TSTP Solution File: SWW222+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWW222+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.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 20:08:50 EDT 2023
% Result : Theorem 48.81s 6.85s
% Output : CNFRefutation 48.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 130 ( 77 unt; 0 def)
% Number of atoms : 204 ( 84 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 134 ( 60 ~; 54 |; 4 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 132 ( 0 sgn; 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',conj_0) ).
fof(fact_Bit0__def,axiom,
! [X16] : c_Int_OBit0(X16) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X16),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X16] : c_Int_OBit1(X16) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16),X16),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_Bit1__def) ).
fof(fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096,axiom,
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).
fof(fact_add__Pls__right,axiom,
! [X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Int_OPls) = X16,
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_add__Pls__right) ).
fof(fact_complex__diff__def,axiom,
! [X23,X9] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X9,X23) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X9,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X23)),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_complex__diff__def) ).
fof(fact_minus__real__def,axiom,
! [X23,X9] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X9,X23) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23)),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_minus__real__def) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X7] :
( class_Int_Onumber__ring(X7)
=> c_Groups_Ozero__class_Ozero(X7) = c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_semiring__norm_I112_J) ).
fof(fact_w,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_w) ).
fof(fact_zero__less__norm__iff,axiom,
! [X15,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X15))
<=> X15 != c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_zero__less__norm__iff) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X8,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X8) = X8 ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(fact_diff__add__cancel,axiom,
! [X10,X8,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X8,X10),X10) = X8 ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_diff__add__cancel) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X31,X8,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,X8,X31) = c_Groups_Oplus__class_Oplus(X7,X31,X8) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_add__diff__cancel,axiom,
! [X10,X8,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X8,X10),X10) = X8 ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_add__diff__cancel) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(fact_add__special_I2_J,axiom,
! [X6,X7] :
( class_Int_Onumber__ring(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Int_Onumber__class_Onumber__of(X7,X6)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X6)) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_add__special_I2_J) ).
fof(fact_semiring__norm_I110_J,axiom,
! [X7] :
( class_Int_Onumber__ring(X7)
=> c_Groups_Oone__class_Oone(X7) = c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_semiring__norm_I110_J) ).
fof(fact_one__add__one__is__two,axiom,
! [X7] :
( class_Int_Onumber__ring(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7)) = c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_one__add__one__is__two) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(fact_real__sum__of__halves,axiom,
! [X9] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X9,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X9,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X9,
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_real__sum__of__halves) ).
fof(fact_minus__minus,axiom,
! [X8,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ouminus__class_Ouminus(X7,X8)) = X8 ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_minus__minus) ).
fof(fact_norm__number__of,axiom,
! [X6,X7] :
( ( class_Int_Onumber__ring(X7)
& class_RealVector_Oreal__normed__algebra__1(X7) )
=> c_RealVector_Onorm__class_Onorm(X7,c_Int_Onumber__class_Onumber__of(X7,X6)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X6)) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_norm__number__of) ).
fof(fact_abs__zero,axiom,
! [X7] :
( class_Groups_Oordered__ab__group__add__abs(X7)
=> c_Groups_Oabs__class_Oabs(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_abs__zero) ).
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,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_e) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X12,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X12,X12))
<=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X12) ) ),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(c_0_33,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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])]) ).
fof(c_0_34,plain,
! [X1108] : c_Int_OBit0(X1108) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1108,X1108),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_35,plain,
! [X1102] : c_Int_OBit1(X1102) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1102),X1102),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_36,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,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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_nnf,[status(thm)],[fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096]) ).
cnf(c_0_37,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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_33]) ).
cnf(c_0_38,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,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_35]) ).
fof(c_0_40,plain,
! [X1107] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1107,c_Int_OPls) = X1107,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
cnf(c_0_41,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_42,plain,
! [X1525,X1526] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1526,X1525) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1526,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1525)),
inference(variable_rename,[status(thm)],[fact_complex__diff__def]) ).
