TSTP Solution File: SWW221+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW221+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : 300s
% DateTime : Thu Sep 29 20:57:57 EDT 2022
% Result : Theorem 5.46s 3.79s
% Output : Proof 5.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW221+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 13:09:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 5.46/3.79 % SZS status Theorem
% 5.46/3.79 % SZS output start Proof
% 5.46/3.79 tff(c_Orderings_Oord__class_Oless_type, type, (
% 5.46/3.79 c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o)).
% 5.46/3.79 tff(c_RealVector_Onorm__class_Onorm_type, type, (
% 5.46/3.79 c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i)).
% 5.46/3.79 tff(c_Groups_Ominus__class_Ominus_type, type, (
% 5.46/3.79 c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i)).
% 5.46/3.79 tff(v_z_____type, type, (
% 5.46/3.79 v_z____: $i)).
% 5.46/3.79 tff(tptp_fun_B_w_35_type, type, (
% 5.46/3.79 tptp_fun_B_w_35: $i > $i)).
% 5.46/3.79 tff(tptp_fun_B_d_1_type, type, (
% 5.46/3.79 tptp_fun_B_d_1: $i)).
% 5.46/3.79 tff(tc_Complex_Ocomplex_type, type, (
% 5.46/3.79 tc_Complex_Ocomplex: $i)).
% 5.46/3.79 tff(c_Groups_Ozero__class_Ozero_type, type, (
% 5.46/3.79 c_Groups_Ozero__class_Ozero: $i > $i)).
% 5.46/3.79 tff(tc_RealDef_Oreal_type, type, (
% 5.46/3.79 tc_RealDef_Oreal: $i)).
% 5.46/3.79 tff(c_Rings_Oinverse__class_Odivide_type, type, (
% 5.46/3.79 c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i)).
% 5.46/3.79 tff(c_Int_Onumber__class_Onumber__of_type, type, (
% 5.46/3.79 c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i)).
% 5.46/3.79 tff(c_Int_OBit0_type, type, (
% 5.46/3.79 c_Int_OBit0: $i > $i)).
% 5.46/3.79 tff(c_Int_OBit1_type, type, (
% 5.46/3.79 c_Int_OBit1: $i > $i)).
% 5.46/3.79 tff(tc_Int_Oint_type, type, (
% 5.46/3.79 tc_Int_Oint: $i)).
% 5.46/3.79 tff(c_Groups_Oabs__class_Oabs_type, type, (
% 5.46/3.79 c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i)).
% 5.46/3.79 tff(c_Groups_Ouminus__class_Ouminus_type, type, (
% 5.46/3.79 c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i)).
% 5.46/3.79 tff(v_s_____type, type, (
% 5.46/3.79 v_s____: $i)).
% 5.46/3.79 tff(hAPP_type, type, (
% 5.46/3.79 hAPP: ( $i * $i ) > $i)).
% 5.46/3.79 tff(c_Polynomial_Opoly_type, type, (
% 5.46/3.79 c_Polynomial_Opoly: ( $i * $i ) > $i)).
% 5.46/3.79 tff(v_p_type, type, (
% 5.46/3.79 v_p: $i)).
% 5.46/3.79 tff(c_Int_OPls_type, type, (
% 5.46/3.79 c_Int_OPls: $i)).
% 5.46/3.79 tff(v_thesis_____type, type, (
% 5.46/3.79 v_thesis____: $o)).
% 5.46/3.79 tff(1,plain,
% 5.46/3.79 (^[B_d: $i] : refl(((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____))))))) <=> ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____))))))))),
% 5.46/3.79 inference(bind,[status(th)],[])).
% 5.46/3.79 tff(2,plain,
% 5.46/3.79 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____))))))) <=> ![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____)))))))),
% 5.46/3.79 inference(quant_intro,[status(thm)],[1])).
% 5.46/3.79 tff(3,plain,
% 5.46/3.79 (^[B_d: $i] : rewrite(((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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, tptp_fun_B_w_35(B_d), 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, tptp_fun_B_w_35(B_d), v_z____)), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))) <=> ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____))))))))),
% 5.46/3.79 inference(bind,[status(th)],[])).
% 5.46/3.79 tff(4,plain,
% 5.46/3.79 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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, tptp_fun_B_w_35(B_d), 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, tptp_fun_B_w_35(B_d), v_z____)), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))) <=> ![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____)))))))),
% 5.46/3.79 inference(quant_intro,[status(thm)],[3])).
