TSTP Solution File: SWW265+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWW265+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 20:08:56 EDT 2023
% Result : Theorem 421.45s 53.97s
% Output : CNFRefutation 421.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 37
% Syntax : Number of formulae : 123 ( 62 unt; 0 def)
% Number of atoms : 261 ( 73 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 245 ( 107 ~; 88 |; 14 &)
% ( 9 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 152 ( 2 sgn; 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_abs__inverse,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) = c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Oabs__class_Oabs(X10,X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_abs__inverse) ).
fof(fact_real__norm__def,axiom,
! [X18] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X18) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_real__norm__def) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X6),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_abs__add__one__not__less__self) ).
fof(fact_inverse__nonzero__iff__nonzero,axiom,
! [X32,X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> ( c_Rings_Oinverse__class_Oinverse(X10,X32) = c_Groups_Ozero__class_Ozero(X10)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_inverse__nonzero__iff__nonzero) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(fact_inverse__inverse__eq,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_inverse__inverse__eq) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(fact_add__0,axiom,
! [X11,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X11) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_add__0) ).
fof(fact_inverse__1,axiom,
! [X10] :
( class_Rings_Odivision__ring(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_inverse__1) ).
fof(fact_less__le__not__le,axiom,
! [X14,X15,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
& ~ c_Orderings_Oord__class_Oless__eq(X10,X14,X15) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_less__le__not__le) ).
fof(fact_xt1_I6_J,axiom,
! [X26,X6,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X26,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X26,X6) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_xt1_I6_J) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(fact_less__imp__inverse__less,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X24),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_less__imp__inverse__less) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(fact_abs__real__def,axiom,
! [X11] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) = X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_abs__real__def) ).
fof(fact_less__eq__real__def,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
| X15 = X14 ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_less__eq__real__def) ).
fof(fact_norm__le__zero__iff,axiom,
! [X15,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X15 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_norm__le__zero__iff) ).
fof(fact_tw,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_tw) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Orderings_Oorder) ).
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/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_t_I2_J) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(fact_t_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_t_I1_J) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_no__zero__divisors,axiom,
! [X24,X11,X10] :
( class_Rings_Ono__zero__divisors(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> ( X24 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24) != c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_no__zero__divisors) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(fact_linorder__not__le,axiom,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
<=> c_Orderings_Oord__class_Oless(X10,X14,X15) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_linorder__not__le) ).
fof(fact_of__real__eq__0__iff,axiom,
! [X15,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> ( c_RealVector_Oof__real(X10,X15) = c_Groups_Ozero__class_Ozero(X10)
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_of__real__eq__0__iff) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(fact_w0,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_w0) ).
fof(conj_2,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',conj_2) ).
fof(fact_real__mult__assoc,axiom,
! [X29,X30,X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X31),X30)),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X29)),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_real__mult__assoc) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_zero__less__power,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',fact_zero__less__power) ).
fof(conj_1,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),v_m____),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',conj_1) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.8x9xmTQB9e/E---3.1_18176.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(c_0_37,plain,
! [X1252,X1253] :
( ~ class_Fields_Olinordered__field__inverse__zero(X1253)
| c_Groups_Oabs__class_Oabs(X1253,c_Rings_Oinverse__class_Oinverse(X1253,X1252)) = c_Rings_Oinverse__class_Oinverse(X1253,c_Groups_Oabs__class_Oabs(X1253,X1252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__inverse])]) ).
fof(c_0_38,plain,
! [X1013] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1013) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1013),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_39,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X6),
inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self]) ).
fof(c_0_40,plain,
! [X682,X683] :
( ( c_Rings_Oinverse__class_Oinverse(X683,X682) != c_Groups_Ozero__class_Ozero(X683)
| X682 = c_Groups_Ozero__class_Ozero(X683)
| ~ class_Rings_Odivision__ring__inverse__zero(X683) )
& ( X682 != c_Groups_Ozero__class_Ozero(X683)
| c_Rings_Oinverse__class_Oinverse(X683,X682) = c_Groups_Ozero__class_Ozero(X683)
| ~ class_Rings_Odivision__ring__inverse__zero(X683) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero])])]) ).
cnf(c_0_41,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oabs__class_Oabs(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c_0_43,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_38]) ).
fof(c_0_44,plain,
! [X636,X637] :
( ~ class_Rings_Odivision__ring__inverse__zero(X637)
| c_Rings_Oinverse__class_Oinverse(X637,c_Rings_Oinverse__class_Oinverse(X637,X636)) = X636 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])]) ).