fof(c_0_43,plain,
! [X793,X794] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X794,X793) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X794,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X793)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_44,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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)],[c_0_37,c_0_38]),c_0_39]),c_0_39]) ).
cnf(c_0_45,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_46,plain,
! [X250] :
( ~ class_Int_Onumber__ring(X250)
| c_Groups_Ozero__class_Ozero(X250) = c_Int_Onumber__class_Onumber__of(X250,c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
cnf(c_0_47,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_38]),c_0_39]),c_0_39]) ).
cnf(c_0_48,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,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_50,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____)),v_d____),
inference(split_conjunct,[status(thm)],[fact_w]) ).
cnf(c_0_51,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),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,hAPP(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)],[c_0_44,c_0_45]),c_0_45]),c_0_45]),c_0_45]) ).
fof(c_0_52,plain,
! [X139,X140] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X140,X139))
| X139 != c_Groups_Ozero__class_Ozero(X140)
| ~ class_RealVector_Oreal__normed__vector(X140) )
& ( X139 = c_Groups_Ozero__class_Ozero(X140)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X140,X139))
| ~ class_RealVector_Oreal__normed__vector(X140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
cnf(c_0_53,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_46]) ).
cnf(c_0_54,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(c_0_55,plain,
! [X1379,X1380] :
( ~ class_Rings_Ocomm__semiring__1(X1380)
| c_Groups_Oplus__class_Oplus(X1380,c_Groups_Ozero__class_Ozero(X1380),X1379) = X1379 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
cnf(c_0_56,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]) ).
fof(c_0_57,plain,
! [X618,X619,X620] :
( ~ class_Groups_Ogroup__add(X620)
| c_Groups_Oplus__class_Oplus(X620,c_Groups_Ominus__class_Ominus(X620,X619,X618),X618) = X619 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(c_0_58,plain,
! [X1289,X1290,X1291] :
( ~ class_Rings_Ocomm__semiring__1(X1291)
| c_Groups_Oplus__class_Oplus(X1291,X1290,X1289) = c_Groups_Oplus__class_Oplus(X1291,X1289,X1290) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(c_0_59,plain,
! [X615,X616,X617] :
( ~ class_Groups_Ogroup__add(X617)
| c_Groups_Ominus__class_Ominus(X617,c_Groups_Oplus__class_Oplus(X617,X616,X615),X615) = X616 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
cnf(c_0_60,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,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)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_wa____,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_wa____,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z____))),v_d____) ),
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_47,c_0_48]),c_0_49]),c_0_45]),c_0_45]),c_0_45]),c_0_45]),c_0_48]),c_0_48]) ).
cnf(c_0_61,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_wa____,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z____))),v_d____),
inference(rw,[status(thm)],[c_0_50,c_0_48]) ).
cnf(c_0_62,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_wa____),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,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)],[c_0_51,c_0_48]),c_0_49]) ).
cnf(c_0_63,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(c_0_67,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls),
inference(spm,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_68,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(c_0_70,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_71,plain,
! [X521,X522] :
( ~ class_Int_Onumber__ring(X522)
| c_Groups_Oplus__class_Oplus(X522,c_Groups_Oone__class_Oone(X522),c_Int_Onumber__class_Onumber__of(X522,X521)) = c_Int_Onumber__class_Onumber__of(X522,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X521)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).
fof(c_0_72,plain,
! [X833] :
( ~ class_Int_Onumber__ring(X833)
| c_Groups_Oone__class_Oone(X833) = c_Int_Onumber__class_Onumber__of(X833,c_Int_OBit1(c_Int_OPls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).
fof(c_0_73,plain,
! [X681] :
( ~ class_Int_Onumber__ring(X681)
| c_Groups_Oplus__class_Oplus(X681,c_Groups_Oone__class_Oone(X681),c_Groups_Oone__class_Oone(X681)) = c_Int_Onumber__class_Onumber__of(X681,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])]) ).