% 5.46/3.79 tff(5,plain,
% 5.46/3.79 (^[B_d: $i] : rewrite(((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))))),
% 5.46/3.79 inference(bind,[status(th)],[])).
% 5.46/3.79 tff(6,plain,
% 5.46/3.79 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))) <=> ![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))))),
% 5.46/3.79 inference(quant_intro,[status(thm)],[5])).
% 5.46/3.79 tff(7,plain,
% 5.46/3.79 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))) <=> ![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))),
% 5.46/3.79 inference(rewrite,[status(thm)],[])).
% 5.46/3.79 tff(8,plain,
% 5.46/3.79 (^[B_d: $i] : trans(monotonicity(iff_false(asserted(~v_thesis____), (v_thesis____ <=> $false)), rewrite((~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))) <=> (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))), ((v_thesis____ | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, v_z____))) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, v_z____)), B_d))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), B_w), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____))), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____)), c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v_s____))), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) <=> ($false | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, v_z____))) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, v_z____)), B_d))) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), B_w), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____))), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), v_z____)), c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v_s____))), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))), rewrite(($false | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))), ((v_thesis____ | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))))),
% 5.46/3.79 inference(bind,[status(th)],[])).
% 5.46/3.79 tff(9,plain,
% 5.46/3.79 (![B_d: $i] : (v_thesis____ | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))) <=> ![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))),
% 5.46/3.79 inference(quant_intro,[status(thm)],[8])).
% 5.46/3.79 tff(10,plain,
% 5.46/3.79 (^[B_d: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B_w: $i] : rewrite(((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))), (![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) <=> ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))), ((![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) => v_thesis____) <=> (![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) => v_thesis____))), rewrite((![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) => v_thesis____) <=> (v_thesis____ | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))), ((![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) => v_thesis____) <=> (v_thesis____ | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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), B_d) => (![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) => v_thesis____)) <=> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) => (v_thesis____ | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))))), rewrite((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) => (v_thesis____ | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))) <=> (v_thesis____ | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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), B_d) => (![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) => v_thesis____)) <=> (v_thesis____ | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))))),
% 5.46/3.80 inference(bind,[status(th)],[])).
% 5.46/3.80 tff(11,plain,
% 5.46/3.80 (![B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) => (![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) => v_thesis____)) <=> ![B_d: $i] : (v_thesis____ | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))),
% 5.46/3.80 inference(quant_intro,[status(thm)],[10])).
% 5.46/3.80 tff(12,axiom,(![B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) => (![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))) => v_thesis____))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_0')).
% 5.46/3.80 tff(13,plain,
% 5.46/3.80 (![B_d: $i] : (v_thesis____ | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))),
% 5.46/3.80 inference(modus_ponens,[status(thm)],[12, 11])).
% 5.46/3.80 tff(14,plain,
% 5.46/3.80 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))),
% 5.46/3.80 inference(modus_ponens,[status(thm)],[13, 9])).
% 5.46/3.80 tff(15,plain,
% 5.46/3.80 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))),
% 5.46/3.80 inference(modus_ponens,[status(thm)],[14, 7])).
% 5.46/3.80 tff(16,plain,
% 5.46/3.80 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d)) | (~![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))))),
% 5.46/3.80 inference(modus_ponens,[status(thm)],[15, 6])).
% 5.46/3.80 tff(17,plain,(
% 5.46/3.80 ![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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, tptp_fun_B_w_35(B_d), 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, tptp_fun_B_w_35(B_d), v_z____)), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))))),
% 5.46/3.80 inference(skolemize,[status(sab)],[16])).
% 5.46/3.80 tff(18,plain,
% 5.46/3.80 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____)))))))),
% 5.46/3.80 inference(modus_ponens,[status(thm)],[17, 4])).
% 5.46/3.80 tff(19,plain,
% 5.46/3.80 (![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____)))))))),
% 5.46/3.80 inference(modus_ponens,[status(thm)],[18, 2])).
% 5.46/3.80 tff(20,plain,
% 5.46/3.80 ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d!1) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))) <=> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d!1) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))),
% 5.46/3.80 inference(rewrite,[status(thm)],[])).
