TSTP Solution File: SWW227+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWW227+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 20:08:51 EDT 2023
% Result : Theorem 253.28s 33.03s
% Output : CNFRefutation 253.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 155 ( 114 unt; 0 def)
% Number of atoms : 278 ( 106 equ)
% Maximal formula atoms : 62 ( 1 avg)
% Number of connectives : 206 ( 83 ~; 84 |; 16 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 10 con; 0-3 aty)
% Number of variables : 174 ( 5 sgn; 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_add__0,axiom,
! [X11,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X11) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_add__0) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls) ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_semiring__norm_I112_J) ).
fof(fact_real__diff__def,axiom,
! [X33,X27] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X27,X33) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X27,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X33)),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_real__diff__def) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(fact_one__add__one__is__two,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_one__add__one__is__two) ).
fof(fact_Bit0__def,axiom,
! [X10] : c_Int_OBit0(X10) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X10),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X10] : c_Int_OBit1(X10) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10),X10),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_Bit1__def) ).
fof(fact_real__of__nat__Suc,axiom,
! [X38] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X38)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X38),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_real__of__nat__Suc) ).
fof(fact_Suc__eq__plus1,axiom,
! [X38] : c_Nat_OSuc(X38) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_Suc__eq__plus1) ).
fof(fact_add__Pls,axiom,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X10) = X10,
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_add__Pls) ).
fof(fact_diff__int__def,axiom,
! [X4,X12] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X12,X4) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4)),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_diff__int__def) ).
fof(fact_number__of__diff,axiom,
! [X4,X5,X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Onumber__class_Onumber__of(X3,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5,X4)) = c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,X5),c_Int_Onumber__class_Onumber__of(X3,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_number__of__diff) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(fact_add__Pls__right,axiom,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Int_OPls) = X10,
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_add__Pls__right) ).
fof(fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096) ).
fof(fact_abs__minus__add__cancel,axiom,
! [X13,X14] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X14))),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_abs__minus__add__cancel) ).
fof(fact_real__norm__def,axiom,
! [X27] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X27) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X27),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_real__norm__def) ).
fof(fact_nat__add__commute,axiom,
! [X38,X37] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X38) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_nat__add__commute) ).
fof(fact_arith__simps_I30_J,axiom,
! [X4,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Ouminus__class_Ouminus(X3,c_Int_Onumber__class_Onumber__of(X3,X4)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_arith__simps_I30_J) ).
fof(fact_minus__minus,axiom,
! [X11,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Ouminus__class_Ouminus(X3,c_Groups_Ouminus__class_Ouminus(X3,X11)) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_minus__minus) ).
fof(fact_zminus__zminus,axiom,
! [X12] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X12)) = X12,
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_zminus__zminus) ).
fof(fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',conj_0) ).
fof(fact_real__of__nat__add,axiom,
! [X38,X37] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X38)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X37),c_RealDef_Oreal(tc_Nat_Onat,X38)),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_real__of__nat__add) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_real__mult__1,axiom,
! [X12] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X12) = X12,
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_real__mult__1) ).
fof(fact_real__divide__def,axiom,
! [X62,X63] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X63,X62) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X63,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X62)),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_real__divide__def) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_real__of__nat__1) ).
fof(fact_inverse__inverse__eq,axiom,
! [X11,X3] :
( class_Rings_Odivision__ring__inverse__zero(X3)
=> c_Rings_Oinverse__class_Oinverse(X3,c_Rings_Oinverse__class_Oinverse(X3,X11)) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_inverse__inverse__eq) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [X14] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14)) = c_RealDef_Oreal(tc_Nat_Onat,X14),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_abs__real__of__nat__cancel) ).
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.AhVqSPU3LR/E---3.1_28533.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(fact_inverse__divide,axiom,
! [X29,X11,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> c_Rings_Oinverse__class_Oinverse(X3,c_Rings_Oinverse__class_Odivide(X3,X11,X29)) = c_Rings_Oinverse__class_Odivide(X3,X29,X11) ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_inverse__divide) ).
fof(fact_zadd__commute,axiom,
! [X4,X12] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X4) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X12),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_zadd__commute) ).
fof(fact_mult_Ozero__right,axiom,
! [X11,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,X11,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_mult_Ozero__right) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X14] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X14))),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_abs__add__one__gt__zero) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(fact_less__divide__eq,axiom,
! [X58,X43,X26,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X26,c_Rings_Oinverse__class_Odivide(X3,X43,X58))
<=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X58)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X26,X58),X43) )
& ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X58)
=> ( ( c_Orderings_Oord__class_Oless(X3,X58,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,X43,c_Groups_Otimes__class_Otimes(X3,X26,X58)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X58,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,X26,c_Groups_Ozero__class_Ozero(X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_less__divide__eq) ).
fof(fact_real__mult__commute,axiom,
! [X4,X12] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X4) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4,X12),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_real__mult__commute) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(fact_e,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
file('/export/starexec/sandbox2/tmp/tmp.AhVqSPU3LR/E---3.1_28533.p',fact_e) ).