fof(c_0_45,plain,
! [X1157] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1157),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1157),
inference(variable_rename,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_43]) ).
cnf(c_0_48,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]) ).
cnf(c_0_49,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_50,plain,
! [X1594,X1595] :
( ~ class_Groups_Ocomm__monoid__add(X1595)
| c_Groups_Oplus__class_Oplus(X1595,c_Groups_Ozero__class_Ozero(X1595),X1594) = X1594 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(c_0_51,plain,
! [X685] :
( ~ class_Rings_Odivision__ring(X685)
| c_Rings_Oinverse__class_Oinverse(X685,c_Groups_Oone__class_Oone(X685)) = c_Groups_Oone__class_Oone(X685) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__1])]) ).
fof(c_0_52,plain,
! [X14,X15,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
& ~ c_Orderings_Oord__class_Oless__eq(X10,X14,X15) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_53,plain,
! [X2270,X2271,X2272,X2273] :
( ~ class_Orderings_Oorder(X2273)
| ~ c_Orderings_Oord__class_Oless__eq(X2273,X2272,X2271)
| ~ c_Orderings_Oord__class_Oless__eq(X2273,X2270,X2272)
| c_Orderings_Oord__class_Oless__eq(X2273,X2270,X2271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
cnf(c_0_54,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_56,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_57,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
fof(c_0_59,plain,
! [X1269,X1270,X1271] :
( ~ class_Fields_Olinordered__field(X1271)
| ~ c_Orderings_Oord__class_Oless(X1271,X1270,X1269)
| ~ c_Orderings_Oord__class_Oless(X1271,c_Groups_Ozero__class_Ozero(X1271),X1270)
| c_Orderings_Oord__class_Oless(X1271,c_Rings_Oinverse__class_Oinverse(X1271,X1269),c_Rings_Oinverse__class_Oinverse(X1271,X1270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less])]) ).
cnf(c_0_60,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
fof(c_0_62,plain,
! [X11] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) = X11 ) ),
inference(fof_simplification,[status(thm)],[fact_abs__real__def]) ).
fof(c_0_63,plain,
! [X2362,X2363,X2364] :
( ( c_Orderings_Oord__class_Oless__eq(X2364,X2363,X2362)
| ~ c_Orderings_Oord__class_Oless(X2364,X2363,X2362)
| ~ class_Orderings_Opreorder(X2364) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2364,X2362,X2363)
| ~ c_Orderings_Oord__class_Oless(X2364,X2363,X2362)
| ~ class_Orderings_Opreorder(X2364) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2364,X2363,X2362)
| c_Orderings_Oord__class_Oless__eq(X2364,X2362,X2363)
| c_Orderings_Oord__class_Oless(X2364,X2363,X2362)
| ~ class_Orderings_Opreorder(X2364) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
fof(c_0_64,plain,
! [X201,X202] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X202,X201)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X202,X201)
| X202 = X201 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X202,X201)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X202,X201) )
& ( X202 != X201
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X202,X201) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(c_0_65,plain,
! [X127,X128] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X128,X127),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X127 = c_Groups_Ozero__class_Ozero(X128)
| ~ class_RealVector_Oreal__normed__vector(X128) )
& ( X127 != c_Groups_Ozero__class_Ozero(X128)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X128,X127),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X128) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
cnf(c_0_66,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_53]) ).
cnf(c_0_67,plain,
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)],[fact_tw]) ).
cnf(c_0_68,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(c_0_69,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),
inference(rw,[status(thm)],[c_0_54,c_0_43]) ).
cnf(c_0_70,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_71,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_72,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_73,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_74,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_75,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
cnf(c_0_76,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_77,plain,
! [X1155] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1155,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1155) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1155) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1155,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1155) = X1155 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])]) ).
cnf(c_0_78,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_63]) ).
cnf(c_0_79,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_64]) ).
cnf(c_0_80,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_81,plain,
! [X451,X452,X453] :
( ~ class_Rings_Ono__zero__divisors(X453)
| X452 = c_Groups_Ozero__class_Ozero(X453)
| X451 = c_Groups_Ozero__class_Ozero(X453)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X453),X452),X451) != c_Groups_Ozero__class_Ozero(X453) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
cnf(c_0_82,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_65]) ).
cnf(c_0_83,plain,
( 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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_84,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_85,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_86,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_75]),c_0_76])]) ).
