TSTP Solution File: SWW222+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW222+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n020.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 : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:10:19 EDT 2022
% Result : Theorem 0.36s 4.53s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 80 ( 50 unt; 0 def)
% Number of atoms : 132 ( 65 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 97 ( 45 ~; 37 |; 4 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 77 ( 0 sgn 44 !; 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/solver/bin/../tmp/theBenchmark.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/solver/bin/../tmp/theBenchmark.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/solver/bin/../tmp/theBenchmark.p',fact_Bit1__def) ).
fof(fact_mult__2__right,axiom,
! [X33,X7] :
( class_Int_Onumber__ring(X7)
=> c_Groups_Otimes__class_Otimes(X7,X33,c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X7,X33,X33) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_mult__2__right) ).
fof(fact_add__Pls__right,axiom,
! [X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Int_OPls) = X16,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_abs__minus__add__cancel,axiom,
! [X23,X9] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X9,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X9))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_abs__minus__add__cancel) ).
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/solver/bin/../tmp/theBenchmark.p',fact_minus__real__def) ).
fof(fact_e2,axiom,
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_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/solver/bin/../tmp/theBenchmark.p',fact_e2) ).
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/solver/bin/../tmp/theBenchmark.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_real__mult__1,axiom,
! [X33] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X33) = X33,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_real__mult__1) ).
fof(fact_norm__eq__zero,axiom,
! [X15,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> ( c_RealVector_Onorm__class_Onorm(X7,X15) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_norm__eq__zero) ).
fof(fact_norm__minus__cancel,axiom,
! [X9,X7] :
( class_RealVector_Oreal__normed__vector(X7)
=> c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ouminus__class_Ouminus(X7,X9)) = c_RealVector_Onorm__class_Onorm(X7,X9) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_norm__minus__cancel) ).
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/solver/bin/../tmp/theBenchmark.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/solver/bin/../tmp/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
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/solver/bin/../tmp/theBenchmark.p',fact_w) ).
fof(fact_right__minus__eq,axiom,
! [X11,X12,X7] :
( class_Groups_Ogroup__add(X7)
=> ( c_Groups_Ominus__class_Ominus(X7,X12,X11) = c_Groups_Ozero__class_Ozero(X7)
<=> X12 = X11 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_diff__self,axiom,
! [X8,X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Ominus__class_Ominus(X7,X8,X8) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_diff__self) ).
fof(fact_minus__zero,axiom,
! [X7] :
( class_Groups_Ogroup__add(X7)
=> c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_minus__zero) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(c_0_20,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(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_21,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)],[c_0_20]) ).
fof(c_0_22,plain,
! [X17] : c_Int_OBit0(X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X17),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_23,plain,
! [X17] : c_Int_OBit1(X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X17),X17),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_24,plain,
! [X34,X35] :
( ~ class_Int_Onumber__ring(X35)
| c_Groups_Otimes__class_Otimes(X35,X34,c_Int_Onumber__class_Onumber__of(X35,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X35,X34,X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).
cnf(c_0_25,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_21]) ).
cnf(c_0_26,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,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_23]) ).
fof(c_0_28,plain,
! [X17] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Int_OPls) = X17,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_29,plain,
! [X24,X25] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X24))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X24,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X25))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(c_0_30,plain,
! [X24,X25] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X25,X24) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X24)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_31,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,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_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)],[fact_e2]) ).
fof(c_0_33,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_34,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_25,c_0_26]),c_0_27]),c_0_27]) ).
cnf(c_0_35,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,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_29]) ).
cnf(c_0_37,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_30]) ).
fof(c_0_38,plain,
! [X34] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X34) = X34,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
cnf(c_0_39,plain,
( c_Groups_Otimes__class_Otimes(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),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(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_26]),c_0_27]),c_0_27]) ).
fof(c_0_40,plain,
! [X16,X17] :
( ( c_RealVector_Onorm__class_Onorm(X17,X16) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X16 = c_Groups_Ozero__class_Ozero(X17)
| ~ class_RealVector_Oreal__normed__vector(X17) )
& ( X16 != c_Groups_Ozero__class_Ozero(X17)
| c_RealVector_Onorm__class_Onorm(X17,X16) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(c_0_41,plain,
! [X10,X11] :
( ~ class_RealVector_Oreal__normed__vector(X11)
| c_RealVector_Onorm__class_Onorm(X11,c_Groups_Ouminus__class_Ouminus(X11,X10)) = c_RealVector_Onorm__class_Onorm(X11,X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel])]) ).
