%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW221+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:04:53 AM UTC 2026
% Result : Theorem 142.24s 142.55s
% Output : Proof 142.37s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
! [V_ga_2,V_fa_2] :
( ! [B_x] : hAPP(V_fa_2,B_x) = hAPP(V_ga_2,B_x)
=> V_fa_2 = V_ga_2 ),
file('theBenchmark.p',fact_ext) ).
fof(fact_fz_I1_J,axiom,
c_SEQ_Osubseq(v_f____),
file('theBenchmark.p',fact_fz_I1_J) ).
fof(fact_e,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
file('theBenchmark.p',fact_e) ).
fof(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,axiom,
? [B_d] :
( ! [B_w] :
( ( 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_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,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) ),
file('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) ).
fof(fact_e2,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_e2) ).
fof(fact_half__gt__zero__iff,axiom,
! [V_ra_2,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ra_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ra_2) ) ),
file('theBenchmark.p',fact_half__gt__zero__iff) ).
fof(fact_half__gt__zero,axiom,
! [V_r,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
file('theBenchmark.p',fact_half__gt__zero) ).
fof(fact_abs__number__of,axiom,
! [V_x,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) = c_Int_Onumber__class_Onumber__of(T_a,V_x) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) ) ) ),
file('theBenchmark.p',fact_abs__number__of) ).
fof(fact_abs__real__def,axiom,
! [V_a] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) ) ),
file('theBenchmark.p',fact_abs__real__def) ).
fof(fact_real__abs__def,axiom,
! [V_r] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) ) ),
file('theBenchmark.p',fact_real__abs__def) ).
fof(fact_norm__number__of,axiom,
! [V_w,T_a] :
( ( class_RealVector_Oreal__normed__algebra__1(T_a)
& class_Int_Onumber__ring(T_a) )
=> c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w)) ),
file('theBenchmark.p',fact_norm__number__of) ).
fof(fact_nonzero__norm__divide,axiom,
! [V_a,V_b,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ),
file('theBenchmark.p',fact_nonzero__norm__divide) ).
fof(fact_divide__numeral__1,axiom,
! [V_a,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield(T_a) )
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ),
file('theBenchmark.p',fact_divide__numeral__1) ).
fof(fact_divide__Numeral1,axiom,
! [V_x,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield(T_a) )
=> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x ),
file('theBenchmark.p',fact_divide__Numeral1) ).
fof(fact_zero__less__norm__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_abs__div__pos,axiom,
! [V_x,V_y,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ),
file('theBenchmark.p',fact_abs__div__pos) ).
fof(fact_divide__Numeral0,axiom,
! [V_x,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide__Numeral0) ).
fof(fact_zero__is__num__zero,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
file('theBenchmark.p',fact_zero__is__num__zero) ).
fof(fact_bin__less__0__simps_I1_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(fact_bin__less__0__simps_I3_J,axiom,
! [V_wa_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
fof(fact_bin__less__0__simps_I4_J,axiom,
! [V_wa_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
fof(fact_minus__Pls,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_minus__Pls) ).
fof(fact_minus__Bit0,axiom,
! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)),
file('theBenchmark.p',fact_minus__Bit0) ).
fof(fact_less__int__code_I16_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__int__code_I16_J) ).
fof(fact_rel__simps_I17_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I17_J) ).
fof(fact_rel__simps_I2_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('theBenchmark.p',fact_rel__simps_I2_J) ).
fof(fact_less__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__int__code_I13_J) ).
fof(fact_rel__simps_I14_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I14_J) ).
fof(fact_real__norm__def,axiom,
! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
file('theBenchmark.p',fact_real__norm__def) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_Pls__def) ).
fof(fact_rel__simps_I12_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ),
file('theBenchmark.p',fact_rel__simps_I12_J) ).
fof(fact_less__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__int__code_I15_J) ).
fof(fact_rel__simps_I16_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I16_J) ).
fof(fact_rel__simps_I10_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ),
file('theBenchmark.p',fact_rel__simps_I10_J) ).
fof(fact_rel__simps_I4_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I4_J) ).
fof(fact_eq__number__of,axiom,
! [V_y_2,V_x_2,T_a] :
( ( class_Int_Oring__char__0(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_eq__number__of) ).
fof(fact_number__of__reorient,axiom,
! [V_x_2,V_wa_2,T_a] :
( class_Int_Onumber(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
<=> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) ) ),
file('theBenchmark.p',fact_number__of__reorient) ).
fof(fact_rel__simps_I51_J,axiom,
! [V_l_2,V_k_2] :
( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
<=> V_k_2 = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I51_J) ).
fof(fact_rel__simps_I48_J,axiom,
! [V_l_2,V_k_2] :
( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
<=> V_k_2 = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I48_J) ).
fof(fact_less__number__of,axiom,
! [V_y_2,V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_less__number__of) ).
fof(fact_number__of__diff,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__diff) ).
fof(fact_divide_Ozero,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide_Ozero) ).
fof(fact_number__of__minus,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__minus) ).
fof(fact_arith__simps_I30_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ),
file('theBenchmark.p',fact_arith__simps_I30_J) ).
fof(fact_divide_Odiff,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ),
file('theBenchmark.p',fact_divide_Odiff) ).
fof(fact_rel__simps_I46_J,axiom,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I46_J) ).
fof(fact_rel__simps_I39_J,axiom,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
file('theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_rel__simps_I50_J,axiom,
! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
file('theBenchmark.p',fact_rel__simps_I50_J) ).
fof(fact_rel__simps_I49_J,axiom,
! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
file('theBenchmark.p',fact_rel__simps_I49_J) ).
fof(fact_rel__simps_I44_J,axiom,
! [V_k_2] :
( c_Int_OBit0(V_k_2) = c_Int_OPls
<=> V_k_2 = c_Int_OPls ),
file('theBenchmark.p',fact_rel__simps_I44_J) ).
fof(fact_rel__simps_I38_J,axiom,
! [V_l_2] :
( c_Int_OPls = c_Int_OBit0(V_l_2)
<=> c_Int_OPls = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I38_J) ).
fof(fact_Bit0__Pls,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_Bit0__Pls) ).
fof(fact_norm__minus__commute,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ),
file('theBenchmark.p',fact_norm__minus__commute) ).
fof(fact_minus__divide__divide,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_minus__divide__divide) ).
fof(fact_divide_Ominus,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ),
file('theBenchmark.p',fact_divide_Ominus) ).
fof(fact_minus__divide__right,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__divide__right) ).
fof(fact_norm__minus__cancel,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ),
file('theBenchmark.p',fact_norm__minus__cancel) ).
fof(fact_abs__divide,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ),
file('theBenchmark.p',fact_abs__divide) ).
fof(fact_abs__norm__cancel,axiom,
! [V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ),
file('theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_divide__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_divide__neg__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_divide__neg__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_divide__pos__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_divide__less__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_number__of__Pls,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_number__of__Pls) ).
fof(fact_norm__zero,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_norm__zero) ).
fof(fact_norm__eq__zero,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_norm__eq__zero) ).
fof(fact_nonzero__abs__divide,axiom,
! [V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ),
file('theBenchmark.p',fact_nonzero__abs__divide) ).
fof(fact_norm__not__less__zero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_norm__divide,axiom,
! [V_b,V_a,T_a] :
( ( class_RealVector_Oreal__normed__field(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ),
file('theBenchmark.p',fact_norm__divide) ).
fof(fact_less__special_I3_J,axiom,
! [V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) ) ),
file('theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_less__special_I1_J,axiom,
! [V_y_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) ) ),
file('theBenchmark.p',fact_less__special_I1_J) ).
fof(fact_abs__of__neg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ),
file('theBenchmark.p',fact_abs__of__neg) ).
fof(fact_abs__if,axiom,
! [V_a,T_a] :
( class_Groups_Oabs__if(T_a)
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
& ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ),
file('theBenchmark.p',fact_abs__if) ).
fof(fact_pos2,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_pos2) ).
fof(fact_abs__less__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_abs__less__iff) ).
fof(fact_nonzero__minus__divide__divide,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(fact_nonzero__minus__divide__right,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
file('theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(fact_abs__of__pos,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ),
file('theBenchmark.p',fact_abs__of__pos) ).
fof(fact_zero__less__abs__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact_abs__not__less__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_semiring__norm_I112_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ),
file('theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_diff__0,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ),
file('theBenchmark.p',fact_diff__0) ).
fof(fact_neg__less__nonneg,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_zminus__0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zminus__0) ).
fof(fact_number__of__is__id,axiom,
! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k,
file('theBenchmark.p',fact_number__of__is__id) ).
fof(fact_zabs__def,axiom,
! [V_i] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) ) ),
file('theBenchmark.p',fact_zabs__def) ).
fof(fact_zminus__zminus,axiom,
! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
file('theBenchmark.p',fact_zminus__zminus) ).
fof(fact_minus__numeral__code_I5_J,axiom,
! [V_w] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_minus__numeral__code_I5_J) ).
fof(fact_less__bin__lemma,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_zless__linear,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) ),
file('theBenchmark.p',fact_zless__linear) ).
fof(fact_less__number__of__int__code,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_diff__bin__simps_I1_J,axiom,
! [V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
file('theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(fact_diff__bin__simps_I7_J,axiom,
! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I7_J) ).
fof(fact_diff__bin__simps_I9_J,axiom,
! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I9_J) ).
fof(fact_diff__bin__simps_I10_J,axiom,
! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I10_J) ).
fof(fact_diff__bin__simps_I3_J,axiom,
! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I3_J) ).
fof(fact_zero__reorient,axiom,
! [V_x_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__reorient) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_diff__eq__diff__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( class_Groups_Oab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
=> ( V_a_2 = V_b_2
<=> V_c_2 = V_d_2 ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_minus__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ),
file('theBenchmark.p',fact_minus__minus) ).
fof(fact_equation__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) ),
file('theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_minus__equation__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
<=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2 ) ),
file('theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_less__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) ) ) ),
file('theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_less__0__number__of,axiom,
! [V_v_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ),
file('theBenchmark.p',fact_less__0__number__of) ).
fof(fact_nat__number__of__Pls,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__number__of__Pls) ).
fof(fact_semiring__norm_I113_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
file('theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(fact_abs__idempotent,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
file('theBenchmark.p',fact_abs__idempotent) ).
fof(fact_diff__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_diff__0__right) ).
fof(fact_diff__self,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_diff__self) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oab__group__add(T_a)
=> ( V_a_2 = V_b_2
<=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_right__minus__eq) ).
fof(fact_diff__eq__diff__less,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_minus__zero,axiom,
! [T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_minus__zero) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
<=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ),
file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_equal__neg__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_neg__equal__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_less__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ),
file('theBenchmark.p',fact_less__minus__iff) ).
fof(fact_minus__less__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ),
file('theBenchmark.p',fact_minus__less__iff) ).
fof(fact_neg__less__iff__less,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_divide__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide__zero__left) ).
fof(fact_divide__zero,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide__zero) ).
fof(fact_minus__diff__eq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ),
file('theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_abs__zero,axiom,
! [T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_abs__zero) ).
fof(fact_abs__eq__0,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_abs__eq__0) ).
fof(fact_diff__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_diff__divide__distrib) ).
fof(fact_minus__divide__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ),
file('theBenchmark.p',fact_minus__divide__left) ).
fof(fact_abs__minus__commute,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ),
file('theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_abs__minus__cancel,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
file('theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_less__iff__diff__less__0,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_neg__0__less__iff__less,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_less__minus__self__iff,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_neg__less__0__iff__less,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_less__zeroE,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_less__zeroE) ).
fof(fact_subseq__def,axiom,
! [V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
<=> ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)) ) ),
file('theBenchmark.p',fact_subseq__def) ).
fof(fact_fz_I2_J,axiom,
! [B_e] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
=> ? [B_N] :
! [B_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),B_e) ) ),
file('theBenchmark.p',fact_fz_I2_J) ).
fof(fact_poly__minus,axiom,
! [V_x,V_p,T_a] :
( class_Rings_Ocomm__ring(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ),
file('theBenchmark.p',fact_poly__minus) ).
fof(fact_poly__diff,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__ring(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__diff) ).
fof(fact_poly__0,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_poly__0) ).
fof(fact_not__less0,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_not__less0) ).
fof(fact_neq0__conv,axiom,
! [V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ),
file('theBenchmark.p',fact_neq0__conv) ).
fof(fact_zero__less__diff,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
file('theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__nat__zero__code,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_le0,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_le0) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_abs__poly__def,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x) ) ) ),
file('theBenchmark.p',fact_abs__poly__def) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [V_q,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q) ),
file('theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_diff__poly__code_I2_J,axiom,
! [V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
file('theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_le__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ),
file('theBenchmark.p',fact_le__diff__iff) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [V_n,V_m,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_eq__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_diff__diff__cancel,axiom,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ),
file('theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_diff__le__mono,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)) ),
file('theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ),
file('theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_diff__commute,axiom,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j),
file('theBenchmark.p',fact_diff__commute) ).
fof(fact_diff__le__self,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m),
file('theBenchmark.p',fact_diff__le__self) ).
fof(fact_le__number__of,axiom,
! [V_y_2,V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_le__number__of) ).
fof(fact_le__refl,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_le__refl) ).
fof(fact_nat__le__linear,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_nat__le__linear) ).
fof(fact_eq__imp__le,axiom,
! [V_n,V_m] :
( V_m = V_n
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_eq__imp__le) ).
fof(fact_le__trans,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ),
file('theBenchmark.p',fact_le__trans) ).
fof(fact_le__antisym,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_le__antisym) ).
fof(fact_diff__is__0__eq_H,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_diff__is__0__eq,axiom,
! [V_n_2,V_m_2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
file('theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_le__0__eq,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_le__0__eq) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_less__or__eq__imp__le,axiom,
! [V_n,V_m] :
( ( V_m = V_n
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_less__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ),
file('theBenchmark.p',fact_less__diff__iff) ).