cnf(c_0_87,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_88,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
fof(c_0_89,plain,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
<=> c_Orderings_Oord__class_Oless(X10,X14,X15) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(c_0_90,plain,
! [X253,X254] :
( ( c_RealVector_Oof__real(X254,X253) != c_Groups_Ozero__class_Ozero(X254)
| X253 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X254) )
& ( X253 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X254,X253) = c_Groups_Ozero__class_Ozero(X254)
| ~ class_RealVector_Oreal__algebra__1(X254) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__0__iff])])]) ).
cnf(c_0_91,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_92,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
cnf(c_0_93,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
cnf(c_0_94,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_w0]) ).
cnf(c_0_95,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,v_t____) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_96,plain,
( c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[c_0_87,c_0_43]) ).
cnf(c_0_97,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_88,c_0_76]) ).
fof(c_0_98,plain,
! [X2353,X2354,X2355] :
( ( c_Orderings_Oord__class_Oless__eq(X2355,X2354,X2353)
| c_Orderings_Oord__class_Oless(X2355,X2353,X2354)
| ~ class_Orderings_Olinorder(X2355) )
& ( ~ c_Orderings_Oord__class_Oless(X2355,X2353,X2354)
| ~ c_Orderings_Oord__class_Oless__eq(X2355,X2354,X2353)
| ~ class_Orderings_Olinorder(X2355) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])])]) ).
fof(c_0_99,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_2])]) ).
fof(c_0_100,plain,
! [X170,X171,X172] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X172),X171)),X170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X171),X170)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
cnf(c_0_101,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_102,plain,
( c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]),c_0_94]) ).
cnf(c_0_103,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__algebra__1]) ).
cnf(c_0_104,plain,
v_t____ != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_105,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_106,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_107,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_108,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_109,plain,
! [X114,X115,X116] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X116),X115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X116),X114))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X115,X114)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X116) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X115,X114)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X116),X115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X116),X114))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).
cnf(c_0_110,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103])]),c_0_104]) ).
cnf(c_0_111,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),v_m____))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_108]) ).
cnf(c_0_113,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_114,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
fof(c_0_115,plain,
! [X219,X220,X221] :
( ~ class_Rings_Olinordered__semidom(X221)
| ~ c_Orderings_Oord__class_Oless(X221,c_Groups_Ozero__class_Ozero(X221),X220)
| c_Orderings_Oord__class_Oless(X221,c_Groups_Ozero__class_Ozero(X221),hAPP(hAPP(c_Power_Opower__class_Opower(X221),X220),X219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
cnf(c_0_116,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),v_m____)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114])]) ).
cnf(c_0_117,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),v_m____),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_118,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_119,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c_0_120,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_113]),c_0_117])]) ).
cnf(c_0_121,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_114])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.25 % Problem : SWW265+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.26 % Command : run_E %s %d THM
% 0.26/0.48 % Computer : n011.cluster.edu
% 0.26/0.48 % Model : x86_64 x86_64
% 0.26/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.48 % Memory : 8042.1875MB
% 0.26/0.48 % OS : Linux 3.10.0-693.el7.x86_64
% 0.26/0.48 % CPULimit : 2400
% 0.26/0.48 % WCLimit : 300
% 0.26/0.48 % DateTime : Mon Oct 2 22:22:53 EDT 2023
% 0.26/0.48 % CPUTime :
% 0.46/0.76 Running first-order theorem proving
% 0.46/0.76 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.8x9xmTQB9e/E---3.1_18176.p
% 421.45/53.97 # Version: 3.1pre001
% 421.45/53.97 # Preprocessing class: FMLMSMSMSSSNFFN.
% 421.45/53.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 421.45/53.97 # Starting new_bool_3 with 300s (1) cores
% 421.45/53.97 # Starting new_bool_1 with 300s (1) cores
% 421.45/53.97 # Starting sh5l with 300s (1) cores
% 421.45/53.97 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 18254 completed with status 0
% 421.45/53.97 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 421.45/53.97 # Preprocessing class: FMLMSMSMSSSNFFN.
% 421.45/53.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 421.45/53.97 # No SInE strategy applied
% 421.45/53.97 # Search class: FGHSM-SSLM32-DFFFFFNN
% 421.45/53.97 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 421.45/53.97 # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 421.45/53.97 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 421.45/53.97 # G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 18265 completed with status 0
% 421.45/53.97 # Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 421.45/53.97 # Preprocessing class: FMLMSMSMSSSNFFN.
