,
    ! [X25,X8,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X8),X25))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X25),X8)) ) ),
    inference(fof_simplification,[status(thm)],[635,theory(equality)]) ).

fof(1311,plain,
    ! [X25,X8,X4] :
      ( class_Orderings_Olinorder(X4)
     => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X8),X25))
      <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X25),X8)) ) ),
    inference(fof_simplification,[status(thm)],[936,theory(equality)]) ).

fof(1416,plain,
    ! [X25,X8] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8),X25))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8),X25))
        | X8 = X25 )
      & ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8),X25))
          & X8 != X25 )
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8),X25)) ) ),
    inference(fof_nnf,[status(thm)],[37]) ).

fof(1417,plain,
    ! [X26,X27] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27),X26))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X27),X26))
        | X27 = X26 )
      & ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X27),X26))
          & X27 != X26 )
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27),X26)) ) ),
    inference(variable_rename,[status(thm)],[1416]) ).

fof(1418,plain,
    ! [X26,X27] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27),X26))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X27),X26))
        | X27 = X26 )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X27),X26))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27),X26)) )
      & ( X27 != X26
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X27),X26)) ) ),
    inference(distribute,[status(thm)],[1417]) ).

cnf(1420,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[1418]) ).

cnf(1421,plain,
    ( X1 = X2
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[1418]) ).

fof(1488,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))))
    | ? [X29] : ~ 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____,X29)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(fof_nnf,[status(thm)],[1270]) ).

fof(1489,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))))
    | ? [X30] : ~ 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____,X30)))))),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)],[1488]) ).

fof(1490,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____,esk1_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)],[1489]) ).

cnf(1491,negated_conjecture,
    ( ~ 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____,esk1_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(split_conjunct,[status(thm)],[1490]) ).

cnf(2024,plain,
    hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[223]) ).

fof(2186,plain,
    ! [X30] : 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,X30)))),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)],[274]) ).

cnf(2187,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)],[2186]) ).

cnf(2295,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[310]) ).

fof(2425,plain,
    ! [X3,X4] :
      ( ~ class_Rings_Olinordered__semidom(X4)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X3),c_Groups_Oone__class_Oone(X4)))) ),
    inference(fof_nnf,[status(thm)],[356]) ).

fof(2426,plain,
    ! [X5,X6] :
      ( ~ class_Rings_Olinordered__semidom(X6)
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X5),c_Groups_Oone__class_Oone(X6)))) ),
    inference(variable_rename,[status(thm)],[2425]) ).

cnf(2427,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)],[2426]) ).

cnf(2495,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[381]) ).

fof(2692,plain,
    ! [X22,X21,X20] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20),X21))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21),X22))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20),X22)) ),
    inference(fof_nnf,[status(thm)],[457]) ).

fof(2693,plain,
    ! [X23,X24,X25] :
      ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25),X24))
      | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24),X23))
      | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25),X23)) ),
    inference(variable_rename,[status(thm)],[2692]) ).

cnf(2694,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,X3),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[2693]) ).

fof(3202,plain,
    ! [X25,X8,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X8),X25))
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X25),X8)) )
        & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X25),X8))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X8),X25)) ) ) ),
    inference(fof_nnf,[status(thm)],[1297]) ).

fof(3203,plain,
    ! [X26,X27,X28] :
      ( ~ class_Orderings_Olinorder(X28)
      | ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X28,X27),X26))
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,X26),X27)) )
        & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,X26),X27))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X28,X27),X26)) ) ) ),
    inference(variable_rename,[status(thm)],[3202]) ).

fof(3204,plain,
    ! [X26,X27,X28] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X28,X27),X26))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,X26),X27))
        | ~ class_Orderings_Olinorder(X28) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,X26),X27))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X28,X27),X26))
        | ~ class_Orderings_Olinorder(X28) ) ),
    inference(distribute,[status(thm)],[3203]) ).

cnf(3206,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[3204]) ).

cnf(3311,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[668]) ).

cnf(3373,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)],[685]) ).

fof(4140,plain,
    ! [X25,X8,X4] :
      ( ~ class_Orderings_Olinorder(X4)
      | ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X8),X25))
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X25),X8)) )
        & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X4,X25),X8))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X4,X8),X25)) ) ) ),
    inference(fof_nnf,[status(thm)],[1311]) ).

fof(4141,plain,
    ! [X26,X27,X28] :
      ( ~ class_Orderings_Olinorder(X28)
      | ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,X27),X26))
          | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X28,X26),X27)) )
        & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X28,X26),X27))
          | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,X27),X26)) ) ) ),
    inference(variable_rename,[status(thm)],[4140]) ).

fof(4142,plain,
    ! [X26,X27,X28] :
      ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,X27),X26))
        | hBOOL(hAPP(c_Orderings_Oord__class_Oless(X28,X26),X27))
        | ~ class_Orderings_Olinorder(X28) )
      & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X28,X26),X27))
        | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,X27),X26))
        | ~ class_Orderings_Olinorder(X28) ) ),
    inference(distribute,[status(thm)],[4141]) ).

cnf(4143,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[4142]) ).

fof(4660,plain,
    ! [X15,X14,X4] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
      | ( ( X14 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X14),X15)
          | X15 = c_Groups_Ozero__class_Ozero(X4) )
        & ( X15 != c_Groups_Ozero__class_Ozero(X4)
          | X14 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X14),X15) ) ) ),
    inference(fof_nnf,[status(thm)],[1114]) ).