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.AhVqSPU3LR/E---3.1_28533.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(c_0_41,plain,
! [X2226,X2227] :
( ~ class_Groups_Ocomm__monoid__add(X2227)
| c_Groups_Oplus__class_Oplus(X2227,c_Groups_Ozero__class_Ozero(X2227),X2226) = X2226 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(c_0_42,plain,
! [X1318] :
( ~ class_Int_Onumber__ring(X1318)
| c_Groups_Ozero__class_Ozero(X1318) = c_Int_Onumber__class_Onumber__of(X1318,c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
fof(c_0_43,plain,
! [X426,X427] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X427,X426) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X427,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X426)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
cnf(c_0_44,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_41]) ).
cnf(c_0_45,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
fof(c_0_46,plain,
! [X93] :
( ~ class_Int_Onumber__ring(X93)
| c_Groups_Oplus__class_Oplus(X93,c_Groups_Oone__class_Oone(X93),c_Groups_Oone__class_Oone(X93)) = c_Int_Onumber__class_Onumber__of(X93,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two])]) ).
fof(c_0_47,plain,
! [X138] : c_Int_OBit0(X138) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X138,X138),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_48,plain,
! [X108] : c_Int_OBit1(X108) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X108),X108),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_49,plain,
! [X441] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X441)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X441),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(c_0_50,plain,
! [X1330] : c_Nat_OSuc(X1330) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1330,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_51,plain,
! [X135] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X135) = X135,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(c_0_52,plain,
! [X309,X310] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X310,X309) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X310,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X309)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(c_0_53,plain,
! [X213,X214,X215] :
( ~ class_Int_Onumber__ring(X215)
| c_Int_Onumber__class_Onumber__of(X215,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X214,X213)) = c_Groups_Ominus__class_Ominus(X215,c_Int_Onumber__class_Onumber__of(X215,X214),c_Int_Onumber__class_Onumber__of(X215,X213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).
cnf(c_0_54,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_55,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
cnf(c_0_56,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_57,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_44,c_0_45]) ).
cnf(c_0_58,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_61,plain,
! [X134] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X134,c_Int_OPls) = X134,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_62,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ),
inference(fof_nnf,[status(thm)],[fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096]) ).
fof(c_0_63,plain,
! [X430,X431] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X431,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X430))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X430,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X431))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(c_0_64,plain,
! [X149] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X149) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X149),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
cnf(c_0_65,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_66,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_67,plain,
! [X912,X913] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X913,X912) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X912,X913),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(c_0_68,plain,
! [X218,X219] :
( ~ class_Int_Onumber__ring(X219)
| c_Groups_Ouminus__class_Ouminus(X219,c_Int_Onumber__class_Onumber__of(X219,X218)) = c_Int_Onumber__class_Onumber__of(X219,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X218)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).
cnf(c_0_69,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_70,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_71,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_72,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_73,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_74,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_60]) ).
cnf(c_0_75,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_76,plain,
! [X2216,X2217] :
( ~ class_Groups_Ogroup__add(X2217)
| c_Groups_Ouminus__class_Ouminus(X2217,c_Groups_Ouminus__class_Ouminus(X2217,X2216)) = X2216 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(c_0_77,plain,
! [X292] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X292)) = X292,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
cnf(c_0_78,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(split_conjunct,[status(thm)],[fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096]) ).
fof(c_0_79,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_80,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_81,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_82,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_64]) ).
fof(c_0_83,plain,
! [X424,X425] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X425,X424)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X425),c_RealDef_Oreal(tc_Nat_Onat,X424)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).
cnf(c_0_84,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_85,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_86,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_87,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_88,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_55])]) ).
cnf(c_0_89,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75]),c_0_75]),c_0_75]),c_0_75]) ).
cnf(c_0_90,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_91,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(c_0_92,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_93,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_59]),c_0_66]),c_0_60]),c_0_60]) ).
