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