cnf(c_0_42,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_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_32,c_0_26]),c_0_27]),c_0_27]) ).
cnf(c_0_43,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_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(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_44,plain,
! [X16,X17] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X17,X16))
| X16 != c_Groups_Ozero__class_Ozero(X17)
| ~ class_RealVector_Oreal__normed__vector(X17) )
& ( X16 = c_Groups_Ozero__class_Ozero(X17)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X17,X16))
| ~ class_RealVector_Oreal__normed__vector(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
cnf(c_0_45,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_34,c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_46,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_47,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_38]) ).
cnf(c_0_48,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,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,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_49,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
cnf(c_0_50,plain,
( c_RealVector_Onorm__class_Onorm(X1,X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c_0_52,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_53,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_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_42,c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_54,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_43,c_0_26]),c_0_27]),c_0_27]) ).
cnf(c_0_55,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_56,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,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_Groups_Ouminus__class_Ouminus(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_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)],[c_0_45,c_0_46]) ).
cnf(c_0_58,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(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_59,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_61,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_Oabs__class_Oabs(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,hAPP(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)],[c_0_53,c_0_46]) ).
fof(c_0_62,plain,
! [X13,X14,X15] :
( ( c_Groups_Ominus__class_Ominus(X15,X14,X13) != c_Groups_Ozero__class_Ozero(X15)
| X14 = X13
| ~ class_Groups_Ogroup__add(X15) )
& ( X14 != X13
| c_Groups_Ominus__class_Ominus(X15,X14,X13) = c_Groups_Ozero__class_Ozero(X15)
| ~ class_Groups_Ogroup__add(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
cnf(c_0_63,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____))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_55])]),c_0_45]) ).
cnf(c_0_64,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_51]) ).
fof(c_0_65,plain,
! [X9,X10] :
( ~ class_Groups_Ogroup__add(X10)
| c_Groups_Ominus__class_Ominus(X10,X9,X9) = c_Groups_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(c_0_66,plain,
! [X8] :
( ~ class_Groups_Ogroup__add(X8)
| c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
cnf(c_0_67,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_Groups_Ouminus__class_Ouminus(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)],[c_0_57,c_0_58]) ).
cnf(c_0_68,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,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_Oabs__class_Oabs(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,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)],[c_0_61,c_0_58]) ).
cnf(c_0_70,plain,
( X2 = X3
| ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_wa____,v_z____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(c_0_73,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,negated_conjecture,
c_Groups_Ouminus__class_Ouminus(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_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_76,plain,
v_wa____ = v_z____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_77,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_73,c_0_72]) ).
cnf(c_0_78,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_74,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW222+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 4 12:05:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.36/4.53 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.36/4.53 # Preprocessing time : 0.101 s
% 0.36/4.53
% 0.36/4.53 # Proof found!
% 0.36/4.53 # SZS status Theorem
% 0.36/4.53 # SZS output start CNFRefutation
% See solution above
% 0.36/4.53 # Proof object total steps : 80
% 0.36/4.53 # Proof object clause steps : 44
% 0.36/4.53 # Proof object formula steps : 36
% 0.36/4.53 # Proof object conjectures : 10
% 0.36/4.53 # Proof object clause conjectures : 7
% 0.36/4.53 # Proof object formula conjectures : 3
% 0.36/4.53 # Proof object initial clauses used : 20
% 0.36/4.53 # Proof object initial formulas used : 20
% 0.36/4.53 # Proof object generating inferences : 10
% 0.36/4.53 # Proof object simplifying inferences : 47
% 0.36/4.53 # Training examples: 0 positive, 0 negative
% 0.36/4.53 # Parsed axioms : 1251
% 0.36/4.53 # Removed by relevancy pruning/SinE : 0
% 0.36/4.53 # Initial clauses : 1832
% 0.36/4.53 # Removed in clause preprocessing : 80
% 0.36/4.53 # Initial clauses in saturation : 1752