fof(4661,plain,
    ! [X16,X17,X18] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18)
      | ( ( X17 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18),X17),X16)
          | X16 = c_Groups_Ozero__class_Ozero(X18) )
        & ( X16 != c_Groups_Ozero__class_Ozero(X18)
          | X17 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18),X17),X16) ) ) ),
    inference(variable_rename,[status(thm)],[4660]) ).

fof(4662,plain,
    ! [X16,X17,X18] :
      ( ( X17 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18),X17),X16)
        | X16 = c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18) )
      & ( X16 != c_Groups_Ozero__class_Ozero(X18)
        | X17 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18),X17),X16)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18) ) ),
    inference(distribute,[status(thm)],[4661]) ).

cnf(4664,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) ),
    inference(split_conjunct,[status(thm)],[4662]) ).

cnf(4773,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[1146]) ).

cnf(5100,plain,
    hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[1259]) ).

cnf(5426,plain,
    hAPP(c_Complex_OIm,c_Complex_Oii) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(rw,[status(thm)],[2495,5100,theory(equality)]) ).

cnf(5427,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),hAPP(c_Complex_OIm,c_Complex_Oii))))
    | ~ 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____,esk1_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
    inference(rw,[status(thm)],[1491,5100,theory(equality)]) ).

cnf(5428,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),hAPP(c_Complex_OIm,c_Complex_Oii))))
    | ~ 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____,esk1_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))) ),
    inference(rw,[status(thm)],[5427,5100,theory(equality)]) ).

cnf(5432,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),hAPP(c_Complex_OIm,c_Complex_Oii)))),
    inference(rw,[status(thm)],[2187,5100,theory(equality)]) ).

cnf(5433,negated_conjecture,
    ( $false
    | ~ 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),hAPP(c_Complex_OIm,c_Complex_Oii)))) ),
    inference(rw,[status(thm)],[5428,5432,theory(equality)]) ).

cnf(5434,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),hAPP(c_Complex_OIm,c_Complex_Oii)))),
    inference(cn,[status(thm)],[5433,theory(equality)]) ).

cnf(5448,plain,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r)),
    inference(rw,[status(thm)],[3373,2024,theory(equality)]) ).

cnf(6371,plain,
    ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X1)) ),
    inference(spm,[status(thm)],[4143,1420,theory(equality)]) ).

cnf(6426,plain,
    ( $false
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X1)) ),
    inference(rw,[status(thm)],[6371,4773,theory(equality)]) ).

cnf(6427,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
    | ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X1)) ),
    inference(cn,[status(thm)],[6426,theory(equality)]) ).

cnf(9578,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X1)) ),
    inference(spm,[status(thm)],[3206,4773,theory(equality)]) ).

cnf(100823,plain,
    hAPP(c_Complex_ORe,c_Complex_Oii) != hAPP(c_Complex_OIm,c_Complex_Oii),
    inference(rw,[status(thm)],[5426,2024,theory(equality)]) ).

cnf(100824,negated_conjecture,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))),
    inference(rw,[status(thm)],[5434,2024,theory(equality)]) ).

cnf(101144,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),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
    inference(spm,[status(thm)],[2694,5448,theory(equality)]) ).

cnf(116358,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1))
    | ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[6427,2427,theory(equality)]) ).

cnf(116410,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),hAPP(c_Complex_OIm,c_Complex_Oii))),X1))
    | ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
    inference(rw,[status(thm)],[116358,5100,theory(equality)]) ).

cnf(116411,plain,
    ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),hAPP(c_Complex_OIm,c_Complex_Oii))),X1))
    | $false ),
    inference(rw,[status(thm)],[116410,2295,theory(equality)]) ).

cnf(116412,plain,
    ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),hAPP(c_Complex_OIm,c_Complex_Oii))),X1)),
    inference(cn,[status(thm)],[116411,theory(equality)]) ).

cnf(116978,plain,
    ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r))
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
    inference(spm,[status(thm)],[101144,9578,theory(equality)]) ).

cnf(117025,negated_conjecture,
    hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii))),v_r)),
    inference(spm,[status(thm)],[100824,116978,theory(equality)]) ).

cnf(117109,negated_conjecture,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)) = v_r
    | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii))),v_r)) ),
    inference(spm,[status(thm)],[1421,117025,theory(equality)]) ).

cnf(117122,negated_conjecture,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)) = v_r,
    inference(sr,[status(thm)],[117109,116412,theory(equality)]) ).

cnf(117145,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_OIm,c_Complex_Oii)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[4664,117122,theory(equality)]) ).

cnf(117178,negated_conjecture,
    ( hAPP(c_Complex_ORe,c_Complex_Oii) = hAPP(c_Complex_OIm,c_Complex_Oii)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
    inference(rw,[status(thm)],[117145,2024,theory(equality)]) ).

cnf(117179,negated_conjecture,
    ( hAPP(c_Complex_ORe,c_Complex_Oii) = hAPP(c_Complex_OIm,c_Complex_Oii)
    | $false ),
    inference(rw,[status(thm)],[117178,3311,theory(equality)]) ).

cnf(117180,negated_conjecture,
    hAPP(c_Complex_ORe,c_Complex_Oii) = hAPP(c_Complex_OIm,c_Complex_Oii),
    inference(cn,[status(thm)],[117179,theory(equality)]) ).

cnf(117181,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[117180,100823,theory(equality)]) ).

cnf(117182,negated_conjecture,
    $false,
    117181,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW208+1.p
% --creating new selector for []
% -running prover on /tmp/tmpodmhmL/sel_SWW208+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW208+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW208+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW208+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------