% 5.46/3.80 tff(21,plain,
% 5.46/3.80 (^[B_d: $i] : rewrite((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))))),
% 5.46/3.80 inference(bind,[status(th)],[])).
% 5.46/3.80 tff(22,plain,
% 5.46/3.80 (?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))) <=> ?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))),
% 5.46/3.80 inference(quant_intro,[status(thm)],[21])).
% 5.46/3.80 tff(23,plain,
% 5.46/3.80 (?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))) <=> ?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))),
% 5.46/3.80 inference(rewrite,[status(thm)],[])).
% 5.46/3.80 tff(24,plain,
% 5.46/3.80 (^[B_d: $i] : rewrite((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))))),
% 5.46/3.80 inference(bind,[status(th)],[])).
% 5.46/3.80 tff(25,plain,
% 5.46/3.80 (?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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))))))) <=> ?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))),
% 5.46/3.80 inference(quant_intro,[status(thm)],[24])).
% 5.46/3.80 tff(26,axiom,(?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((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, B_w, 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, B_w, v_z____)), B_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), B_w), 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/sandbox2/benchmark/theBenchmark.p','fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_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')).
% 5.46/3.80 tff(27,plain,
% 5.46/3.80 (?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))),
% 5.46/3.80 inference(modus_ponens,[status(thm)],[26, 25])).
% 5.46/3.80 tff(28,plain,
% 5.46/3.80 (?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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)))))))),
% 5.46/3.81 inference(modus_ponens,[status(thm)],[27, 23])).
% 5.46/3.81 tff(29,plain,
% 5.46/3.81 (?[B_d: $i] : (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))),
% 5.46/3.81 inference(modus_ponens,[status(thm)],[28, 22])).
% 5.46/3.81 tff(30,plain,
% 5.46/3.81 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d!1) & ![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))),
% 5.46/3.81 inference(modus_ponens,[status(thm)],[29, 20])).
% 5.46/3.81 tff(31,plain,
% 5.46/3.81 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d!1)),
% 5.46/3.81 inference(and_elim,[status(thm)],[30])).
% 5.46/3.81 tff(32,plain,
% 5.46/3.81 (((~![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____)))))))) | ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d!1)) | (~(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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____)))))))) <=> ((~![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____)))))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d!1)) | (~(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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____)))))))),
% 5.46/3.81 inference(rewrite,[status(thm)],[])).
% 5.46/3.81 tff(33,plain,
% 5.46/3.81 ((~![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____)))))))) | ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d!1)) | (~(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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____)))))))),
% 5.46/3.81 inference(quant_inst,[status(thm)],[])).
% 5.46/3.81 tff(34,plain,
% 5.46/3.81 ((~![B_d: $i] : ((~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_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), tptp_fun_B_w_35(B_d)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d), v_z____)), B_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, tptp_fun_B_w_35(B_d), v_z____)))))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), B_d!1)) | (~(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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____))))))),
% 5.46/3.81 inference(modus_ponens,[status(thm)],[33, 32])).
% 5.46/3.81 tff(35,plain,
% 5.46/3.81 (~(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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____)))))),
% 5.46/3.81 inference(unit_resolution,[status(thm)],[34, 31, 19])).
% 5.46/3.81 tff(36,plain,
% 5.46/3.81 ((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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____))))) | 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, tptp_fun_B_w_35(B_d!1), v_z____)))),
% 5.46/3.81 inference(tautology,[status(thm)],[])).
% 5.46/3.81 tff(37,plain,
% 5.46/3.81 (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, tptp_fun_B_w_35(B_d!1), v_z____)))),
% 5.46/3.81 inference(unit_resolution,[status(thm)],[36, 35])).
% 5.46/3.81 tff(38,plain,
% 5.46/3.81 ((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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), 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, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)),
% 5.46/3.81 inference(tautology,[status(thm)],[])).
% 5.46/3.81 tff(39,plain,
% 5.46/3.81 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)),
% 5.46/3.81 inference(unit_resolution,[status(thm)],[38, 35])).
% 5.46/3.81 tff(40,plain,
% 5.46/3.81 ((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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), 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, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))),
% 5.46/3.81 inference(tautology,[status(thm)],[])).
% 5.46/3.81 tff(41,plain,
% 5.46/3.81 (~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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
% 5.46/3.81 inference(unit_resolution,[status(thm)],[40, 35])).