% 0.36/4.53 # Processed clauses : 17330
% 0.36/4.53 # ...of these trivial : 397
% 0.36/4.53 # ...subsumed : 12038
% 0.36/4.53 # ...remaining for further processing : 4895
% 0.36/4.53 # Other redundant clauses eliminated : 372
% 0.36/4.53 # Clauses deleted for lack of memory : 0
% 0.36/4.53 # Backward-subsumed : 107
% 0.36/4.53 # Backward-rewritten : 346
% 0.36/4.53 # Generated clauses : 153653
% 0.36/4.53 # ...of the previous two non-trivial : 138995
% 0.36/4.53 # Contextual simplify-reflections : 1607
% 0.36/4.53 # Paramodulations : 153137
% 0.36/4.53 # Factorizations : 16
% 0.36/4.53 # Equation resolutions : 497
% 0.36/4.53 # Current number of processed clauses : 4415
% 0.36/4.53 # Positive orientable unit clauses : 644
% 0.36/4.54 # Positive unorientable unit clauses: 17
% 0.36/4.54 # Negative unit clauses : 551
% 0.36/4.54 # Non-unit-clauses : 3203
% 0.36/4.54 # Current number of unprocessed clauses: 116812
% 0.36/4.54 # ...number of literals in the above : 349278
% 0.36/4.54 # Current number of archived formulas : 0
% 0.36/4.54 # Current number of archived clauses : 459
% 0.36/4.54 # Clause-clause subsumption calls (NU) : 1604522
% 0.36/4.54 # Rec. Clause-clause subsumption calls : 933769
% 0.36/4.54 # Non-unit clause-clause subsumptions : 5721
% 0.36/4.54 # Unit Clause-clause subsumption calls : 50069
% 0.36/4.54 # Rewrite failures with RHS unbound : 0
% 0.36/4.54 # BW rewrite match attempts : 8225
% 0.36/4.54 # BW rewrite match successes : 2181
% 0.36/4.54 # Condensation attempts : 0
% 0.36/4.54 # Condensation successes : 0
% 0.36/4.54 # Termbank termtop insertions : 11020440
% 0.36/4.54
% 0.36/4.54 # -------------------------------------------------
% 0.36/4.54 # User time : 3.745 s
% 0.36/4.54 # System time : 0.060 s
% 0.36/4.54 # Total time : 3.805 s
% 0.36/4.54 # Maximum resident set size: 110008 pages
% 0.36/23.51 eprover: CPU time limit exceeded, terminating
% 0.36/23.51 eprover: CPU time limit exceeded, terminating
% 0.36/23.52 eprover: CPU time limit exceeded, terminating
% 0.36/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.53 eprover: No such file or directory
% 0.36/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.53 eprover: No such file or directory
% 0.36/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.53 eprover: No such file or directory
% 0.36/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.53 eprover: No such file or directory
% 0.36/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.53 eprover: No such file or directory
% 0.36/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.54 eprover: No such file or directory
% 0.36/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.54 eprover: No such file or directory
% 0.36/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.54 eprover: No such file or directory
% 0.36/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.54 eprover: No such file or directory
% 0.36/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.54 eprover: No such file or directory
% 0.36/23.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.54 eprover: No such file or directory
% 0.36/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.55 eprover: No such file or directory
% 0.36/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.55 eprover: No such file or directory
% 0.36/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.55 eprover: No such file or directory
% 0.36/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.55 eprover: No such file or directory
% 0.36/23.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.55 eprover: No such file or directory
% 0.36/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56 eprover: No such file or directory
% 0.36/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56 eprover: No such file or directory
% 0.36/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.56 eprover: No such file or directory
% 0.36/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56 eprover: No such file or directory
% 0.36/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56 eprover: No such file or directory
% 0.36/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.56 eprover: No such file or directory
% 0.36/23.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.56 eprover: No such file or directory
% 0.36/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.57 eprover: No such file or directory
% 0.36/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.ineprover:
% 0.36/23.57 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.57 eprover: No such file or directory
% 0.36/23.57 eprover: No such file or directory
% 0.36/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.57 eprover: No such file or directory
% 0.36/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.57 eprover: No such file or directory
% 0.36/23.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.57 eprover: No such file or directory
% 0.36/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.58 eprover: No such file or directory
% 0.36/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.58 eprover: No such file or directory
% 0.36/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/23.58 eprover: No such file or directory
% 0.36/23.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/23.58 eprover: No such file or directory
%------------------------------------------------------------------------------