cnf(c_0_74,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_75,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,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_wa____,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z____)))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]),c_0_62]) ).
cnf(c_0_76,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_RealVector_Onorm__class_Onorm(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_77,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_78,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_79,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_80,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1),
inference(spm,[status(thm)],[c_0_70,c_0_66]) ).
cnf(c_0_81,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_82,plain,
( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
fof(c_0_83,plain,
! [X846] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X846,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X846,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X846,
inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).
cnf(c_0_84,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_73]) ).
fof(c_0_85,plain,
! [X285,X286] :
( ~ class_Groups_Ogroup__add(X286)
| c_Groups_Ouminus__class_Ouminus(X286,c_Groups_Ouminus__class_Ouminus(X286,X285)) = X285 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
cnf(c_0_86,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_74,c_0_69]) ).
cnf(c_0_87,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_wa____,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_z____)))),
inference(rw,[status(thm)],[c_0_75,c_0_64]) ).
cnf(c_0_88,plain,
( X1 = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_67]) ).
cnf(c_0_89,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls),X1),
inference(spm,[status(thm)],[c_0_48,c_0_78]) ).
cnf(c_0_90,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_91,plain,
! [X92,X93] :
( ~ class_Int_Onumber__ring(X93)
| ~ class_RealVector_Oreal__normed__algebra__1(X93)
| c_RealVector_Onorm__class_Onorm(X93,c_Int_Onumber__class_Onumber__of(X93,X92)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__number__of])]) ).
fof(c_0_92,plain,
! [X336] :
( ~ class_Groups_Oordered__ab__group__add__abs(X336)
| c_Groups_Oabs__class_Oabs(X336,c_Groups_Ozero__class_Ozero(X336)) = c_Groups_Ozero__class_Ozero(X336) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).
cnf(c_0_93,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = 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),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_81,c_0_39]) ).
cnf(c_0_94,plain,
( 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_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_82,c_0_39]) ).
cnf(c_0_95,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X1,
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_96,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_84,c_0_38]),c_0_39]),c_0_39]) ).
cnf(c_0_97,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,hAPP(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_98,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_85]) ).
cnf(c_0_99,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(c_0_100,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_86,c_0_80]) ).
cnf(c_0_101,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls),v_z____),v_wa____) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_80]) ).
cnf(c_0_102,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_86,c_0_90]) ).
cnf(c_0_103,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_104,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).
cnf(c_0_105,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_106,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(c_0_107,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c_0_108,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_45]),c_0_45]) ).
cnf(c_0_109,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_45]),c_0_45]) ).
fof(c_0_110,plain,
! [X688,X689] :
( ( ~ c_Orderings_Oord__class_Oless(X689,c_Groups_Ozero__class_Ozero(X689),c_Groups_Oplus__class_Oplus(X689,X688,X688))
| c_Orderings_Oord__class_Oless(X689,c_Groups_Ozero__class_Ozero(X689),X688)
| ~ class_Groups_Olinordered__ab__group__add(X689) )
& ( ~ c_Orderings_Oord__class_Oless(X689,c_Groups_Ozero__class_Ozero(X689),X688)
| c_Orderings_Oord__class_Oless(X689,c_Groups_Ozero__class_Ozero(X689),c_Groups_Oplus__class_Oplus(X689,X688,X688))
| ~ class_Groups_Olinordered__ab__group__add(X689) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])]) ).
cnf(c_0_111,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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))))) = X1,
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_95,c_0_38]),c_0_38]),c_0_39]),c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_112,plain,
( 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))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_45]),c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_113,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_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))),
inference(rw,[status(thm)],[c_0_97,c_0_49]) ).
cnf(c_0_114,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_98,c_0_99]) ).
cnf(c_0_115,plain,
v_wa____ = v_z____,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_116,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_56])]) ).
cnf(c_0_117,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_64]),c_0_64]) ).