cnf(c_0_94,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
fof(c_0_95,plain,
! [X609] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X609) = X609,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_96,plain,
! [X672,X673] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X673,X672) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X673,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X672)),
inference(variable_rename,[status(thm)],[fact_real__divide__def]) ).
cnf(c_0_97,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_59]),c_0_59]),c_0_59]),c_0_66]),c_0_66]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]) ).
cnf(c_0_98,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_56]),c_0_82]),c_0_56]),c_0_82]) ).
cnf(c_0_99,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_100,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__1]) ).
cnf(c_0_101,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_102,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_103,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_55])]) ).
cnf(c_0_104,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_105,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_87]),c_0_87]) ).
cnf(c_0_106,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_75]),c_0_75]),c_0_75]),c_0_75]),c_0_82]),c_0_84]) ).
fof(c_0_107,plain,
! [X1417,X1418] :
( ~ class_Rings_Odivision__ring__inverse__zero(X1418)
| c_Rings_Oinverse__class_Oinverse(X1418,c_Rings_Oinverse__class_Oinverse(X1418,X1417)) = X1417 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])]) ).
cnf(c_0_108,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_59]),c_0_66]),c_0_60]),c_0_60]) ).
cnf(c_0_109,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_110,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
fof(c_0_111,plain,
! [X415] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X415)) = c_RealDef_Oreal(tc_Nat_Onat,X415),
inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
cnf(c_0_112,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_84]),c_0_75]),c_0_75]),c_0_75]),c_0_75]),c_0_82]),c_0_98]),c_0_75]),c_0_75]),c_0_75]),c_0_75]),c_0_82]),c_0_98]),c_0_75]),c_0_75]),c_0_75]),c_0_75]),c_0_82]),c_0_98]),c_0_84]) ).
cnf(c_0_113,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_114,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_105]),c_0_55])]) ).
cnf(c_0_115,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rw,[status(thm)],[c_0_106,c_0_98]) ).
cnf(c_0_116,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_107]) ).
cnf(c_0_117,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]) ).
fof(c_0_118,plain,
! [X1890,X1891,X1892] :
( ~ class_Fields_Ofield__inverse__zero(X1892)
| c_Rings_Oinverse__class_Oinverse(X1892,c_Rings_Oinverse__class_Odivide(X1892,X1891,X1890)) = c_Rings_Oinverse__class_Odivide(X1892,X1890,X1891) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__divide])]) ).
cnf(c_0_119,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_84]),c_0_82]),c_0_75]),c_0_75]),c_0_75]),c_0_75]) ).
cnf(c_0_120,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
fof(c_0_121,plain,
! [X111,X112] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X112,X111) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X111,X112),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(c_0_122,plain,
! [X536,X537] :
( ~ class_RealVector_Oreal__normed__algebra(X537)
| c_Groups_Otimes__class_Otimes(X537,X536,c_Groups_Ozero__class_Ozero(X537)) = c_Groups_Ozero__class_Ozero(X537) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(c_0_123,plain,
! [X283] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X283))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
cnf(c_0_124,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_RealDef_Oreal(tc_Nat_Onat,X1),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_125,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113]),c_0_114]),c_0_114]),c_0_113]),c_0_114]) ).
cnf(c_0_126,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_113]),c_0_114]) ).
cnf(c_0_127,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_116,c_0_117]) ).
cnf(c_0_128,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_129,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
cnf(c_0_130,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120]),c_0_98]) ).
cnf(c_0_131,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
fof(c_0_132,plain,
! [X58,X43,X26,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X26,c_Rings_Oinverse__class_Odivide(X3,X43,X58))
<=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X58)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X26,X58),X43) )
& ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X58)
=> ( ( c_Orderings_Oord__class_Oless(X3,X58,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,X43,c_Groups_Otimes__class_Otimes(X3,X26,X58)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X58,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,X26,c_Groups_Ozero__class_Ozero(X3)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).
fof(c_0_133,plain,
! [X499,X500] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X500,X499) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X499,X500),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_134,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_135,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(c_0_136,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_137,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_RealDef_Oreal(tc_Nat_Onat,X1),
inference(rw,[status(thm)],[c_0_124,c_0_82]) ).
cnf(c_0_138,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
inference(split_conjunct,[status(thm)],[fact_e]) ).
cnf(c_0_139,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126])]) ).
cnf(c_0_140,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129])]) ).
cnf(c_0_141,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_113]),c_0_114]) ).