fof(fact_diff__less__mono,axiom,
! [V_c,V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ),
file('theBenchmark.p',fact_diff__less__mono) ).
fof(fact_le__neq__implies__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( V_m != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_less__imp__le__nat,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_le__eq__less__or__eq,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
<=> ( V_m_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
file('theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
<=> ( V_m_2 != V_n_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__less__le) ).
fof(fact_seq__suble,axiom,
! [V_n_2,V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ),
file('theBenchmark.p',fact_seq__suble) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_le__imp__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ),
file('theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_neg__le__iff__le,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_minus__le__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ),
file('theBenchmark.p',fact_minus__le__iff) ).
fof(fact_le__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ),
file('theBenchmark.p',fact_le__minus__iff) ).
fof(fact_abs__le__D1,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_abs__le__D1) ).
fof(fact_abs__ge__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
file('theBenchmark.p',fact_abs__ge__self) ).
fof(fact_le__special_I3_J,axiom,
! [V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) ) ),
file('theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_le__special_I1_J,axiom,
! [V_y_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) ) ),
file('theBenchmark.p',fact_le__special_I1_J) ).
fof(fact_le__iff__diff__le__0,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [V_wa_2,V_v_2,T_a] :
( ( class_Orderings_Olinorder(T_a)
& class_Int_Onumber(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
<=> ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) ) ),
file('theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_minus__le__self__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_le__minus__self__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_neg__0__le__iff__le,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_divide__right__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_divide__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_divide__right__mono) ).
fof(fact_divide__le__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_zero__le__divide__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_abs__of__nonneg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ),
file('theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__le__zero__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_abs__ge__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
file('theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_abs__triangle__ineq2__sym,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) ),
file('theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
fof(fact_abs__triangle__ineq2,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_abs__triangle__ineq2) ).
fof(fact_abs__triangle__ineq3,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_abs__le__D2,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ),
file('theBenchmark.p',fact_abs__le__D2) ).
fof(fact_abs__leI,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) ) ) ),
file('theBenchmark.p',fact_abs__leI) ).
fof(fact_abs__le__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__ge__minus__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
file('theBenchmark.p',fact_abs__ge__minus__self) ).
fof(fact_divide__nonpos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_divide__nonpos__neg) ).
fof(fact_divide__nonpos__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_divide__nonpos__pos) ).
fof(fact_frac__le,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ),
file('theBenchmark.p',fact_frac__le) ).
fof(fact_frac__less,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ),
file('theBenchmark.p',fact_frac__less) ).
fof(fact_frac__less2,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
=> ( c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ),
file('theBenchmark.p',fact_frac__less2) ).
fof(fact_divide__nonneg__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_divide__nonneg__neg) ).
fof(fact_divide__nonneg__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_divide__nonneg__pos) ).
fof(fact_abs__of__nonpos,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ),
file('theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__minus__le__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_diffs0__imp__equal,axiom,
! [V_n,V_m] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_diff__self__eq__0,axiom,
! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_diff__0__eq__0,axiom,
! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_nat__less__cases,axiom,
! [V_P_2,V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> ( ( V_m_2 = V_n_2
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
fof(fact_diff__less__mono2,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ),
file('theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_less__imp__diff__less,axiom,
! [V_n,V_k,V_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ),
file('theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_less__not__refl3,axiom,
! [V_t,V_s] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
=> V_s != V_t ),
file('theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> V_m != V_n ),
file('theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__irrefl__nat,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_linorder__neqE__nat,axiom,
! [V_y,V_x] :
( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_nat__neq__iff,axiom,
! [V_n_2,V_m_2] :
( V_m_2 != V_n_2
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_less__not__refl,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__not__refl) ).
fof(fact_poly__zero,axiom,
! [V_pa_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
<=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_poly__zero) ).
fof(fact_poly__eq__iff,axiom,
! [V_q_2,V_pa_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
<=> V_pa_2 = V_q_2 ) ),
file('theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_gr0I,axiom,
! [V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
file('theBenchmark.p',fact_gr0I) ).
fof(fact_gr__implies__not0,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_diff__less,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ),
file('theBenchmark.p',fact_diff__less) ).
fof(fact_psize__eq__0__iff,axiom,
! [V_pa_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_order__root,axiom,
! [V_a_2,V_pa_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_order__root) ).
fof(fact_order__refl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ),
file('theBenchmark.p',fact_order__refl) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_poly__cont,axiom,
! [V_p,V_z,V_e] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)
=> ? [B_d] :
( ! [B_w] :
( ( 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_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,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),V_z))),V_e) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ) ),
file('theBenchmark.p',fact_poly__cont) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) ),
file('theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(fact_decseq__def,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Odecseq(T_a,V_X_2)
<=> ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ),
file('theBenchmark.p',fact_decseq__def) ).
fof(fact_compl__mono,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ),
file('theBenchmark.p',fact_compl__mono) ).
fof(fact_rp,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
file('theBenchmark.p',fact_rp) ).
fof(fact_g_I1_J,axiom,
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(B_n)),v_r),
file('theBenchmark.p',fact_g_I1_J) ).
fof(fact_zle__antisym,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
=> V_z = V_w ) ),
file('theBenchmark.p',fact_zle__antisym) ).
fof(fact_zle__trans,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ),
file('theBenchmark.p',fact_zle__trans) ).
fof(fact_zle__linear,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
file('theBenchmark.p',fact_zle__linear) ).
fof(fact_zle__refl,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w),
file('theBenchmark.p',fact_zle__refl) ).
fof(fact_rel__simps_I34_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I34_J) ).
fof(fact_less__eq__int__code_I16_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__eq__int__code_I16_J) ).
fof(fact_rel__simps_I19_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('theBenchmark.p',fact_rel__simps_I19_J) ).
fof(fact_rel__simps_I31_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I31_J) ).
fof(fact_less__eq__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__eq__int__code_I13_J) ).
fof(fact_real__less__def,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__less__def) ).
fof(fact_less__eq__real__def,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_zless__le,axiom,
! [V_wa_2,V_za_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
<=> ( V_za_2 != V_wa_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) ) ),
file('theBenchmark.p',fact_zless__le) ).
fof(fact_less__eq__number__of__int__code,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_less__eq__number__of__int__code) ).
fof(fact_rel__simps_I22_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I22_J) ).
fof(fact_rel__simps_I32_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I32_J) ).
fof(fact_less__eq__int__code_I14_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__eq__int__code_I14_J) ).
fof(fact_rel__simps_I21_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I21_J) ).
fof(fact_rel__simps_I27_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) ),
file('theBenchmark.p',fact_rel__simps_I27_J) ).
fof(fact_norm__ge__zero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
file('theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_real__0__le__divide__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
file('theBenchmark.p',fact_real__0__le__divide__iff) ).
fof(fact_real__le__eq__diff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__le__eq__diff) ).
fof(fact_abs__le__interval__iff,axiom,
! [V_ra_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) ) ),
file('theBenchmark.p',fact_abs__le__interval__iff) ).
fof(fact_norm__le__zero__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_eq__number__of__0,axiom,
! [V_v_2] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ),
file('theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_eq__0__number__of,axiom,
! [V_v_2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ),
file('theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_rel__simps_I5_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I5_J) ).
fof(fact_rel__simps_I29_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ),
file('theBenchmark.p',fact_rel__simps_I29_J) ).
fof(fact_rel__simps_I15_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I15_J) ).
fof(fact_less__int__code_I14_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__int__code_I14_J) ).
fof(fact_rel__simps_I33_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I33_J) ).
fof(fact_less__eq__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__eq__int__code_I15_J) ).
fof(fact_linorder__le__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_le__funE,axiom,
! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funE) ).
fof(fact_xt1_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_xt1_I5_J,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__trans) ).
fof(fact_order__antisym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I4_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I4_J) ).
fof(fact_ord__le__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__le__eq__trans) ).
fof(fact_xt1_I3_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I3_J) ).
fof(fact_ord__eq__le__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__le__trans) ).
fof(fact_order__antisym__conv,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_le__funD,axiom,
! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funD) ).
fof(fact_order__eq__refl,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( V_x = V_y
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__eq__refl) ).
fof(fact_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_x_2 = V_y_2
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__eq__iff) ).
fof(fact_linorder__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__linear) ).
fof(fact_le__fun__def,axiom,
! [V_ga_2,V_fa_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
<=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_ga_2,B_x)) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
fof(fact_le__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ),
file('theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_order__less__irrefl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ),
file('theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_linorder__neq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x_2 != V_y_2
<=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ),
file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__neqE) ).
fof(fact_less__imp__neq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_x != V_y ) ),
file('theBenchmark.p',fact_less__imp__neq) ).
fof(fact_order__less__not__sym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__imp__not__less,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__imp__not__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_x != V_y ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_y != V_x ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__asym_H,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ),
file('theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_xt1_I9_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_ord__eq__less__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__less__trans) ).
fof(fact_xt1_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I1_J) ).
fof(fact_ord__less__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__less__eq__trans) ).
fof(fact_xt1_I2_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I2_J) ).
fof(fact_order__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_order__less__asym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__asym) ).
fof(fact_linorder__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( V_x != V_y
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__cases) ).
fof(fact_norm__triangle__ineq2,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_norm__triangle__ineq2) ).
fof(fact_minus__apply,axiom,
! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
( class_Groups_Ominus(T_a)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_minus__apply) ).
fof(fact_double__compl,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ),
file('theBenchmark.p',fact_double__compl) ).
fof(fact_uminus__apply,axiom,
! [V_x_2,V_A_2,T_b,T_a] :
( class_Groups_Ouminus(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_uminus__apply) ).
fof(fact_compl__eq__compl__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_norm__triangle__ineq3,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_norm__triangle__ineq3) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__le__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__le__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_leI,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_not__leE) ).
fof(fact_linorder__antisym__conv1,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_order__neq__le__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_xt1_I12_J,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_leD,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_leD) ).
fof(fact_order__less__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_a != V_b
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_a != V_b
=> c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__less__le__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I7_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__le__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_xt1_I8_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_compl__le__compl__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(fact_number__of1,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_n)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_n))) ) ),
file('theBenchmark.p',fact_number__of1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_s1m,axiom,
! [V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_z))) ),
file('theBenchmark.p',fact_s1m) ).
fof(fact_number__of2,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
file('theBenchmark.p',fact_number__of2) ).
fof(fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096,axiom,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r) ),
file('theBenchmark.p',fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096) ).
fof(fact_wr,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
file('theBenchmark.p',fact_wr) ).
fof(fact_s,axiom,
! [B_y] :
( ? [B_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
& ? [B_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,v_s____) ),
file('theBenchmark.p',fact_s) ).
fof(fact_less__fun__def,axiom,
! [V_ga_2,V_fa_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2,V_fa_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
fof(fact_real__le__antisym,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
=> V_z = V_w ) ),
file('theBenchmark.p',fact_real__le__antisym) ).
fof(fact_real__le__trans,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ),
file('theBenchmark.p',fact_real__le__trans) ).
fof(fact_real__le__linear,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
file('theBenchmark.p',fact_real__le__linear) ).
fof(fact_real__le__refl,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
file('theBenchmark.p',fact_real__le__refl) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096,axiom,
( ? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
file('theBenchmark.p',fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096) ).
fof(fact_s1,axiom,
! [V_y_2] :
( ? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),V_y_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) ),
file('theBenchmark.p',fact_s1) ).
fof(fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096,axiom,
! [V_y_2] :
( ? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)))),V_y_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) ),
file('theBenchmark.p',fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096) ).
fof(fact_mth2,axiom,
? [B_z] :
! [B_x] :
( ? [B_za] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_za)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_za),v_r) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_z) ),
file('theBenchmark.p',fact_mth2) ).
fof(fact_calculation,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
=> ? [B_z] :
! [B_w] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_w),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_w))) ) ),
file('theBenchmark.p',fact_calculation) ).
fof(fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096,axiom,
! [V_x_2,V_z_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r)
=> ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_z_2)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('theBenchmark.p',fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),
file('theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096,axiom,
? [B_s] :
! [B_y] :
( ? [B_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
& ? [B_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ),
file('theBenchmark.p',fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096) ).
fof(fact_mth1,axiom,
? [B_x,B_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
file('theBenchmark.p',fact_mth1) ).
fof(fact_tsub__def,axiom,
! [V_x,V_y] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ),
file('theBenchmark.p',fact_tsub__def) ).
fof(fact_one__reorient,axiom,
! [V_x_2,T_a] :
( class_Groups_Oone(T_a)
=> ( c_Groups_Oone__class_Oone(T_a) = V_x_2
<=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_one__reorient) ).
fof(fact_norm__one,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_norm__one) ).
fof(fact_poly__1,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_poly__1) ).
fof(fact_zero__neq__one,axiom,
! [T_a] :
( class_Rings_Ozero__neq__one(T_a)
=> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [T_a] :
( class_Rings_Ozero__neq__one(T_a)
=> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_one__neq__zero) ).
fof(fact_divide__1,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_divide__1) ).
fof(fact_abs__one,axiom,
! [T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__one) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_not__one__le__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_zero__le__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_zero__le__one) ).
fof(fact_zero__less__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_zero__less__one) ).
fof(fact_not__one__less__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_right__inverse__eq,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
<=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_divide__self,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_divide__self) ).
fof(fact_divide__self__if,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
& ( V_a = c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divide__self__if) ).
fof(fact_numeral__1__eq__1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_numeral__1__eq__1) ).
fof(fact_semiring__norm_I110_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ),
file('theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_tsub__eq,axiom,
! [V_x,V_y] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ),
file('theBenchmark.p',fact_tsub__eq) ).