% 5.46/3.81 tff(42,plain,
% 5.46/3.81 (^[B_w: $i] : refl((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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1))) <=> (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1))))),
% 5.46/3.81 inference(bind,[status(th)],[])).
% 5.46/3.81 tff(43,plain,
% 5.46/3.81 (![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1))) <=> ![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))),
% 5.46/3.81 inference(quant_intro,[status(thm)],[42])).
% 5.46/3.81 tff(44,plain,
% 5.46/3.81 (^[B_w: $i] : trans(monotonicity(trans(monotonicity(rewrite((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, B_w, 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, B_w, v_z____)), B_d!1)) <=> (~((~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, B_w, 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, B_w, v_z____)), B_d!1))))), ((~(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, B_w, 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, B_w, v_z____)), B_d!1))) <=> (~(~((~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, B_w, 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, B_w, v_z____)), B_d!1))))))), rewrite((~(~((~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, B_w, 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, B_w, v_z____)), B_d!1))))) <=> ((~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, B_w, 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, B_w, v_z____)), B_d!1)))), ((~(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, B_w, 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, B_w, v_z____)), B_d!1))) <=> ((~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, B_w, 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, B_w, v_z____)), B_d!1))))), (((~(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, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))), rewrite((((~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, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) <=> (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))), (((~(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, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) <=> (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))))),
% 5.46/3.81 inference(bind,[status(th)],[])).
% 5.46/3.81 tff(45,plain,
% 5.46/3.81 (![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) <=> ![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))),
% 5.46/3.81 inference(quant_intro,[status(thm)],[44])).
% 5.46/3.81 tff(46,plain,
% 5.46/3.81 (![B_w: $i] : ((~(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, B_w, 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, B_w, v_z____)), B_d!1))) | 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), B_w), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))),
% 5.46/3.81 inference(and_elim,[status(thm)],[30])).
% 5.46/3.81 tff(47,plain,
% 5.46/3.81 (![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))),
% 5.46/3.82 inference(modus_ponens,[status(thm)],[46, 45])).
% 5.46/3.82 tff(48,plain,
% 5.46/3.82 (![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))),
% 5.46/3.82 inference(modus_ponens,[status(thm)],[47, 43])).
% 5.46/3.82 tff(49,plain,
% 5.46/3.82 (((~![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))) | (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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____)))))) <=> ((~![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))) | 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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____)))))),
% 5.46/3.82 inference(rewrite,[status(thm)],[])).
% 5.46/3.82 tff(50,plain,
% 5.46/3.82 ((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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), 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, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1))) <=> (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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____)))))),
% 5.46/3.82 inference(rewrite,[status(thm)],[])).
% 5.46/3.82 tff(51,plain,
% 5.46/3.82 (((~![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))) | (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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), 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, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)))) <=> ((~![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))) | (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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____))))))),
% 5.46/3.82 inference(monotonicity,[status(thm)],[50])).
% 5.46/3.82 tff(52,plain,
% 5.46/3.82 (((~![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))) | (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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), 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, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)))) <=> ((~![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))) | 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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____)))))),
% 5.46/3.82 inference(transitivity,[status(thm)],[51, 49])).
% 5.46/3.82 tff(53,plain,
% 5.46/3.82 ((~![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))) | (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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), 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, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)))),
% 5.46/3.82 inference(quant_inst,[status(thm)],[])).
% 5.46/3.82 tff(54,plain,
% 5.46/3.82 ((~![B_w: $i] : (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), B_w), 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_Groups_Ozero__class_Ozero(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_Ominus__class_Ominus(tc_Complex_Ocomplex, B_w, 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, B_w, v_z____)), B_d!1)))) | 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), tptp_fun_B_w_35(B_d!1)), 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_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) | (~c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, tptp_fun_B_w_35(B_d!1), v_z____)), B_d!1)) | (~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, tptp_fun_B_w_35(B_d!1), v_z____))))),
% 5.57/3.88 inference(modus_ponens,[status(thm)],[53, 52])).
% 5.57/3.88 tff(55,plain,
% 5.57/3.88 ($false),
% 5.57/3.88 inference(unit_resolution,[status(thm)],[54, 48, 41, 39, 37])).
% 5.57/3.88 % SZS output end Proof
%------------------------------------------------------------------------------