fof(c_0_142,plain,
! [X2019,X2020,X2021,X2022] :
( ( ~ c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| c_Orderings_Oord__class_Oless(X2022,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019),X2020)
| ~ c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,X2020,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019))
| c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| ~ c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| ~ c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2021,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| ~ c_Orderings_Oord__class_Oless(X2022,X2020,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019))
| c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2021,c_Groups_Ozero__class_Ozero(X2022))
| ~ c_Orderings_Oord__class_Oless(X2022,X2020,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019))
| c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,c_Groups_Ozero__class_Ozero(X2022),X2019)
| ~ c_Orderings_Oord__class_Oless(X2022,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019),X2020)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| ~ c_Orderings_Oord__class_Oless(X2022,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019),X2020)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2021,c_Groups_Ozero__class_Ozero(X2022))
| c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| ~ c_Orderings_Oord__class_Oless(X2022,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019),X2020)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2019,c_Groups_Ozero__class_Ozero(X2022))
| ~ c_Orderings_Oord__class_Oless(X2022,X2020,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019))
| ~ c_Orderings_Oord__class_Oless(X2022,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019),X2020)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) )
& ( ~ c_Orderings_Oord__class_Oless(X2022,X2021,c_Groups_Ozero__class_Ozero(X2022))
| ~ c_Orderings_Oord__class_Oless(X2022,X2020,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019))
| ~ c_Orderings_Oord__class_Oless(X2022,c_Groups_Otimes__class_Otimes(X2022,X2021,X2019),X2020)
| c_Orderings_Oord__class_Oless(X2022,X2021,c_Rings_Oinverse__class_Odivide(X2022,X2020,X2019))
| ~ class_Fields_Olinordered__field__inverse__zero(X2022) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])])]) ).
cnf(c_0_143,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_144,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_145,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1))),
inference(rw,[status(thm)],[c_0_136,c_0_82]) ).
cnf(c_0_146,plain,
c_RealVector_Onorm__class_Onorm(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_137,c_0_100]) ).
cnf(c_0_147,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
inference(rw,[status(thm)],[c_0_138,c_0_82]) ).
cnf(c_0_148,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_141]) ).
cnf(c_0_149,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_150,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_151,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_152,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(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_145,c_0_146]) ).
cnf(c_0_153,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(rw,[status(thm)],[c_0_147,c_0_98]) ).
cnf(c_0_154,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_150]),c_0_151]),c_0_152]),c_0_153])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.21 % Problem : SWW227+1 : TPTP v8.1.2. Released v5.2.0.
% 0.21/0.21 % Command : run_E %s %d THM
% 0.21/0.42 % Computer : n013.cluster.edu
% 0.21/0.42 % Model : x86_64 x86_64
% 0.21/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.42 % Memory : 8042.1875MB
% 0.21/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.42 % CPULimit : 2400
% 0.21/0.42 % WCLimit : 300
% 0.21/0.42 % DateTime : Mon Oct 2 22:04:59 EDT 2023
% 0.21/0.42 % CPUTime :
% 0.26/0.63 Running first-order theorem proving
% 0.26/0.63 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.AhVqSPU3LR/E---3.1_28533.p
% 253.28/33.03 # Version: 3.1pre001
% 253.28/33.03 # Preprocessing class: FMLSSMSMSSSNFFN.
% 253.28/33.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 253.28/33.03 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 253.28/33.03 # Starting new_bool_3 with 600s (2) cores
% 253.28/33.03 # Starting new_bool_1 with 600s (2) cores
% 253.28/33.03 # Starting sh5l with 300s (1) cores
% 253.28/33.03 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 28659 completed with status 0
% 253.28/33.03 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 253.28/33.03 # Preprocessing class: FMLSSMSMSSSNFFN.
% 253.28/33.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 253.28/33.03 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 253.28/33.03 # No SInE strategy applied
% 253.28/33.03 # Search class: FGHSM-SMLM31-DFFFFFNN
% 253.28/33.03 # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 253.28/33.03 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 520s (1) cores
% 253.28/33.03 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 253.28/33.03 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 82s (1) cores
% 253.28/33.03 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 28669 completed with status 0
% 253.28/33.03 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 253.28/33.03 # Preprocessing class: FMLSSMSMSSSNFFN.
% 253.28/33.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 253.28/33.03 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 253.28/33.03 # No SInE strategy applied
% 253.28/33.03 # Search class: FGHSM-SMLM31-DFFFFFNN
% 253.28/33.03 # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 253.28/33.03 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 520s (1) cores
% 253.28/33.03 # Preprocessing time : 0.022 s
% 253.28/33.03 # Presaturation interreduction done
% 253.28/33.03
% 253.28/33.03 # Proof found!