fof(fact_le__special_I4_J,axiom,
! [V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ),
file('theBenchmark.p',fact_le__special_I4_J) ).
fof(fact_le__special_I2_J,axiom,
! [V_y_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ),
file('theBenchmark.p',fact_le__special_I2_J) ).
fof(fact_less__special_I4_J,axiom,
! [V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ),
file('theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_less__special_I2_J,axiom,
! [V_y_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ),
file('theBenchmark.p',fact_less__special_I2_J) ).
fof(fact_half,axiom,
! [T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_half) ).
fof(fact_power2__less__imp__less,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_power2__less__imp__less) ).
fof(fact_g_I2_J,axiom,
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(B_n))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))),
file('theBenchmark.p',fact_g_I2_J) ).
fof(fact_poly__bound__exists,axiom,
! [V_p,V_r] :
? [B_m] :
( ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),V_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_z)),B_m) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
file('theBenchmark.p',fact_poly__bound__exists) ).
fof(fact_lemma__real__divide__sqrt__less,axiom,
! [V_u] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u) ),
file('theBenchmark.p',fact_lemma__real__divide__sqrt__less) ).
fof(fact_lessI,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_lessI) ).
fof(fact_Suc__mono,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_Suc__mono) ).
fof(fact_zero__less__Suc,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
file('theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_real__sqrt__eq__1__iff,axiom,
! [V_x_2] :
( c_NthRoot_Osqrt(V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__eq__1__iff) ).
fof(fact_real__sqrt__one,axiom,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__sqrt__one) ).
fof(fact_real__of__nat__Suc,axiom,
! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_real__of__nat__Suc) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__1) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_One__nat__def) ).
fof(fact_real__of__nat__one,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__one) ).
fof(fact_diff__Suc__1,axiom,
! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
file('theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_norm__power__ineq,axiom,
! [V_n,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n)) ),
file('theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_norm__triangle__ineq,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
file('theBenchmark.p',fact_norm__triangle__ineq) ).
fof(fact_real__sqrt__le__mono,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ),
file('theBenchmark.p',fact_real__sqrt__le__mono) ).
fof(fact_real__sqrt__le__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_NthRoot_Osqrt(V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__le__iff) ).
fof(fact_realpow__two__disj,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_x_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(T_a,V_y_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_realpow__two__disj) ).
fof(fact_add__number__of__diff1,axiom,
! [V_c,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c) ),
file('theBenchmark.p',fact_add__number__of__diff1) ).
fof(fact_real__sqrt__eq__0__iff,axiom,
! [V_x_2] :
( c_NthRoot_Osqrt(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__eq__0__iff) ).
fof(fact_real__sqrt__zero,axiom,
c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__sqrt__zero) ).
fof(fact_n__not__Suc__n,axiom,
! [V_n] : V_n != c_Nat_OSuc(V_n),
file('theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_Suc__n__not__n,axiom,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
file('theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_nat_Oinject,axiom,
! [V_nat_H_2,V_nat_2] :
( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
<=> V_nat_2 = V_nat_H_2 ),
file('theBenchmark.p',fact_nat_Oinject) ).
fof(fact_poly__power,axiom,
! [V_x,V_n,V_p,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),V_p,V_n)),V_x) = c_Power_Opower__class_Opower(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),V_n) ),
file('theBenchmark.p',fact_poly__power) ).
fof(fact_poly__add,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__add) ).
fof(fact_Suc__inject,axiom,
! [V_y,V_x] :
( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
=> V_x = V_y ),
file('theBenchmark.p',fact_Suc__inject) ).
fof(fact_real__of__nat__power,axiom,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_m,V_n)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),V_n),
file('theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_power__real__of__nat,axiom,
! [V_n,V_m] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),V_n) = c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_real__of__nat__inject,axiom,
! [V_m_2,V_n_2] :
( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
<=> V_n_2 = V_m_2 ),
file('theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_norm__power,axiom,
! [V_n,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n) ),
file('theBenchmark.p',fact_norm__power) ).
fof(fact_number__of__add,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__add) ).
fof(fact_add__number__of__eq,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ),
file('theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_add__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z) ),
file('theBenchmark.p',fact_add__number__of__left) ).
fof(fact_real__sqrt__power,axiom,
! [V_k,V_x] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),V_k),
file('theBenchmark.p',fact_real__sqrt__power) ).
fof(fact_real__sqrt__eq__iff,axiom,
! [V_y_2,V_x_2] :
( c_NthRoot_Osqrt(V_x_2) = c_NthRoot_Osqrt(V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_real__sqrt__eq__iff) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_add__left__cancel,axiom,
! [V_c_2,V_b_2,V_a_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
<=> V_b_2 = V_c_2 ) ),
file('theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__right__cancel,axiom,
! [V_c_2,V_a_2,V_b_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
<=> V_b_2 = V_c_2 ) ),
file('theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__ab__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__right__imp__eq,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ),
file('theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ),
file('theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__less__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_real__sqrt__minus,axiom,
! [V_x] : c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)),
file('theBenchmark.p',fact_real__sqrt__minus) ).
fof(fact_add__le__imp__le__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__imp__le__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__mono) ).
fof(fact_add__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ),
file('theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ),
file('theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__le__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_double__eq__0__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_add_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add__0__right) ).
fof(fact_double__zero__sym,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_add__0__left) ).
fof(fact_real__sqrt__divide,axiom,
! [V_y,V_x] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)),
file('theBenchmark.p',fact_real__sqrt__divide) ).
fof(fact_real__sqrt__less__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_NthRoot_Osqrt(V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__less__iff) ).
fof(fact_real__sqrt__less__mono,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ),
file('theBenchmark.p',fact_real__sqrt__less__mono) ).
fof(fact_norm__add__less,axiom,
! [V_s,V_y,V_r,V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ),
file('theBenchmark.p',fact_norm__add__less) ).
fof(fact_real__of__nat__Suc__gt__zero,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),
file('theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
fof(fact_diff__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ),
file('theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_add__diff__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ),
file('theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_minus__add__distrib,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ),
file('theBenchmark.p',fact_minus__add) ).
fof(fact_add__minus__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ),
file('theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_minus__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ),
file('theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_Zero__not__Suc,axiom,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
file('theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H),
file('theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Suc__not__Zero,axiom,
! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
file('theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_Suc__neq__Zero,axiom,
! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_add__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_divide_Oadd,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ),
file('theBenchmark.p',fact_divide_Oadd) ).
fof(fact_real__add__left__mono,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ),
file('theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_not__less__eq,axiom,
! [V_n_2,V_m_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ),
file('theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> ( V_m_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
file('theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__less__eq,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
<=> V_n_2 = V_m_2 ) ),
file('theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [V_m,V_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_less__SucI) ).
fof(fact_Suc__lessI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ( c_Nat_OSuc(V_m) != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ),
file('theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__trans__Suc,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ),
file('theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_less__SucE,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__SucE) ).
fof(fact_Suc__lessD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__less__SucD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_abs__add__abs,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ),
file('theBenchmark.p',fact_abs__add__abs) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
file('theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(fact_Suc__leD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__leD) ).
fof(fact_le__SucE,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> V_m = c_Nat_OSuc(V_n) ) ),
file('theBenchmark.p',fact_le__SucE) ).
fof(fact_le__SucI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_le__SucI) ).
fof(fact_Suc__le__mono,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
file('theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_le__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> ( V_m_2 = c_Nat_OSuc(V_n_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
file('theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_not__less__eq__eq,axiom,
! [V_n_2,V_m_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ),
file('theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_Suc__n__not__le__n,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n),
file('theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_diff__Suc__Suc,axiom,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_Suc__diff__diff,axiom,
! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k),
file('theBenchmark.p',fact_Suc__diff__diff) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('theBenchmark.p',fact_int__0__neq__1) ).
fof(fact_realpow__Suc__le__self,axiom,
! [V_n,V_r,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_r,c_Nat_OSuc(V_n)),V_r) ) ) ),
file('theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(fact_nat__less__real__le,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) ),
file('theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_norm__diff__triangle__ineq,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ),
file('theBenchmark.p',fact_norm__diff__triangle__ineq) ).
fof(fact_add__number__of__diff2,axiom,
! [V_w,V_c,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,V_c,c_Int_Onumber__class_Onumber__of(T_a,V_w))) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_c) ),
file('theBenchmark.p',fact_add__number__of__diff2) ).
fof(fact_Suc__pred_H,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_Suc__diff__1,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ),
file('theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_real__sqrt__sum__squares__triangle__ineq,axiom,
! [V_d,V_b,V_c,V_a] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__triangle__ineq) ).
fof(fact_real__sqrt__sum__squares__ge2,axiom,
! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__ge2) ).
fof(fact_real__sqrt__sum__squares__ge1,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__ge1) ).
fof(fact_real__sqrt__sum__squares__eq__cancel,axiom,
! [V_y,V_x] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_x
=> V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel) ).
fof(fact_real__sqrt__sum__squares__eq__cancel2,axiom,
! [V_y,V_x] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_y
=> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel2) ).
fof(fact_real__sqrt__sum__squares__ge__zero,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__ge__zero) ).
fof(fact_real__sqrt__ge__abs1,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_real__sqrt__ge__abs1) ).
fof(fact_real__sqrt__ge__abs2,axiom,
! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_real__sqrt__ge__abs2) ).
fof(fact_lemma__NBseq__def2,axiom,
! [V_X_2,T_b] :
( class_RealVector_Oreal__normed__vector(T_b)
=> ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_lemma__NBseq__def2) ).
fof(fact_lemma__NBseq__def,axiom,
! [V_X_2,T_b] :
( class_RealVector_Oreal__normed__vector(T_b)
=> ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_lemma__NBseq__def) ).
fof(fact_add__special_I3_J,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_add__special_I3_J) ).
fof(fact_add__special_I2_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w)) ),
file('theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_real__sqrt__ge__0__iff,axiom,
! [V_y_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__ge__0__iff) ).
fof(fact_real__sqrt__le__0__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__sqrt__le__0__iff) ).
fof(fact_real__sqrt__ge__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ),
file('theBenchmark.p',fact_real__sqrt__ge__zero) ).
fof(fact_real__sqrt__eq__zero__cancel,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_NthRoot_Osqrt(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_real__sqrt__eq__zero__cancel) ).
fof(fact_real__sqrt__gt__0__iff,axiom,
! [V_y_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__gt__0__iff) ).
fof(fact_real__sqrt__lt__0__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__sqrt__lt__0__iff) ).
fof(fact_real__sqrt__not__eq__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_NthRoot_Osqrt(V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__not__eq__zero) ).
fof(fact_real__sqrt__gt__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ),
file('theBenchmark.p',fact_real__sqrt__gt__zero) ).
fof(fact_real__sqrt__ge__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ),
file('theBenchmark.p',fact_real__sqrt__ge__one) ).
fof(fact_real__sqrt__le__1__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__sqrt__le__1__iff) ).
fof(fact_real__sqrt__ge__1__iff,axiom,
! [V_y_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__ge__1__iff) ).
fof(fact_real__sqrt__lt__1__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__sqrt__lt__1__iff) ).
fof(fact_real__sqrt__gt__1__iff,axiom,
! [V_y_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__gt__1__iff) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [V_n_2] :
( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__zero) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(fact_expand__Suc,axiom,
! [V_v] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('theBenchmark.p',fact_expand__Suc) ).
fof(fact_real__of__nat__less__iff,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ),
file('theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_add__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__increasing2,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__increasing) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_add__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_add__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__pos) ).
fof(fact_pos__add__strict,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_even__less__0__iff,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_real__of__nat__le__iff,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
file('theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_add__le__less__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_less__add__one,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_less__add__one) ).
fof(fact_right__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_right__minus) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_left__minus) ).
fof(fact_ab__left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_ab__left__minus) ).
fof(fact_minus__unique,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ),
file('theBenchmark.p',fact_minus__unique) ).
fof(fact_add__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ),
file('theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_diff__def,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_diff__def) ).
fof(fact_ab__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__minus__eq__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_add__numeral__0__right,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ),
file('theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_add__numeral__0,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ),
file('theBenchmark.p',fact_add__numeral__0) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n)) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_abs__triangle__ineq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ),
file('theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_gr0__conv__Suc,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
<=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ),
file('theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_less__Suc0,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_less__Suc0) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> ( ? [B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
& V_m_2 = c_Nat_OSuc(B_j) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_Suc__le__lessD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_le__less__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
<=> V_n_2 = V_m_2 ) ),
file('theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__leI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
file('theBenchmark.p',fact_Suc__leI) ).
fof(fact_le__imp__less__Suc,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_Suc__le__eq,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__Suc__eq__le,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
file('theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_less__eq__Suc__le,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ),
file('theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_diff__less__Suc,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
file('theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_Suc__diff__le,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
file('theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_real__add__eq__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ),
file('theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_real__add__minus__iff,axiom,
! [V_a_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = V_a_2 ),
file('theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_int__0__less__1,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_int__0__less__1) ).
fof(fact_real__diff__def,axiom,
! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)),
file('theBenchmark.p',fact_real__diff__def) ).
fof(fact_minus__real__def,axiom,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)),
file('theBenchmark.p',fact_minus__real__def) ).
fof(fact_abs__minus__add__cancel,axiom,
! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))),
file('theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(fact_real__sqrt__abs,axiom,
! [V_x] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),
file('theBenchmark.p',fact_real__sqrt__abs) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
fof(fact_two__realpow__gt,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)),
file('theBenchmark.p',fact_two__realpow__gt) ).
fof(fact_realpow__two__sum__zero__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_realpow__two__sum__zero__iff) ).
fof(fact_real__sqrt__sum__squares__less,axiom,
! [V_y,V_u,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(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_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(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_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ),
file('theBenchmark.p',fact_real__sqrt__sum__squares__less) ).