% 421.45/53.97 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 421.45/53.97 # No SInE strategy applied
% 421.45/53.97 # Search class: FGHSM-SSLM32-DFFFFFNN
% 421.45/53.97 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 421.45/53.97 # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 421.45/53.97 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 421.45/53.97 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 421.45/53.97 # Preprocessing time : 0.022 s
% 421.45/53.97 # Presaturation interreduction done
% 421.45/53.97
% 421.45/53.97 # Proof found!
% 421.45/53.97 # SZS status Theorem
% 421.45/53.97 # SZS output start CNFRefutation
% See solution above
% 421.45/53.97 # Parsed axioms : 1290
% 421.45/53.97 # Removed by relevancy pruning/SinE : 0
% 421.45/53.97 # Initial clauses : 1648
% 421.45/53.97 # Removed in clause preprocessing : 45
% 421.45/53.97 # Initial clauses in saturation : 1603
% 421.45/53.97 # Processed clauses : 141026
% 421.45/53.97 # ...of these trivial : 3250
% 421.45/53.97 # ...subsumed : 115520
% 421.45/53.97 # ...remaining for further processing : 22256
% 421.45/53.97 # Other redundant clauses eliminated : 3892
% 421.45/53.97 # Clauses deleted for lack of memory : 0
% 421.45/53.97 # Backward-subsumed : 1485
% 421.45/53.97 # Backward-rewritten : 2886
% 421.45/53.97 # Generated clauses : 1221590
% 421.45/53.97 # ...of the previous two non-redundant : 1113031
% 421.45/53.97 # ...aggressively subsumed : 0
% 421.45/53.97 # Contextual simplify-reflections : 176
% 421.45/53.97 # Paramodulations : 1217547
% 421.45/53.97 # Factorizations : 12
% 421.45/53.97 # NegExts : 0
% 421.45/53.97 # Equation resolutions : 4040
% 421.45/53.97 # Total rewrite steps : 991925
% 421.45/53.97 # Propositional unsat checks : 4
% 421.45/53.97 # Propositional check models : 0
% 421.45/53.97 # Propositional check unsatisfiable : 0
% 421.45/53.97 # Propositional clauses : 0
% 421.45/53.97 # Propositional clauses after purity: 0
% 421.45/53.97 # Propositional unsat core size : 0
% 421.45/53.97 # Propositional preprocessing time : 0.000
% 421.45/53.97 # Propositional encoding time : 2.661
% 421.45/53.97 # Propositional solver time : 1.657
% 421.45/53.97 # Success case prop preproc time : 0.000
% 421.45/53.97 # Success case prop encoding time : 0.000
% 421.45/53.97 # Success case prop solver time : 0.000
% 421.45/53.97 # Current number of processed clauses : 16393
% 421.45/53.97 # Positive orientable unit clauses : 2101
% 421.45/53.97 # Positive unorientable unit clauses: 92
% 421.45/53.97 # Negative unit clauses : 2658
% 421.45/53.97 # Non-unit-clauses : 11542
% 421.45/53.97 # Current number of unprocessed clauses: 958599
% 421.45/53.97 # ...number of literals in the above : 2545101
% 421.45/53.97 # Current number of archived formulas : 0
% 421.45/53.97 # Current number of archived clauses : 5747
% 421.45/53.97 # Clause-clause subsumption calls (NU) : 18851538
% 421.45/53.97 # Rec. Clause-clause subsumption calls : 11544171
% 421.45/53.97 # Non-unit clause-clause subsumptions : 46975
% 421.45/53.97 # Unit Clause-clause subsumption calls : 1351942
% 421.45/53.97 # Rewrite failures with RHS unbound : 5
% 421.45/53.97 # BW rewrite match attempts : 147675
% 421.45/53.97 # BW rewrite match successes : 1946
% 421.45/53.97 # Condensation attempts : 0
% 421.45/53.97 # Condensation successes : 0
% 421.45/53.97 # Termbank termtop insertions : 34842377
% 421.45/53.97
% 421.45/53.97 # -------------------------------------------------
% 421.45/53.97 # User time : 51.694 s
% 421.45/53.97 # System time : 0.950 s
% 421.45/53.97 # Total time : 52.644 s
% 421.45/53.97 # Maximum resident set size: 8096 pages
% 421.45/53.97
% 421.45/53.97 # -------------------------------------------------
% 421.45/53.97 # User time : 257.134 s
% 421.45/53.97 # System time : 4.405 s
% 421.45/53.97 # Total time : 261.538 s
% 421.45/53.97 # Maximum resident set size: 3124 pages
% 421.45/53.97 % E---3.1 exiting
% 421.45/53.97 % E---3.1 exiting
%------------------------------------------------------------------------------