% 253.28/33.03 # SZS status Theorem
% 253.28/33.03 # SZS output start CNFRefutation
% See solution above
% 253.28/33.03 # Parsed axioms : 1171
% 253.28/33.03 # Removed by relevancy pruning/SinE : 0
% 253.28/33.03 # Initial clauses : 1749
% 253.28/33.03 # Removed in clause preprocessing : 79
% 253.28/33.03 # Initial clauses in saturation : 1670
% 253.28/33.03 # Processed clauses : 82792
% 253.28/33.03 # ...of these trivial : 1158
% 253.28/33.03 # ...subsumed : 68226
% 253.28/33.03 # ...remaining for further processing : 13408
% 253.28/33.03 # Other redundant clauses eliminated : 5895
% 253.28/33.03 # Clauses deleted for lack of memory : 0
% 253.28/33.03 # Backward-subsumed : 707
% 253.28/33.03 # Backward-rewritten : 342
% 253.28/33.03 # Generated clauses : 1095094
% 253.28/33.03 # ...of the previous two non-redundant : 1031614
% 253.28/33.03 # ...aggressively subsumed : 0
% 253.28/33.03 # Contextual simplify-reflections : 97
% 253.28/33.03 # Paramodulations : 1089142
% 253.28/33.03 # Factorizations : 24
% 253.28/33.03 # NegExts : 0
% 253.28/33.03 # Equation resolutions : 5946
% 253.28/33.03 # Total rewrite steps : 1386497
% 253.28/33.03 # Propositional unsat checks : 2
% 253.28/33.03 # Propositional check models : 0
% 253.28/33.03 # Propositional check unsatisfiable : 0
% 253.28/33.03 # Propositional clauses : 0
% 253.28/33.03 # Propositional clauses after purity: 0
% 253.28/33.03 # Propositional unsat core size : 0
% 253.28/33.03 # Propositional preprocessing time : 0.000
% 253.28/33.03 # Propositional encoding time : 2.187
% 253.28/33.03 # Propositional solver time : 0.932
% 253.28/33.03 # Success case prop preproc time : 0.000
% 253.28/33.03 # Success case prop encoding time : 0.000
% 253.28/33.03 # Success case prop solver time : 0.000
% 253.28/33.03 # Current number of processed clauses : 10949
% 253.28/33.03 # Positive orientable unit clauses : 1117
% 253.28/33.03 # Positive unorientable unit clauses: 201
% 253.28/33.03 # Negative unit clauses : 2248
% 253.28/33.03 # Non-unit-clauses : 7383
% 253.28/33.03 # Current number of unprocessed clauses: 949810
% 253.28/33.03 # ...number of literals in the above : 2115821
% 253.28/33.03 # Current number of archived formulas : 0
% 253.28/33.03 # Current number of archived clauses : 2333
% 253.28/33.03 # Clause-clause subsumption calls (NU) : 4738327
% 253.28/33.03 # Rec. Clause-clause subsumption calls : 3035718
% 253.28/33.03 # Non-unit clause-clause subsumptions : 23244
% 253.28/33.03 # Unit Clause-clause subsumption calls : 765740
% 253.28/33.03 # Rewrite failures with RHS unbound : 0
% 253.28/33.03 # BW rewrite match attempts : 75918
% 253.28/33.03 # BW rewrite match successes : 1531
% 253.28/33.03 # Condensation attempts : 0
% 253.28/33.03 # Condensation successes : 0
% 253.28/33.03 # Termbank termtop insertions : 36651197
% 253.28/33.03
% 253.28/33.03 # -------------------------------------------------
% 253.28/33.03 # User time : 30.790 s
% 253.28/33.03 # System time : 0.823 s
% 253.28/33.03 # Total time : 31.612 s
% 253.28/33.03 # Maximum resident set size: 7912 pages
% 253.28/33.03
% 253.28/33.03 # -------------------------------------------------
% 253.28/33.03 # User time : 89.858 s
% 253.28/33.03 # System time : 2.438 s
% 253.28/33.03 # Total time : 92.296 s
% 253.28/33.03 # Maximum resident set size: 3064 pages
% 253.28/33.03 % E---3.1 exiting
% 253.28/33.04 % E---3.1 exiting
%------------------------------------------------------------------------------