fof(fact_subseq__Suc__iff,axiom,
! [V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
<=> ! [B_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))) ),
file('theBenchmark.p',fact_subseq__Suc__iff) ).
fof(fact_real__sqrt__pow2__iff,axiom,
! [V_x_2] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x_2
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
file('theBenchmark.p',fact_real__sqrt__pow2__iff) ).
fof(fact_real__sqrt__pow2,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x ),
file('theBenchmark.p',fact_real__sqrt__pow2) ).
fof(fact_real__sqrt__unique,axiom,
! [V_x,V_y] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> c_NthRoot_Osqrt(V_x) = V_y ) ),
file('theBenchmark.p',fact_real__sqrt__unique) ).
fof(fact_real__sqrt__pow2__gt__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_real__sqrt__pow2__gt__zero) ).
fof(fact_lemma__sqrt__hcomplex__capprox,axiom,
! [V_y,V_x,V_u] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,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,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ) ) ) ),
file('theBenchmark.p',fact_lemma__sqrt__hcomplex__capprox) ).
fof(fact_sum__power2__ge__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('theBenchmark.p',fact_sum__power2__ge__zero) ).
fof(fact_sum__power2__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_not__sum__power2__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__sum__power2__lt__zero) ).
fof(fact_sum__power2__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
fof(fact_add__pos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__strict__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__neg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_zero__less__two,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_zero__less__two) ).
fof(fact_number__of__Bit0,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__Bit0) ).
fof(fact_less__half__sum,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))) ) ),
file('theBenchmark.p',fact_less__half__sum) ).
fof(fact_gt__half__sum,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b) ) ),
file('theBenchmark.p',fact_gt__half__sum) ).
fof(fact_number__of__Bit1,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_abs__triangle__ineq4,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ),
file('theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ),
file('theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_real__of__nat__diff,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ),
file('theBenchmark.p',fact_real__of__nat__diff) ).
fof(fact_norm__triangle__ineq4,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))) ),
file('theBenchmark.p',fact_norm__triangle__ineq4) ).
fof(fact_Suc__pred,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ),
file('theBenchmark.p',fact_Suc__pred) ).
fof(fact_diff__Suc__less,axiom,
! [V_i,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n) ),
file('theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_zero__le__zpower__abs,axiom,
! [V_n,V_x] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x),V_n)),
file('theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_norm__diff__ineq,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_real__0__le__add__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ),
file('theBenchmark.p',fact_real__0__le__add__iff) ).
fof(fact_real__add__le__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ),
file('theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_real__0__less__add__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ),
file('theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_real__add__less__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ),
file('theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
file('theBenchmark.p',fact_abs__add__one__not__less__self) ).
fof(fact_Numeral1__eq1__nat,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(fact_nat__numeral__1__eq__1,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__numeral__1__eq__1) ).
fof(fact_abs__sum__triangle__ineq,axiom,
! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))),
file('theBenchmark.p',fact_abs__sum__triangle__ineq) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_one__is__num__one) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [V_za_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) ),
file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zle__diff1__eq,axiom,
! [V_za_2,V_wa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ),
file('theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_zabs__less__one__iff,axiom,
! [V_za_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> V_za_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ),
file('theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_numeral__1__eq__Suc__0,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
fof(fact_numeral__3__eq__3,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('theBenchmark.p',fact_numeral__3__eq__3) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2),V_n_2))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))),
file('theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_zero__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_zero__power2) ).
fof(fact_zero__eq__power2,axiom,
! [V_a_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_one__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_one__power2) ).
fof(fact_power2__minus,axiom,
! [V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_power2__minus) ).
fof(fact_abs__power2,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_abs__power2) ).
fof(fact_power2__abs,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_power2__abs) ).
fof(fact_one__add__one__is__two,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_one__add__one__is__two) ).
fof(fact_semiring__norm_I115_J,axiom,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_numeral__2__eq__2,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_numeral__2__eq__2) ).
fof(fact_Suc__diff__eq__diff__pred,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).
fof(fact_real__sqrt__two__ge__zero,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_real__sqrt__two__ge__zero) ).
fof(fact_real__sqrt__two__gt__zero,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_real__sqrt__two__gt__zero) ).
fof(fact_real__sqrt__two__gt__one,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_real__sqrt__two__gt__one) ).
fof(fact_zero__le__power2,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_zero__le__power2) ).
fof(fact_power2__le__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_power2__eq__imp__eq,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> V_x = V_y ) ) ) ),
file('theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_power2__less__0,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_power2__less__0) ).
fof(fact_zero__less__power2,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__less__power2) ).
fof(fact_power2__eq__1__iff,axiom,
! [V_a_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a)
<=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_a_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power2__eq__1__iff) ).
fof(fact_less__2__cases,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( V_n = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_less__2__cases) ).
fof(fact_two__realpow__ge__one,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)),
file('theBenchmark.p',fact_two__realpow__ge__one) ).
fof(fact_realpow__square__minus__le,axiom,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_realpow__square__minus__le) ).
fof(fact_real__less__half__sum,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_real__less__half__sum) ).
fof(fact_real__gt__half__sum,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y) ),
file('theBenchmark.p',fact_real__gt__half__sum) ).
fof(fact_th,axiom,
! [B_n] :
? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
file('theBenchmark.p',fact_th) ).
fof(fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096,axiom,
? [B_f] :
! [B_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(B_f,B_x))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_x)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B_f,B_x)),v_r) ),
file('theBenchmark.p',fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) ).
fof(fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096,axiom,
! [V_n_2] :
? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n_2)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
file('theBenchmark.p',fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096) ).
fof(fact_cos__x__y__le__one,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_cos__x__y__le__one) ).
fof(fact_real__average__minus__first,axiom,
! [V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_real__average__minus__first) ).
fof(fact_zless__add1__eq,axiom,
! [V_za_2,V_wa_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( V_wa_2 = V_za_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ),
file('theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_Suc__eq__plus1,axiom,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_Bit1__def,axiom,
! [V_k] : c_Int_OBit1(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k),
file('theBenchmark.p',fact_Bit1__def) ).
fof(fact_odd__nonzero,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_odd__nonzero) ).
fof(fact_le__Suc__ex__iff,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
<=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ),
file('theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_add__Suc__right,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_add__Suc__right) ).
fof(fact_add__Suc,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_zadd__commute,axiom,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
file('theBenchmark.p',fact_zadd__commute) ).
fof(fact_zadd__left__commute,axiom,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
file('theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_zadd__assoc,axiom,
! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
file('theBenchmark.p',fact_zadd__assoc) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n,
file('theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_add__is__0,axiom,
! [V_n_2,V_m_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_add__is__0) ).
fof(fact_add__eq__self__zero,axiom,
! [V_n,V_m] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
=> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_zadd__0,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z,
file('theBenchmark.p',fact_zadd__0) ).
fof(fact_zadd__0__right,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zadd__0__right) ).
fof(fact_add__Pls,axiom,
! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k,
file('theBenchmark.p',fact_add__Pls) ).
fof(fact_add__Pls__right,axiom,
! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
file('theBenchmark.p',fact_add__Pls__right) ).
fof(fact_Bit0__def,axiom,
! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k),
file('theBenchmark.p',fact_Bit0__def) ).
fof(fact_add__Bit0__Bit0,axiom,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_not__add__less1,axiom,
! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i),
file('theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i),
file('theBenchmark.p',fact_not__add__less2) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [V_n_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
file('theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_trans__less__add1,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
file('theBenchmark.p',fact_trans__less__add1) ).
fof(fact_trans__less__add2,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
file('theBenchmark.p',fact_trans__less__add2) ).
fof(fact_add__less__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_add__less__mono1) ).
fof(fact_add__less__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
file('theBenchmark.p',fact_add__less__mono) ).
fof(fact_less__add__eq__less,axiom,
! [V_n,V_m,V_l,V_k] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__lessD1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ),
file('theBenchmark.p',fact_add__lessD1) ).
fof(fact_zadd__left__mono,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ),
file('theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_zadd__strict__right__mono,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ),
file('theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_add__leE,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ),
file('theBenchmark.p',fact_add__leE) ).
fof(fact_add__leD1,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
file('theBenchmark.p',fact_add__leD2) ).
fof(fact_add__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
file('theBenchmark.p',fact_add__le__mono) ).
fof(fact_add__le__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_add__le__mono1) ).
fof(fact_trans__le__add2,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
file('theBenchmark.p',fact_trans__le__add2) ).
fof(fact_trans__le__add1,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
file('theBenchmark.p',fact_trans__le__add1) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [V_n_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
file('theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_le__iff__add,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
<=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ),
file('theBenchmark.p',fact_le__iff__add) ).
fof(fact_le__add1,axiom,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)),
file('theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_le__add2) ).
fof(fact_plus__numeral__code_I9_J,axiom,
! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),
file('theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_diff__cancel2,axiom,
! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__cancel,axiom,
! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__diff__left,axiom,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)),
file('theBenchmark.p',fact_diff__diff__left) ).
fof(fact_diff__add__inverse,axiom,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_add__poly__code_I1_J,axiom,
! [V_q,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ),
file('theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
file('theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_zminus__zadd__distrib,axiom,
! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_complex__diff__def,axiom,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
file('theBenchmark.p',fact_complex__diff__def) ).
fof(fact_add__nat__number__of,axiom,
! [V_v_H,V_v] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) ) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H) ) ),
file('theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_add__Bit1__Bit0,axiom,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_add__Bit1__Bit0) ).
fof(fact_add__Bit0__Bit1,axiom,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_add__Bit0__Bit1) ).
fof(fact_one__is__add,axiom,
! [V_n_2,V_m_2] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
<=> ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [V_n_2,V_m_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_add__is__1) ).
fof(fact_add__gr__0,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ) ),
file('theBenchmark.p',fact_add__gr__0) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_less__iff__Suc__add,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
<=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ),
file('theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__add__Suc2,axiom,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
file('theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_less__add__Suc1,axiom,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
file('theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_odd__less__0,axiom,
! [V_za_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_odd__less__0) ).
fof(fact_zadd__zless__mono,axiom,
! [V_z,V_z_H,V_w,V_w_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ),
file('theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_zle__add1__eq__le,axiom,
! [V_za_2,V_wa_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) ),
file('theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_add1__zle__eq,axiom,
! [V_za_2,V_wa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zless__imp__add1__zle,axiom,
! [V_z,V_w] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ),
file('theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_diff__add__0,axiom,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__add__0) ).
fof(fact_add__diff__inverse,axiom,
! [V_n,V_m] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
file('theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__diff__conv,axiom,
! [V_k_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ),
file('theBenchmark.p',fact_less__diff__conv) ).
fof(fact_diff__add__assoc2,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ),
file('theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_add__diff__assoc2,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_le__imp__diff__is__add,axiom,
! [V_k_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
<=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ),
file('theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_le__add__diff__inverse2,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_le__diff__conv2,axiom,
! [V_i_2,V_j_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ),
file('theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_add__diff__assoc,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_le__add__diff__inverse,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_le__add__diff,axiom,
! [V_m,V_n,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)) ),
file('theBenchmark.p',fact_le__add__diff) ).
fof(fact_le__diff__conv,axiom,
! [V_i_2,V_k_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) ),
file('theBenchmark.p',fact_le__diff__conv) ).
fof(fact_diff__diff__right,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ),
file('theBenchmark.p',fact_diff__diff__right) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_real__of__nat__add,axiom,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
file('theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_diff__int__def__symmetric,axiom,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
file('theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_diff__int__def) ).
fof(fact_diff__number__of__eq,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) ),
file('theBenchmark.p',fact_diff__number__of__eq) ).
fof(fact_le__imp__0__less,axiom,
! [V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ),
file('theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_add__eq__if,axiom,
! [V_n,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) )
& ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n ) ),
file('theBenchmark.p',fact_add__eq__if) ).
fof(fact_nat__diff__split,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
<=> ( ! [B_d] :
( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
=> hBOOL(hAPP(V_P_2,B_d)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_nat__diff__split) ).
fof(fact_nat__diff__split__asm,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
<=> ~ ( ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [V_m,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [V_m,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))),
file('theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_complex__mod__triangle__ineq2,axiom,
! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)),
file('theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
fof(fact_minus__numeral__code_I6_J,axiom,
! [V_w,V_v] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),
file('theBenchmark.p',fact_minus__numeral__code_I6_J) ).
fof(fact_Suc3__eq__add__3,axiom,
! [V_n] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),V_n),
file('theBenchmark.p',fact_Suc3__eq__add__3) ).
fof(fact_nat__1__add__1,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('theBenchmark.p',fact_nat__1__add__1) ).
fof(fact_add__2__eq__Suc,axiom,
! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n) = c_Nat_OSuc(c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_add__2__eq__Suc) ).
fof(fact_add__2__eq__Suc_H,axiom,
! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_add__2__eq__Suc_H) ).
fof(fact_diff__special_I2_J,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_diff__special_I2_J) ).
fof(fact_diff__special_I1_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) ),
file('theBenchmark.p',fact_diff__special_I1_J) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ),
file('theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_less__one__imp__sqr__less__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_less__one__imp__sqr__less__one) ).
fof(fact_real__average__minus__second,axiom,
! [V_a,V_b] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_real__average__minus__second) ).
fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( V_x = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_int__pos__lt__two__imp__zero__or__one) ).
fof(fact_real__sum__of__halves,axiom,
! [V_x] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x,
file('theBenchmark.p',fact_real__sum__of__halves) ).
fof(fact_power__strict__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__strict__mono) ).
fof(fact_nat__add__commute,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
file('theBenchmark.p',fact_nat__add__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
file('theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_nat__add__assoc,axiom,
! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
file('theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__add__left__cancel,axiom,
! [V_n_2,V_m_2,V_k_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_nat__add__right__cancel,axiom,
! [V_n_2,V_k_2,V_m_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_field__power__not__zero,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_power__one,axiom,
! [V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__one) ).