cnf(c_0_118,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_70,c_0_107]) ).
cnf(c_0_119,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),X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)),
inference(spm,[status(thm)],[c_0_108,c_0_54]) ).
cnf(c_0_120,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_109,c_0_54]) ).
cnf(c_0_121,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_122,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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))))) = X1,
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_111,c_0_45]),c_0_45]),c_0_45]),c_0_45]),c_0_45]),c_0_45]),c_0_45]),c_0_45]) ).
cnf(c_0_123,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
cnf(c_0_124,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(spm,[status(thm)],[c_0_112,c_0_54]) ).
cnf(c_0_125,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),v_s____))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_64]),c_0_114]) ).
cnf(c_0_126,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_115]),c_0_89]),c_0_90]),c_0_116]),c_0_117]),c_0_114]),c_0_118]),c_0_119]),c_0_120]) ).
cnf(c_0_127,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]),c_0_64]),c_0_124]),c_0_64]) ).
cnf(c_0_128,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))))),
inference(spm,[status(thm)],[c_0_125,c_0_118]) ).
cnf(c_0_129,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.21 % Problem : SWW222+1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.22 % Command : run_E %s %d THM
% 0.20/0.42 % Computer : n019.cluster.edu
% 0.20/0.42 % Model : x86_64 x86_64
% 0.20/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.42 % Memory : 8042.1875MB
% 0.20/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.42 % CPULimit : 2400
% 0.20/0.42 % WCLimit : 300
% 0.20/0.42 % DateTime : Mon Oct 2 22:10:51 EDT 2023
% 0.20/0.42 % CPUTime :
% 0.45/0.63 Running first-order theorem proving
% 0.45/0.63 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.HGNcwaTwky/E---3.1_21576.p
% 48.81/6.85 # Version: 3.1pre001
% 48.81/6.85 # Preprocessing class: FMLMSMSMSSSNFFN.
% 48.81/6.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.81/6.85 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 48.81/6.85 # Starting new_bool_3 with 300s (1) cores
% 48.81/6.85 # Starting new_bool_1 with 300s (1) cores
% 48.81/6.85 # Starting sh5l with 300s (1) cores
% 48.81/6.85 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 21654 completed with status 0
% 48.81/6.85 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 48.81/6.85 # Preprocessing class: FMLMSMSMSSSNFFN.
% 48.81/6.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.81/6.85 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 48.81/6.85 # No SInE strategy applied
% 48.81/6.85 # Search class: FGHSM-SMLM31-DFFFFFNN
% 48.81/6.85 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 48.81/6.85 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 866s (1) cores
% 48.81/6.85 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 48.81/6.85 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 48.81/6.85 # Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 48.81/6.85 # Starting U----_213g_00_B10_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 48.81/6.85 # U----_213g_00_B10_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 21665 completed with status 0
% 48.81/6.85 # Result found by U----_213g_00_B10_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 48.81/6.85 # Preprocessing class: FMLMSMSMSSSNFFN.
% 48.81/6.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.81/6.85 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 48.81/6.85 # No SInE strategy applied
% 48.81/6.85 # Search class: FGHSM-SMLM31-DFFFFFNN
% 48.81/6.85 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 48.81/6.85 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 866s (1) cores
% 48.81/6.85 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 48.81/6.85 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 48.81/6.85 # Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 48.81/6.85 # Starting U----_213g_00_B10_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 48.81/6.85 # Preprocessing time : 0.022 s
% 48.81/6.85 # Presaturation interreduction done
% 48.81/6.85
% 48.81/6.85 # Proof found!