fof(fact_power__divide,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ),
file('theBenchmark.p',fact_power__divide) ).
fof(fact_power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n) ),
file('theBenchmark.p',fact_power__abs) ).
fof(fact_power__one__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ),
file('theBenchmark.p',fact_power__one__right) ).
fof(fact_power__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ),
file('theBenchmark.p',fact_power__mono) ).
fof(fact_zero__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ),
file('theBenchmark.p',fact_zero__le__power) ).
fof(fact_zero__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ),
file('theBenchmark.p',fact_zero__less__power) ).
fof(fact_one__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ),
file('theBenchmark.p',fact_one__le__power) ).
fof(fact_power__eq__0__iff,axiom,
! [V_n_2,V_a_2,T_a] :
( ( class_Rings_Ozero__neq__one(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Omult__zero(T_a)
& class_Power_Opower(T_a) )
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_power__inject__exp,axiom,
! [V_n_2,V_m_2,V_a_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,V_m_2) = c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
fof(fact_power__0__Suc,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_power__0__Suc) ).
fof(fact_nonzero__power__divide,axiom,
! [V_n,V_a,V_b,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ),
file('theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_power__0,axiom,
! [V_a,T_a] :
( class_Power_Opower(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__0) ).
fof(fact_power__one__over,axiom,
! [V_n,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n) ),
file('theBenchmark.p',fact_power__one__over) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(fact_abs__power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)) = c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) ),
file('theBenchmark.p',fact_abs__power__minus) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [V_m_2,V_x_2] :
( c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_power__Suc__0,axiom,
! [V_n] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_power__Suc__0) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ),
file('theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_power__less__imp__less__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_power__le__imp__le__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)),c_Power_Opower__class_Opower(T_a,V_b,c_Nat_OSuc(V_n)))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_power__inject__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) = c_Power_Opower__class_Opower(T_a,V_b,c_Nat_OSuc(V_n))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> V_a = V_b ) ) ) ),
file('theBenchmark.p',fact_power__inject__base) ).
fof(fact_power__0__left,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power__0__left) ).
fof(fact_zero__le__power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)) ),
file('theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_power__gt1,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n))) ) ),
file('theBenchmark.p',fact_power__gt1) ).
fof(fact_abs__diff__less__iff,axiom,
! [V_ra_2,V_a_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
<=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) ) ) ),
file('theBenchmark.p',fact_abs__diff__less__iff) ).
fof(fact_power__strict__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
fof(fact_power__eq__0__iff__number__of,axiom,
! [V_wa_2,V_a_2,T_a] :
( ( class_Rings_Ozero__neq__one(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Omult__zero(T_a)
& class_Power_Opower(T_a) )
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff__number__of) ).
fof(fact_nat__one__le__power,axiom,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n)) ),
file('theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_zero__less__power__nat__eq__number__of,axiom,
! [V_wa_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).
fof(fact_power__Suc__less__one,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)) ) ) ),
file('theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_power__strict__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_a,V_n) = c_Power_Opower__class_Opower(T_a,V_b,V_n)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> V_a = V_b ) ) ) ) ),
file('theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_power__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__decreasing) ).
fof(fact_power__le__imp__le__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_one__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ),
file('theBenchmark.p',fact_one__less__power) ).
fof(fact_power__0__left__number__of,axiom,
! [V_w,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power__0__left__number__of) ).
fof(fact_power__diff,axiom,
! [V_m,V_n,V_a,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ),
file('theBenchmark.p',fact_power__diff) ).
fof(fact_csqrt,axiom,
! [V_z] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z,
file('theBenchmark.p',fact_csqrt) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_add__0__iff,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_add__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_eq__special_I4_J,axiom,
! [V_x_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) ) ),
file('theBenchmark.p',fact_eq__special_I4_J) ).
fof(fact_eq__special_I2_J,axiom,
! [V_y_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__special_I2_J) ).
fof(fact_iszero__def,axiom,
! [V_za_2,T_a] :
( class_Rings_Osemiring__1(T_a)
=> ( c_Int_Oiszero(T_a,V_za_2)
<=> V_za_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_iszero__def) ).
fof(fact_iszero__0,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_iszero__0) ).
fof(fact_not__iszero__1,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_not__iszero__1) ).
fof(fact_iszero__number__of__Bit1,axiom,
! [V_w,T_a] :
( ( class_Int_Oring__char__0(T_a)
& class_Int_Onumber__ring(T_a) )
=> ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w))) ),
file('theBenchmark.p',fact_iszero__number__of__Bit1) ).
fof(fact_iszero__Numeral0,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) ),
file('theBenchmark.p',fact_iszero__Numeral0) ).
fof(fact_iszero__number__of__Bit0,axiom,
! [V_wa_2,T_a] :
( ( class_Int_Oring__char__0(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2)))
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) ),
file('theBenchmark.p',fact_iszero__number__of__Bit0) ).
fof(fact_not__iszero__Numeral1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_not__iszero__Numeral1) ).
fof(fact_eq__number__of__eq,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__number__of__eq) ).
fof(fact_eq__special_I1_J,axiom,
! [V_y_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__special_I1_J) ).
fof(fact_eq__special_I3_J,axiom,
! [V_x_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) ) ),
file('theBenchmark.p',fact_eq__special_I3_J) ).
fof(fact_natceiling__eq,axiom,
! [V_x,V_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_natceiling__eq) ).
fof(fact_real__sqrt__sum__squares__mult__ge__zero,axiom,
! [V_ya,V_xa,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__mult__ge__zero) ).
fof(fact_mult_Oadd__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)) ),
file('theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_mult__right_Oadd,axiom,
! [V_y,V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)) ),
file('theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [V_b,V_a_H,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)) ),
file('theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_mult__left_Oadd,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)) ),
file('theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_combine__common__factor,axiom,
! [V_c,V_b,V_e,V_a,T_a] :
( class_Rings_Osemiring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c) ),
file('theBenchmark.p',fact_combine__common__factor) ).
fof(fact_real__add__mult__distrib,axiom,
! [V_w,V_z2,V_z1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w)),
file('theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_mult__left_Ominus,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)) ),
file('theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_mult__right_Ominus,axiom,
! [V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x)) ),
file('theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__right,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_square__eq__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_a_2) = c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2)
<=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_square__eq__iff) ).
fof(fact_minus__mult__minus,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_minus__mult__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ),
file('theBenchmark.p',fact_minus__mult__left) ).
fof(fact_minus__mult__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__mult__right) ).
fof(fact_natceiling__real__of__nat,axiom,
! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
file('theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_less__1__mult,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)) ) ) ),
file('theBenchmark.p',fact_less__1__mult) ).
fof(fact_right__distrib__number__of,axiom,
! [V_c,V_b,V_v,T_b] :
( ( class_Rings_Osemiring(T_b)
& class_Int_Onumber(T_b) )
=> c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)) ),
file('theBenchmark.p',fact_right__distrib__number__of) ).
fof(fact_left__distrib__number__of,axiom,
! [V_v,V_b,V_a,T_b] :
( ( class_Rings_Osemiring(T_b)
& class_Int_Onumber(T_b) )
=> c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))) ),
file('theBenchmark.p',fact_left__distrib__number__of) ).
fof(fact_mult__diff__mult,axiom,
! [V_b,V_a,V_y,V_x,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)) ),
file('theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [V_b,V_a,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ),
file('theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)
<=> V_c_2 = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_d_2) ) ),
file('theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_eq__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)
<=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_e_2),V_c_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_right__diff__distrib__number__of,axiom,
! [V_c,V_b,V_v,T_b] :
( ( class_Rings_Oring(T_b)
& class_Int_Onumber(T_b) )
=> c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)) ),
file('theBenchmark.p',fact_right__diff__distrib__number__of) ).
fof(fact_left__diff__distrib__number__of,axiom,
! [V_v,V_b,V_a,T_b] :
( ( class_Rings_Oring(T_b)
& class_Int_Onumber(T_b) )
=> c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))) ),
file('theBenchmark.p',fact_left__diff__distrib__number__of) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
<=> c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_b_2 ) ) ),
file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
<=> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) ) ) ),
file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_divide__eq__imp,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b = c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)
=> c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a ) ) ),
file('theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_eq__divide__imp,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) = V_b
=> V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) ) ) ),
file('theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_eq__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq) ).
fof(fact_divide__eq__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_frac__eq__eq,axiom,
! [V_wa_2,V_x_2,V_za_2,V_y_2,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_za_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)
<=> c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_za_2) = c_Groups_Otimes__class_Otimes(T_a,V_wa_2,V_y_2) ) ) ) ),
file('theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_square__eq__1__iff,axiom,
! [V_x_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2) = c_Groups_Oone__class_Oone(T_a)
<=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_abs__mult__less,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d)) ) ) ),
file('theBenchmark.p',fact_abs__mult__less) ).
fof(fact_not__real__square__gt__zero,axiom,
! [V_x_2] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2))
<=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_real__mult__less__iff1,axiom,
! [V_y_2,V_x_2,V_za_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_za_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_za_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_real__mult__order,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)) ) ),
file('theBenchmark.p',fact_real__mult__order) ).
fof(fact_real__mult__less__mono2,axiom,
! [V_y,V_x,V_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y)) ) ),
file('theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_real__minus__mult__self__le,axiom,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u,V_u)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x)),
file('theBenchmark.p',fact_real__minus__mult__self__le) ).
fof(fact_lemma__MVT,axiom,
! [V_b_2,V_a_2,V_fa_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_a_2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_b_2)),
file('theBenchmark.p',fact_lemma__MVT) ).
fof(fact_real__sqrt__abs2,axiom,
! [V_x] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),
file('theBenchmark.p',fact_real__sqrt__abs2) ).
fof(fact_mult_Odiff__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)) ),
file('theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Odiff,axiom,
! [V_y,V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)) ),
file('theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_mult_Odiff__left,axiom,
! [V_b,V_a_H,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)) ),
file('theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_mult__left_Odiff,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)) ),
file('theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_times__divide__eq__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) ),
file('theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_times__divide__times__eq,axiom,
! [V_w,V_z,V_y,V_x,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w)) ),
file('theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_real__mult__right__cancel,axiom,
! [V_b_2,V_a_2,V_c_2] :
( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_real__mult__left__cancel,axiom,
! [V_b_2,V_a_2,V_c_2] :
( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_abs__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ),
file('theBenchmark.p',fact_abs__mult) ).
fof(fact_abs__mult__self,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_a) ),
file('theBenchmark.p',fact_abs__mult__self) ).
fof(fact_norm__mult__less,axiom,
! [V_s,V_y,V_r,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_s)) ) ) ),
file('theBenchmark.p',fact_norm__mult__less) ).
fof(fact_mult__left__idem,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_mult__left__idem) ).
fof(fact_mult__idem,axiom,
! [V_x,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = V_x ),
file('theBenchmark.p',fact_mult__idem) ).
fof(fact_times_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,V_a) = V_a ),
file('theBenchmark.p',fact_times_Oidem) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__mult(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_mult__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z) ),
file('theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_arith__simps_I32_J,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) ),
file('theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_number__of__mult,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__mult) ).
fof(fact_norm__mult,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ),
file('theBenchmark.p',fact_norm__mult) ).
fof(fact_real__mult__assoc,axiom,
! [V_z3,V_z2,V_z1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_z2),V_z3) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_z3)),
file('theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_real__mult__commute,axiom,
! [V_w,V_z] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_w) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w,V_z),
file('theBenchmark.p',fact_real__mult__commute) ).
fof(fact_poly__mult,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__mult) ).
fof(fact_norm__mult__ineq,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
file('theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_mult__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__zero__left) ).
fof(fact_mult__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult__eq__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_no__zero__divisors,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_divisors__zero,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divisors__zero) ).
fof(fact_mult_Ozero__left,axiom,
! [V_b,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_mult_Ozero__right,axiom,
! [V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_not__square__less__zero,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [V_b_2,V_c_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__pos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_zero__less__mult__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_zero__less__mult__pos2,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_mult__neg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__comm__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_split__mult__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_split__mult__pos__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ),
file('theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_comm__mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__comm__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__le__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__le__square,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)) ),
file('theBenchmark.p',fact_zero__le__square) ).
fof(fact_real__sqrt__mult,axiom,
! [V_y,V_x] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)),
file('theBenchmark.p',fact_real__sqrt__mult) ).
fof(fact_real__divide__square__eq,axiom,
! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_a),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r),
file('theBenchmark.p',fact_real__divide__square__eq) ).
fof(fact_real__mult__1,axiom,
! [V_z] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z) = V_z,
file('theBenchmark.p',fact_real__mult__1) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult__1__right) ).
fof(fact_mult__1,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [V_q,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_q) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),c_Power_Opower__class_Opower(T_a,V_y,V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)) = c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q)) = c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [V_n,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_x,V_n)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),c_Groups_Otimes__class_Otimes(T_a,V_ly,V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ly) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,V_rx)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ry) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_b,V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_power__Suc2,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),V_a) ),
file('theBenchmark.p',fact_power__Suc2) ).
fof(fact_power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Power_Opower(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) ),
file('theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,V_x) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_x) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(T_1)
=> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [T_2,T_1] :
( class_Orderings_Opreorder(T_1)
=> class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [T_2,T_1] :
( class_Orderings_Oorder(T_1)
=> class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [T_2,T_1] :
( class_Orderings_Oord(T_1)
=> class_Orderings_Oord(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [T_2,T_1] :
( class_Groups_Ouminus(T_1)
=> class_Groups_Ouminus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Groups_Ominus,axiom,
! [T_2,T_1] :
( class_Groups_Ominus(T_1)
=> class_Groups_Ominus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_Int__Oint__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Int__Oint__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_Nat__Onat__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Nat__Onat__Int_Onumber,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).
fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(arity_RealDef__Oreal__Rings_Oring,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(arity_RealDef__Oreal__Int_Onumber,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
fof(arity_RealDef__Oreal__Groups_Oone,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring(T_1)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Int_Onumber__ring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [T_1] :
( class_Groups_Ozero(T_1)
=> class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring(T_1)
=> class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Int_Onumber,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Int_Onumber(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(conj_0,hypothesis,
! [B_d] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
=> ( ! [B_w] :
( ( 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_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,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('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
v_thesis____,
file('theBenchmark.p',conj_1) ).
fof(f_1_1,plain,
! [V_ga_2,V_fa_2] :
( V_fa_2 = V_ga_2
| ? [B_x] : hAPP(V_fa_2,B_x) != hAPP(V_ga_2,B_x) ),
inference(fof_nnf,[status(thm)],[fact_ext]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_1 = U_2
| ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,plain,
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
c_SEQ_Osubseq(v_f____),
inference(fof_nnf,[status(thm)],[fact_fz_I1_J]) ).
cnf(f_2_2,plain,
c_SEQ_Osubseq(v_f____),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
inference(fof_nnf,[status(thm)],[fact_e]) ).
cnf(f_3_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
? [B_d] :
( ! [B_w] :
( 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_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_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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ),
inference(fof_nnf,[status(thm)],[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]) ).
fof(f_4_2,plain,
? [U_4] :
( ! [U_3] :
( 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),U_3),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_3,v_z____)),U_4)
| ~ 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,U_3,v_z____))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_3] :
( 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),U_3),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_3,v_z____)),sK2)
| ~ 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,U_3,v_z____))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2)],[f_4_2]) ).
cnf(f_4_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_3),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_3,v_z____)),sK2)
| ~ 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,U_3,v_z____))) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_e2]) ).
cnf(f_5_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
! [V_ra_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ra_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ra_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ra_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ra_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff]) ).
fof(f_6_2,plain,
! [U_6,U_5] :
( ( ( c_Orderings_Oord__class_Oless(U_5,c_Groups_Ozero__class_Ozero(U_5),c_Rings_Oinverse__class_Odivide(U_5,U_6,c_Int_Onumber__class_Onumber__of(U_5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_5,c_Groups_Ozero__class_Ozero(U_5),U_6) )
& ( c_Orderings_Oord__class_Oless(U_5,c_Groups_Ozero__class_Ozero(U_5),U_6)
| ~ c_Orderings_Oord__class_Oless(U_5,c_Groups_Ozero__class_Ozero(U_5),c_Rings_Oinverse__class_Odivide(U_5,U_6,c_Int_Onumber__class_Onumber__of(U_5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Int_Onumber__ring(U_5)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( c_Orderings_Oord__class_Oless(U_5,c_Groups_Ozero__class_Ozero(U_5),U_6)
| ~ c_Orderings_Oord__class_Oless(U_5,c_Groups_Ozero__class_Ozero(U_5),c_Rings_Oinverse__class_Odivide(U_5,U_6,c_Int_Onumber__class_Onumber__of(U_5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_5)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( c_Orderings_Oord__class_Oless(U_5,c_Groups_Ozero__class_Ozero(U_5),c_Rings_Oinverse__class_Odivide(U_5,U_6,c_Int_Onumber__class_Onumber__of(U_5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_5,c_Groups_Ozero__class_Ozero(U_5),U_6)
| ~ class_Int_Onumber__ring(U_5)
| ~ class_Fields_Olinordered__field__inverse__zero(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [V_r,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_half__gt__zero]) ).
fof(f_7_2,plain,
! [U_8,U_7] :
( c_Orderings_Oord__class_Oless(U_7,c_Groups_Ozero__class_Ozero(U_7),c_Rings_Oinverse__class_Odivide(U_7,U_8,c_Int_Onumber__class_Onumber__of(U_7,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_7,c_Groups_Ozero__class_Ozero(U_7),U_8)
| ~ class_Int_Onumber__ring(U_7)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( c_Orderings_Oord__class_Oless(U_7,c_Groups_Ozero__class_Ozero(U_7),c_Rings_Oinverse__class_Odivide(U_7,U_8,c_Int_Onumber__class_Onumber__of(U_7,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_7,c_Groups_Ozero__class_Ozero(U_7),U_8)
| ~ class_Int_Onumber__ring(U_7)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [V_x,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) = c_Int_Onumber__class_Onumber__of(T_a,V_x)
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__number__of]) ).
fof(f_8_2,plain,
! [U_10,U_9] :
( ( ( c_Groups_Oabs__class_Oabs(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10)) = c_Int_Onumber__class_Onumber__of(U_9,U_10)
| c_Orderings_Oord__class_Oless(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10),c_Groups_Ozero__class_Ozero(U_9)) )
& ( c_Groups_Oabs__class_Oabs(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10)) = c_Groups_Ouminus__class_Ouminus(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10))
| ~ c_Orderings_Oord__class_Oless(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10),c_Groups_Ozero__class_Ozero(U_9)) ) )
| ~ class_Rings_Olinordered__idom(U_9)
| ~ class_Int_Onumber__ring(U_9) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( c_Groups_Oabs__class_Oabs(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10)) = c_Groups_Ouminus__class_Ouminus(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10))
| ~ c_Orderings_Oord__class_Oless(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10),c_Groups_Ozero__class_Ozero(U_9))
| ~ class_Rings_Olinordered__idom(U_9)
| ~ class_Int_Onumber__ring(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( c_Groups_Oabs__class_Oabs(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10)) = c_Int_Onumber__class_Onumber__of(U_9,U_10)
| c_Orderings_Oord__class_Oless(U_9,c_Int_Onumber__class_Onumber__of(U_9,U_10),c_Groups_Ozero__class_Ozero(U_9))
| ~ class_Rings_Olinordered__idom(U_9)
| ~ class_Int_Onumber__ring(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [V_a] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_abs__real__def]) ).
fof(f_9_2,plain,
! [U_11] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_11) = U_11
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_11) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_11)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_13] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_13) = U_13
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_12] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_12) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_12)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_12,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_12) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_12)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_12,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_13) = U_13
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [V_r] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__abs__def]) ).
fof(f_10_2,plain,
! [U_14] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_14) = U_14
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_14,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_14) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_14)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_14,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_16] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_16) = U_16
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_16,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_15] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_15) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_15)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_15,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_15) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_15)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_15,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_16) = U_16
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_16,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [V_w,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w))
| ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__number__of]) ).
fof(f_11_2,plain,
! [U_18,U_17] :
( c_RealVector_Onorm__class_Onorm(U_17,c_Int_Onumber__class_Onumber__of(U_17,U_18)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_18))
| ~ class_RealVector_Oreal__normed__algebra__1(U_17)
| ~ class_Int_Onumber__ring(U_17) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( c_RealVector_Onorm__class_Onorm(U_17,c_Int_Onumber__class_Onumber__of(U_17,U_18)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_18))
| ~ class_RealVector_Oreal__normed__algebra__1(U_17)
| ~ class_Int_Onumber__ring(U_17) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [V_a,V_b,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__norm__divide]) ).
fof(f_12_2,plain,
! [U_21,U_20,U_19] :
( c_RealVector_Onorm__class_Onorm(U_19,c_Rings_Oinverse__class_Odivide(U_19,U_21,U_20)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_19,U_21),c_RealVector_Onorm__class_Onorm(U_19,U_20))
| U_20 = c_Groups_Ozero__class_Ozero(U_19)
| ~ class_RealVector_Oreal__normed__field(U_19) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( c_RealVector_Onorm__class_Onorm(U_19,c_Rings_Oinverse__class_Odivide(U_19,U_21,U_20)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_19,U_21),c_RealVector_Onorm__class_Onorm(U_19,U_20))
| U_20 = c_Groups_Ozero__class_Ozero(U_19)
| ~ class_RealVector_Oreal__normed__field(U_19) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__numeral__1]) ).
fof(f_13_2,plain,
! [U_23,U_22] :
( c_Rings_Oinverse__class_Odivide(U_22,U_23,c_Int_Onumber__class_Onumber__of(U_22,c_Int_OBit1(c_Int_OPls))) = U_23
| ~ class_Int_Onumber__ring(U_22)
| ~ class_Fields_Ofield(U_22) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( c_Rings_Oinverse__class_Odivide(U_22,U_23,c_Int_Onumber__class_Onumber__of(U_22,c_Int_OBit1(c_Int_OPls))) = U_23
| ~ class_Int_Onumber__ring(U_22)
| ~ class_Fields_Ofield(U_22) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__Numeral1]) ).
fof(f_14_2,plain,
! [U_25,U_24] :
( c_Rings_Oinverse__class_Odivide(U_24,U_25,c_Int_Onumber__class_Onumber__of(U_24,c_Int_OBit1(c_Int_OPls))) = U_25
| ~ class_Int_Onumber__ring(U_24)
| ~ class_Fields_Ofield(U_24) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( c_Rings_Oinverse__class_Odivide(U_24,U_25,c_Int_Onumber__class_Onumber__of(U_24,c_Int_OBit1(c_Int_OPls))) = U_25
| ~ class_Int_Onumber__ring(U_24)
| ~ class_Fields_Ofield(U_24) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
| V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff]) ).
fof(f_15_2,plain,
! [U_27,U_26] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_26,U_27))
| U_27 = c_Groups_Ozero__class_Ozero(U_26) )
& ( U_27 != c_Groups_Ozero__class_Ozero(U_26)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_26,U_27)) ) )
| ~ class_RealVector_Oreal__normed__vector(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( U_27 != c_Groups_Ozero__class_Ozero(U_26)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_26,U_27))
| ~ class_RealVector_Oreal__normed__vector(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_26,U_27))
| U_27 = c_Groups_Ozero__class_Ozero(U_26)
| ~ class_RealVector_Oreal__normed__vector(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [V_x,V_y,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__div__pos]) ).
fof(f_16_2,plain,
! [U_30,U_29,U_28] :
( c_Rings_Oinverse__class_Odivide(U_28,c_Groups_Oabs__class_Oabs(U_28,U_30),U_29) = c_Groups_Oabs__class_Oabs(U_28,c_Rings_Oinverse__class_Odivide(U_28,U_30,U_29))
| ~ c_Orderings_Oord__class_Oless(U_28,c_Groups_Ozero__class_Ozero(U_28),U_29)
| ~ class_Fields_Olinordered__field__inverse__zero(U_28) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( c_Rings_Oinverse__class_Odivide(U_28,c_Groups_Oabs__class_Oabs(U_28,U_30),U_29) = c_Groups_Oabs__class_Oabs(U_28,c_Rings_Oinverse__class_Odivide(U_28,U_30,U_29))
| ~ c_Orderings_Oord__class_Oless(U_28,c_Groups_Ozero__class_Ozero(U_28),U_29)
| ~ class_Fields_Olinordered__field__inverse__zero(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__Numeral0]) ).
fof(f_17_2,plain,
! [U_32,U_31] :
( c_Rings_Oinverse__class_Odivide(U_31,U_32,c_Int_Onumber__class_Onumber__of(U_31,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_31)
| ~ class_Int_Onumber__ring(U_31)
| ~ class_Fields_Ofield__inverse__zero(U_31) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( c_Rings_Oinverse__class_Odivide(U_31,U_32,c_Int_Onumber__class_Onumber__of(U_31,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_31)
| ~ class_Int_Onumber__ring(U_31)
| ~ class_Fields_Ofield__inverse__zero(U_31) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_zero__is__num__zero]) ).
cnf(f_18_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).
cnf(f_19_2,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
! [V_wa_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J]) ).
fof(f_20_2,plain,
! [U_33] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_33),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_33,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_33,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_35] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_35),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_35,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_34] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_34,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_34),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_34,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_34),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_35),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_35,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [V_wa_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J]) ).
fof(f_21_2,plain,
! [U_36] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_36),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_36,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_36,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_38] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_38),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_38,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_37] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_37,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_37,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_38),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_38,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_minus__Pls]) ).
cnf(f_22_2,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_1,plain,
! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)),
inference(fof_nnf,[status(thm)],[fact_minus__Bit0]) ).
fof(f_23_2,plain,
! [U_39] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(U_39)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_39)),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(U_39)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_39)),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J]) ).
fof(f_24_2,plain,
! [U_41,U_40] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_40),c_Int_OBit1(U_41))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_40,U_41) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_40,U_41)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_40),c_Int_OBit1(U_41)) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_45,U_43] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_43),c_Int_OBit1(U_45))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_43,U_45) )
& ! [U_44,U_42] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_42,U_44)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_42),c_Int_OBit1(U_44)) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_42,U_44)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_42),c_Int_OBit1(U_44)) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_43),c_Int_OBit1(U_45))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_43,U_45) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J]) ).
fof(f_25_2,plain,
! [U_47,U_46] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_46),c_Int_OBit1(U_47))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_46,U_47) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_46,U_47)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_46),c_Int_OBit1(U_47)) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_51,U_49] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_49),c_Int_OBit1(U_51))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_49,U_51) )
& ! [U_50,U_48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_48,U_50)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_48),c_Int_OBit1(U_50)) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_48,U_50)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_48),c_Int_OBit1(U_50)) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_49),c_Int_OBit1(U_51))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_49,U_51) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I2_J]) ).
cnf(f_26_2,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J]) ).
fof(f_27_2,plain,
! [U_53,U_52] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_52),c_Int_OBit0(U_53))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_52,U_53) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_52,U_53)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_52),c_Int_OBit0(U_53)) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_57,U_55] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_55),c_Int_OBit0(U_57))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_55,U_57) )
& ! [U_56,U_54] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_54,U_56)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_54),c_Int_OBit0(U_56)) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_54,U_56)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_54),c_Int_OBit0(U_56)) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_55),c_Int_OBit0(U_57))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_55,U_57) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J]) ).