% 48.81/6.85 # SZS status Theorem
% 48.81/6.85 # SZS output start CNFRefutation
% See solution above
% 48.81/6.85 # Parsed axioms : 1251
% 48.81/6.85 # Removed by relevancy pruning/SinE : 0
% 48.81/6.85 # Initial clauses : 1832
% 48.81/6.85 # Removed in clause preprocessing : 80
% 48.81/6.85 # Initial clauses in saturation : 1752
% 48.81/6.85 # Processed clauses : 29824
% 48.81/6.85 # ...of these trivial : 532
% 48.81/6.85 # ...subsumed : 22114
% 48.81/6.85 # ...remaining for further processing : 7178
% 48.81/6.85 # Other redundant clauses eliminated : 4857
% 48.81/6.85 # Clauses deleted for lack of memory : 0
% 48.81/6.85 # Backward-subsumed : 167
% 48.81/6.85 # Backward-rewritten : 531
% 48.81/6.85 # Generated clauses : 211715
% 48.81/6.85 # ...of the previous two non-redundant : 185825
% 48.81/6.85 # ...aggressively subsumed : 0
% 48.81/6.85 # Contextual simplify-reflections : 28
% 48.81/6.85 # Paramodulations : 206821
% 48.81/6.85 # Factorizations : 14
% 48.81/6.85 # NegExts : 0
% 48.81/6.85 # Equation resolutions : 4901
% 48.81/6.85 # Total rewrite steps : 338538
% 48.81/6.85 # Propositional unsat checks : 0
% 48.81/6.85 # Propositional check models : 0
% 48.81/6.85 # Propositional check unsatisfiable : 0
% 48.81/6.85 # Propositional clauses : 0
% 48.81/6.85 # Propositional clauses after purity: 0
% 48.81/6.85 # Propositional unsat core size : 0
% 48.81/6.85 # Propositional preprocessing time : 0.000
% 48.81/6.85 # Propositional encoding time : 0.000
% 48.81/6.85 # Propositional solver time : 0.000
% 48.81/6.85 # Success case prop preproc time : 0.000
% 48.81/6.85 # Success case prop encoding time : 0.000
% 48.81/6.85 # Success case prop solver time : 0.000
% 48.81/6.85 # Current number of processed clauses : 4982
% 48.81/6.85 # Positive orientable unit clauses : 829
% 48.81/6.85 # Positive unorientable unit clauses: 30
% 48.81/6.85 # Negative unit clauses : 726
% 48.81/6.85 # Non-unit-clauses : 3397
% 48.81/6.85 # Current number of unprocessed clauses: 157798
% 48.81/6.85 # ...number of literals in the above : 409199
% 48.81/6.85 # Current number of archived formulas : 0
% 48.81/6.85 # Current number of archived clauses : 2067
% 48.81/6.85 # Clause-clause subsumption calls (NU) : 944452
% 48.81/6.85 # Rec. Clause-clause subsumption calls : 601816
% 48.81/6.85 # Non-unit clause-clause subsumptions : 6733
% 48.81/6.85 # Unit Clause-clause subsumption calls : 55419
% 48.81/6.85 # Rewrite failures with RHS unbound : 0
% 48.81/6.85 # BW rewrite match attempts : 19010
% 48.81/6.85 # BW rewrite match successes : 976
% 48.81/6.85 # Condensation attempts : 0
% 48.81/6.85 # Condensation successes : 0
% 48.81/6.85 # Termbank termtop insertions : 5529682
% 48.81/6.85
% 48.81/6.85 # -------------------------------------------------
% 48.81/6.85 # User time : 5.923 s
% 48.81/6.85 # System time : 0.124 s
% 48.81/6.85 # Total time : 6.047 s
% 48.81/6.85 # Maximum resident set size: 8072 pages
% 48.81/6.85
% 48.81/6.85 # -------------------------------------------------
% 48.81/6.85 # User time : 29.162 s
% 48.81/6.85 # System time : 0.752 s
% 48.81/6.85 # Total time : 29.915 s
% 48.81/6.85 # Maximum resident set size: 3064 pages
% 48.81/6.85 % E---3.1 exiting
% 48.81/6.85 % E---3.1 exiting
%------------------------------------------------------------------------------