fof(f_28_2,plain,
! [U_59,U_58] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_58),c_Int_OBit0(U_59))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_58,U_59) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_58,U_59)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_58),c_Int_OBit0(U_59)) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_63,U_61] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_61),c_Int_OBit0(U_63))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_61,U_63) )
& ! [U_62,U_60] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_60,U_62)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_60),c_Int_OBit0(U_62)) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_60,U_62)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_60),c_Int_OBit0(U_62)) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_61),c_Int_OBit0(U_63))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_61,U_63) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
inference(fof_nnf,[status(thm)],[fact_real__norm__def]) ).
fof(f_29_2,plain,
! [U_64] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_64) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_64),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_64) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_64),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).
cnf(f_30_2,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J]) ).
fof(f_31_2,plain,
! [U_65] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_65),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_65,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_65,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_65),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_67] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_67),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_67,c_Int_OPls) )
& ! [U_66] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_66,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_66),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_66,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_66),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_67),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_67,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J]) ).
fof(f_32_2,plain,
! [U_69,U_68] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_68),c_Int_OBit0(U_69))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_68,U_69) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_68,U_69)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_68),c_Int_OBit0(U_69)) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_73,U_71] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_71),c_Int_OBit0(U_73))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_71,U_73) )
& ! [U_72,U_70] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_70,U_72)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_70),c_Int_OBit0(U_72)) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_70,U_72)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_70),c_Int_OBit0(U_72)) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_71),c_Int_OBit0(U_73))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_71,U_73) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J]) ).
fof(f_33_2,plain,
! [U_75,U_74] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_74),c_Int_OBit0(U_75))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_74,U_75) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_74,U_75)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_74),c_Int_OBit0(U_75)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_79,U_77] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_77),c_Int_OBit0(U_79))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_77,U_79) )
& ! [U_78,U_76] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_76,U_78)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_76),c_Int_OBit0(U_78)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_76,U_78)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_76),c_Int_OBit0(U_78)) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_77),c_Int_OBit0(U_79))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_77,U_79) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J]) ).
fof(f_34_2,plain,
! [U_80] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_80),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_80,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_80,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_80),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_82] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_82),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_82,c_Int_OPls) )
& ! [U_81] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_81,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_81),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_81,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_81),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_82),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_82,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J]) ).
fof(f_35_2,plain,
! [U_83] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_83))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_83) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_83)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_83)) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_85] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_85))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_85) )
& ! [U_84] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_84)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_84)) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_84)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_84)) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_85))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_85) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
| ~ class_Int_Oring__char__0(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).
fof(f_36_2,plain,
! [U_88,U_87,U_86] :
( ( ( c_Int_Onumber__class_Onumber__of(U_86,U_87) = c_Int_Onumber__class_Onumber__of(U_86,U_88)
| U_87 != U_88 )
& ( U_87 = U_88
| c_Int_Onumber__class_Onumber__of(U_86,U_87) != c_Int_Onumber__class_Onumber__of(U_86,U_88) ) )
| ~ class_Int_Oring__char__0(U_86)
| ~ class_Int_Onumber__ring(U_86) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( U_87 = U_88
| c_Int_Onumber__class_Onumber__of(U_86,U_87) != c_Int_Onumber__class_Onumber__of(U_86,U_88)
| ~ class_Int_Oring__char__0(U_86)
| ~ class_Int_Onumber__ring(U_86) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( c_Int_Onumber__class_Onumber__of(U_86,U_87) = c_Int_Onumber__class_Onumber__of(U_86,U_88)
| U_87 != U_88
| ~ class_Int_Oring__char__0(U_86)
| ~ class_Int_Onumber__ring(U_86) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [V_x_2,V_wa_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
| V_x_2 != c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) )
& ( V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)
| c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != V_x_2 ) )
| ~ class_Int_Onumber(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).
fof(f_37_2,plain,
! [U_91,U_90,U_89] :
( ( ( c_Int_Onumber__class_Onumber__of(U_89,U_90) = U_91
| U_91 != c_Int_Onumber__class_Onumber__of(U_89,U_90) )
& ( U_91 = c_Int_Onumber__class_Onumber__of(U_89,U_90)
| c_Int_Onumber__class_Onumber__of(U_89,U_90) != U_91 ) )
| ~ class_Int_Onumber(U_89) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_91 = c_Int_Onumber__class_Onumber__of(U_89,U_90)
| c_Int_Onumber__class_Onumber__of(U_89,U_90) != U_91
| ~ class_Int_Onumber(U_89) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( c_Int_Onumber__class_Onumber__of(U_89,U_90) = U_91
| U_91 != c_Int_Onumber__class_Onumber__of(U_89,U_90)
| ~ class_Int_Onumber(U_89) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [V_l_2,V_k_2] :
( ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
| V_k_2 != V_l_2 )
& ( V_k_2 = V_l_2
| c_Int_OBit1(V_k_2) != c_Int_OBit1(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J]) ).
fof(f_38_2,plain,
! [U_93,U_92] :
( ( c_Int_OBit1(U_92) = c_Int_OBit1(U_93)
| U_92 != U_93 )
& ( U_92 = U_93
| c_Int_OBit1(U_92) != c_Int_OBit1(U_93) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_97,U_95] :
( c_Int_OBit1(U_95) = c_Int_OBit1(U_97)
| U_95 != U_97 )
& ! [U_96,U_94] :
( U_94 = U_96
| c_Int_OBit1(U_94) != c_Int_OBit1(U_96) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( U_94 = U_96
| c_Int_OBit1(U_94) != c_Int_OBit1(U_96) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( c_Int_OBit1(U_95) = c_Int_OBit1(U_97)
| U_95 != U_97 ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [V_l_2,V_k_2] :
( ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
| V_k_2 != V_l_2 )
& ( V_k_2 = V_l_2
| c_Int_OBit0(V_k_2) != c_Int_OBit0(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J]) ).
fof(f_39_2,plain,
! [U_99,U_98] :
( ( c_Int_OBit0(U_98) = c_Int_OBit0(U_99)
| U_98 != U_99 )
& ( U_98 = U_99
| c_Int_OBit0(U_98) != c_Int_OBit0(U_99) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_103,U_101] :
( c_Int_OBit0(U_101) = c_Int_OBit0(U_103)
| U_101 != U_103 )
& ! [U_102,U_100] :
( U_100 = U_102
| c_Int_OBit0(U_100) != c_Int_OBit0(U_102) ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( U_100 = U_102
| c_Int_OBit0(U_100) != c_Int_OBit0(U_102) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( c_Int_OBit0(U_101) = c_Int_OBit0(U_103)
| U_101 != U_103 ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).
fof(f_40_2,plain,
! [U_106,U_105,U_104] :
( ( ( c_Orderings_Oord__class_Oless(U_104,c_Int_Onumber__class_Onumber__of(U_104,U_105),c_Int_Onumber__class_Onumber__of(U_104,U_106))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_105,U_106) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_105,U_106)
| ~ c_Orderings_Oord__class_Oless(U_104,c_Int_Onumber__class_Onumber__of(U_104,U_105),c_Int_Onumber__class_Onumber__of(U_104,U_106)) ) )
| ~ class_Rings_Olinordered__idom(U_104)
| ~ class_Int_Onumber__ring(U_104) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_105,U_106)
| ~ c_Orderings_Oord__class_Oless(U_104,c_Int_Onumber__class_Onumber__of(U_104,U_105),c_Int_Onumber__class_Onumber__of(U_104,U_106))
| ~ class_Rings_Olinordered__idom(U_104)
| ~ class_Int_Onumber__ring(U_104) ),
inference(clausify,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( c_Orderings_Oord__class_Oless(U_104,c_Int_Onumber__class_Onumber__of(U_104,U_105),c_Int_Onumber__class_Onumber__of(U_104,U_106))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_105,U_106)
| ~ class_Rings_Olinordered__idom(U_104)
| ~ class_Int_Onumber__ring(U_104) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [V_w,V_v,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__diff]) ).
fof(f_41_2,plain,
! [U_109,U_108,U_107] :
( c_Int_Onumber__class_Onumber__of(U_107,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_108,U_109)) = c_Groups_Ominus__class_Ominus(U_107,c_Int_Onumber__class_Onumber__of(U_107,U_108),c_Int_Onumber__class_Onumber__of(U_107,U_109))
| ~ class_Int_Onumber__ring(U_107) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( c_Int_Onumber__class_Onumber__of(U_107,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_108,U_109)) = c_Groups_Ominus__class_Ominus(U_107,c_Int_Onumber__class_Onumber__of(U_107,U_108),c_Int_Onumber__class_Onumber__of(U_107,U_109))
| ~ class_Int_Onumber__ring(U_107) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [V_y,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Ozero]) ).
fof(f_42_2,plain,
! [U_111,U_110] :
( c_Rings_Oinverse__class_Odivide(U_110,c_Groups_Ozero__class_Ozero(U_110),U_111) = c_Groups_Ozero__class_Ozero(U_110)
| ~ class_RealVector_Oreal__normed__field(U_110) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( c_Rings_Oinverse__class_Odivide(U_110,c_Groups_Ozero__class_Ozero(U_110),U_111) = c_Groups_Ozero__class_Ozero(U_110)
| ~ class_RealVector_Oreal__normed__field(U_110) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [V_w,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__minus]) ).
fof(f_43_2,plain,
! [U_113,U_112] :
( c_Int_Onumber__class_Onumber__of(U_112,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_113)) = c_Groups_Ouminus__class_Ouminus(U_112,c_Int_Onumber__class_Onumber__of(U_112,U_113))
| ~ class_Int_Onumber__ring(U_112) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( c_Int_Onumber__class_Onumber__of(U_112,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_113)) = c_Groups_Ouminus__class_Ouminus(U_112,c_Int_Onumber__class_Onumber__of(U_112,U_113))
| ~ class_Int_Onumber__ring(U_112) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [V_w,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J]) ).
fof(f_44_2,plain,
! [U_115,U_114] :
( c_Groups_Ouminus__class_Ouminus(U_114,c_Int_Onumber__class_Onumber__of(U_114,U_115)) = c_Int_Onumber__class_Onumber__of(U_114,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_115))
| ~ class_Int_Onumber__ring(U_114) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_114,c_Int_Onumber__class_Onumber__of(U_114,U_115)) = c_Int_Onumber__class_Onumber__of(U_114,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_115))
| ~ class_Int_Onumber__ring(U_114) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [V_ya,V_y,V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya))
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Odiff]) ).
fof(f_45_2,plain,
! [U_119,U_118,U_117,U_116] :
( c_Rings_Oinverse__class_Odivide(U_116,c_Groups_Ominus__class_Ominus(U_116,U_117,U_118),U_119) = c_Groups_Ominus__class_Ominus(U_116,c_Rings_Oinverse__class_Odivide(U_116,U_117,U_119),c_Rings_Oinverse__class_Odivide(U_116,U_118,U_119))
| ~ class_RealVector_Oreal__normed__field(U_116) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( c_Rings_Oinverse__class_Odivide(U_116,c_Groups_Ominus__class_Ominus(U_116,U_117,U_118),U_119) = c_Groups_Ominus__class_Ominus(U_116,c_Rings_Oinverse__class_Odivide(U_116,U_117,U_119),c_Rings_Oinverse__class_Odivide(U_116,U_118,U_119))
| ~ class_RealVector_Oreal__normed__field(U_116) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(f_46_2,plain,
! [U_120] : c_Int_OBit1(U_120) != c_Int_OPls,
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
c_Int_OBit1(U_120) != c_Int_OPls,
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(f_47_2,plain,
! [U_121] : c_Int_OPls != c_Int_OBit1(U_121),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
c_Int_OPls != c_Int_OBit1(U_121),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I50_J]) ).
fof(f_48_2,plain,
! [U_123,U_122] : c_Int_OBit1(U_122) != c_Int_OBit0(U_123),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
c_Int_OBit1(U_122) != c_Int_OBit0(U_123),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I49_J]) ).
fof(f_49_2,plain,
! [U_125,U_124] : c_Int_OBit0(U_124) != c_Int_OBit1(U_125),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
c_Int_OBit0(U_124) != c_Int_OBit1(U_125),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [V_k_2] :
( ( c_Int_OBit0(V_k_2) = c_Int_OPls
| V_k_2 != c_Int_OPls )
& ( V_k_2 = c_Int_OPls
| c_Int_OBit0(V_k_2) != c_Int_OPls ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J]) ).
fof(f_50_2,plain,
! [U_126] :
( ( c_Int_OBit0(U_126) = c_Int_OPls
| U_126 != c_Int_OPls )
& ( U_126 = c_Int_OPls
| c_Int_OBit0(U_126) != c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( ! [U_128] :
( c_Int_OBit0(U_128) = c_Int_OPls
| U_128 != c_Int_OPls )
& ! [U_127] :
( U_127 = c_Int_OPls
| c_Int_OBit0(U_127) != c_Int_OPls ) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( U_127 = c_Int_OPls
| c_Int_OBit0(U_127) != c_Int_OPls ),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_5,plain,
( c_Int_OBit0(U_128) = c_Int_OPls
| U_128 != c_Int_OPls ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [V_l_2] :
( ( c_Int_OPls = c_Int_OBit0(V_l_2)
| c_Int_OPls != V_l_2 )
& ( c_Int_OPls = V_l_2
| c_Int_OPls != c_Int_OBit0(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J]) ).
fof(f_51_2,plain,
! [U_129] :
( ( c_Int_OPls = c_Int_OBit0(U_129)
| c_Int_OPls != U_129 )
& ( c_Int_OPls = U_129
| c_Int_OPls != c_Int_OBit0(U_129) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_131] :
( c_Int_OPls = c_Int_OBit0(U_131)
| c_Int_OPls != U_131 )
& ! [U_130] :
( c_Int_OPls = U_130
| c_Int_OPls != c_Int_OBit0(U_130) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( c_Int_OPls = U_130
| c_Int_OPls != c_Int_OBit0(U_130) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( c_Int_OPls = c_Int_OBit0(U_131)
| c_Int_OPls != U_131 ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).
cnf(f_52_2,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_52_1]) ).
fof(f_53_1,plain,
! [V_b,V_a,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__minus__commute]) ).
fof(f_53_2,plain,
! [U_134,U_133,U_132] :
( c_RealVector_Onorm__class_Onorm(U_132,c_Groups_Ominus__class_Ominus(U_132,U_133,U_134)) = c_RealVector_Onorm__class_Onorm(U_132,c_Groups_Ominus__class_Ominus(U_132,U_134,U_133))
| ~ class_RealVector_Oreal__normed__vector(U_132) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( c_RealVector_Onorm__class_Onorm(U_132,c_Groups_Ominus__class_Ominus(U_132,U_133,U_134)) = c_RealVector_Onorm__class_Onorm(U_132,c_Groups_Ominus__class_Ominus(U_132,U_134,U_133))
| ~ class_RealVector_Oreal__normed__vector(U_132) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__divide]) ).
fof(f_54_2,plain,
! [U_137,U_136,U_135] :
( c_Rings_Oinverse__class_Odivide(U_135,c_Groups_Ouminus__class_Ouminus(U_135,U_136),c_Groups_Ouminus__class_Ouminus(U_135,U_137)) = c_Rings_Oinverse__class_Odivide(U_135,U_136,U_137)
| ~ class_Fields_Ofield__inverse__zero(U_135) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( c_Rings_Oinverse__class_Odivide(U_135,c_Groups_Ouminus__class_Ouminus(U_135,U_136),c_Groups_Ouminus__class_Ouminus(U_135,U_137)) = c_Rings_Oinverse__class_Odivide(U_135,U_136,U_137)
| ~ class_Fields_Ofield__inverse__zero(U_135) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [V_y,V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Ominus]) ).
fof(f_55_2,plain,
! [U_140,U_139,U_138] :
( c_Rings_Oinverse__class_Odivide(U_138,c_Groups_Ouminus__class_Ouminus(U_138,U_139),U_140) = c_Groups_Ouminus__class_Ouminus(U_138,c_Rings_Oinverse__class_Odivide(U_138,U_139,U_140))
| ~ class_RealVector_Oreal__normed__field(U_138) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( c_Rings_Oinverse__class_Odivide(U_138,c_Groups_Ouminus__class_Ouminus(U_138,U_139),U_140) = c_Groups_Ouminus__class_Ouminus(U_138,c_Rings_Oinverse__class_Odivide(U_138,U_139,U_140))
| ~ class_RealVector_Oreal__normed__field(U_138) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__right]) ).
fof(f_56_2,plain,
! [U_143,U_142,U_141] :
( c_Groups_Ouminus__class_Ouminus(U_141,c_Rings_Oinverse__class_Odivide(U_141,U_142,U_143)) = c_Rings_Oinverse__class_Odivide(U_141,U_142,c_Groups_Ouminus__class_Ouminus(U_141,U_143))
| ~ class_Fields_Ofield__inverse__zero(U_141) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_141,c_Rings_Oinverse__class_Odivide(U_141,U_142,U_143)) = c_Rings_Oinverse__class_Odivide(U_141,U_142,c_Groups_Ouminus__class_Ouminus(U_141,U_143))
| ~ class_Fields_Ofield__inverse__zero(U_141) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel]) ).
fof(f_57_2,plain,
! [U_145,U_144] :
( c_RealVector_Onorm__class_Onorm(U_144,c_Groups_Ouminus__class_Ouminus(U_144,U_145)) = c_RealVector_Onorm__class_Onorm(U_144,U_145)
| ~ class_RealVector_Oreal__normed__vector(U_144) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( c_RealVector_Onorm__class_Onorm(U_144,c_Groups_Ouminus__class_Ouminus(U_144,U_145)) = c_RealVector_Onorm__class_Onorm(U_144,U_145)
| ~ class_RealVector_Oreal__normed__vector(U_144) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__divide]) ).
fof(f_58_2,plain,
! [U_148,U_147,U_146] :
( c_Groups_Oabs__class_Oabs(U_146,c_Rings_Oinverse__class_Odivide(U_146,U_147,U_148)) = c_Rings_Oinverse__class_Odivide(U_146,c_Groups_Oabs__class_Oabs(U_146,U_147),c_Groups_Oabs__class_Oabs(U_146,U_148))
| ~ class_Fields_Olinordered__field__inverse__zero(U_146) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( c_Groups_Oabs__class_Oabs(U_146,c_Rings_Oinverse__class_Odivide(U_146,U_147,U_148)) = c_Rings_Oinverse__class_Odivide(U_146,c_Groups_Oabs__class_Oabs(U_146,U_147),c_Groups_Oabs__class_Oabs(U_146,U_148))
| ~ class_Fields_Olinordered__field__inverse__zero(U_146) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel]) ).
fof(f_59_2,plain,
! [U_150,U_149] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_149,U_150)) = c_RealVector_Onorm__class_Onorm(U_149,U_150)
| ~ class_RealVector_Oreal__normed__vector(U_149) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_149,U_150)) = c_RealVector_Onorm__class_Onorm(U_149,U_150)
| ~ class_RealVector_Oreal__normed__vector(U_149) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg]) ).
fof(f_60_2,plain,
! [U_154,U_153,U_152,U_151] :
( c_Orderings_Oord__class_Oless(U_151,c_Rings_Oinverse__class_Odivide(U_151,U_153,U_154),c_Rings_Oinverse__class_Odivide(U_151,U_152,U_154))
| ~ c_Orderings_Oord__class_Oless(U_151,U_154,c_Groups_Ozero__class_Ozero(U_151))
| ~ c_Orderings_Oord__class_Oless(U_151,U_152,U_153)
| ~ class_Fields_Olinordered__field(U_151) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( c_Orderings_Oord__class_Oless(U_151,c_Rings_Oinverse__class_Odivide(U_151,U_153,U_154),c_Rings_Oinverse__class_Odivide(U_151,U_152,U_154))
| ~ c_Orderings_Oord__class_Oless(U_151,U_154,c_Groups_Ozero__class_Ozero(U_151))
| ~ c_Orderings_Oord__class_Oless(U_151,U_152,U_153)
| ~ class_Fields_Olinordered__field(U_151) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono]) ).
fof(f_61_2,plain,
! [U_158,U_157,U_156,U_155] :
( c_Orderings_Oord__class_Oless(U_155,c_Rings_Oinverse__class_Odivide(U_155,U_156,U_158),c_Rings_Oinverse__class_Odivide(U_155,U_157,U_158))
| ~ c_Orderings_Oord__class_Oless(U_155,c_Groups_Ozero__class_Ozero(U_155),U_158)
| ~ c_Orderings_Oord__class_Oless(U_155,U_156,U_157)
| ~ class_Fields_Olinordered__field(U_155) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( c_Orderings_Oord__class_Oless(U_155,c_Rings_Oinverse__class_Odivide(U_155,U_156,U_158),c_Rings_Oinverse__class_Odivide(U_155,U_157,U_158))
| ~ c_Orderings_Oord__class_Oless(U_155,c_Groups_Ozero__class_Ozero(U_155),U_158)
| ~ c_Orderings_Oord__class_Oless(U_155,U_156,U_157)
| ~ class_Fields_Olinordered__field(U_155) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__neg__neg]) ).
fof(f_62_2,plain,
! [U_161,U_160,U_159] :
( c_Orderings_Oord__class_Oless(U_159,c_Groups_Ozero__class_Ozero(U_159),c_Rings_Oinverse__class_Odivide(U_159,U_160,U_161))
| ~ c_Orderings_Oord__class_Oless(U_159,U_161,c_Groups_Ozero__class_Ozero(U_159))
| ~ c_Orderings_Oord__class_Oless(U_159,U_160,c_Groups_Ozero__class_Ozero(U_159))
| ~ class_Fields_Olinordered__field(U_159) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( c_Orderings_Oord__class_Oless(U_159,c_Groups_Ozero__class_Ozero(U_159),c_Rings_Oinverse__class_Odivide(U_159,U_160,U_161))
| ~ c_Orderings_Oord__class_Oless(U_159,U_161,c_Groups_Ozero__class_Ozero(U_159))
| ~ c_Orderings_Oord__class_Oless(U_159,U_160,c_Groups_Ozero__class_Ozero(U_159))
| ~ class_Fields_Olinordered__field(U_159) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__neg__pos]) ).
fof(f_63_2,plain,
! [U_164,U_163,U_162] :
( c_Orderings_Oord__class_Oless(U_162,c_Rings_Oinverse__class_Odivide(U_162,U_163,U_164),c_Groups_Ozero__class_Ozero(U_162))
| ~ c_Orderings_Oord__class_Oless(U_162,c_Groups_Ozero__class_Ozero(U_162),U_164)
| ~ c_Orderings_Oord__class_Oless(U_162,U_163,c_Groups_Ozero__class_Ozero(U_162))
| ~ class_Fields_Olinordered__field(U_162) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( c_Orderings_Oord__class_Oless(U_162,c_Rings_Oinverse__class_Odivide(U_162,U_163,U_164),c_Groups_Ozero__class_Ozero(U_162))
| ~ c_Orderings_Oord__class_Oless(U_162,c_Groups_Ozero__class_Ozero(U_162),U_164)
| ~ c_Orderings_Oord__class_Oless(U_162,U_163,c_Groups_Ozero__class_Ozero(U_162))
| ~ class_Fields_Olinordered__field(U_162) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__pos__neg]) ).
fof(f_64_2,plain,
! [U_167,U_166,U_165] :
( c_Orderings_Oord__class_Oless(U_165,c_Rings_Oinverse__class_Odivide(U_165,U_166,U_167),c_Groups_Ozero__class_Ozero(U_165))
| ~ c_Orderings_Oord__class_Oless(U_165,U_167,c_Groups_Ozero__class_Ozero(U_165))
| ~ c_Orderings_Oord__class_Oless(U_165,c_Groups_Ozero__class_Ozero(U_165),U_166)
| ~ class_Fields_Olinordered__field(U_165) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( c_Orderings_Oord__class_Oless(U_165,c_Rings_Oinverse__class_Odivide(U_165,U_166,U_167),c_Groups_Ozero__class_Ozero(U_165))
| ~ c_Orderings_Oord__class_Oless(U_165,U_167,c_Groups_Ozero__class_Ozero(U_165))
| ~ c_Orderings_Oord__class_Oless(U_165,c_Groups_Ozero__class_Ozero(U_165),U_166)
| ~ class_Fields_Olinordered__field(U_165) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__pos__pos]) ).
fof(f_65_2,plain,
! [U_170,U_169,U_168] :
( c_Orderings_Oord__class_Oless(U_168,c_Groups_Ozero__class_Ozero(U_168),c_Rings_Oinverse__class_Odivide(U_168,U_169,U_170))
| ~ c_Orderings_Oord__class_Oless(U_168,c_Groups_Ozero__class_Ozero(U_168),U_170)
| ~ c_Orderings_Oord__class_Oless(U_168,c_Groups_Ozero__class_Ozero(U_168),U_169)
| ~ class_Fields_Olinordered__field(U_168) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( c_Orderings_Oord__class_Oless(U_168,c_Groups_Ozero__class_Ozero(U_168),c_Rings_Oinverse__class_Odivide(U_168,U_169,U_170))
| ~ c_Orderings_Oord__class_Oless(U_168,c_Groups_Ozero__class_Ozero(U_168),U_170)
| ~ c_Orderings_Oord__class_Oless(U_168,c_Groups_Ozero__class_Ozero(U_168),U_169)
| ~ class_Fields_Olinordered__field(U_168) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff]) ).
fof(f_66_2,plain,
! [U_173,U_172,U_171] :
( ( ( c_Orderings_Oord__class_Oless(U_171,c_Rings_Oinverse__class_Odivide(U_171,U_172,U_173),c_Groups_Ozero__class_Ozero(U_171))
| ( ( ~ c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_173)
| ~ c_Orderings_Oord__class_Oless(U_171,U_172,c_Groups_Ozero__class_Ozero(U_171)) )
& ( ~ c_Orderings_Oord__class_Oless(U_171,U_173,c_Groups_Ozero__class_Ozero(U_171))
| ~ c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_172) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_173)
& c_Orderings_Oord__class_Oless(U_171,U_172,c_Groups_Ozero__class_Ozero(U_171)) )
| ( c_Orderings_Oord__class_Oless(U_171,U_173,c_Groups_Ozero__class_Ozero(U_171))
& c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_172) )
| ~ c_Orderings_Oord__class_Oless(U_171,c_Rings_Oinverse__class_Odivide(U_171,U_172,U_173),c_Groups_Ozero__class_Ozero(U_171)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_171) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( c_Orderings_Oord__class_Oless(U_171,U_172,c_Groups_Ozero__class_Ozero(U_171))
| c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_172)
| ~ c_Orderings_Oord__class_Oless(U_171,c_Rings_Oinverse__class_Odivide(U_171,U_172,U_173),c_Groups_Ozero__class_Ozero(U_171))
| ~ class_Fields_Olinordered__field__inverse__zero(U_171) ),
inference(clausify,[status(thm)],[f_66_2]) ).
cnf(f_66_4,plain,
( c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_173)
| c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_172)
| ~ c_Orderings_Oord__class_Oless(U_171,c_Rings_Oinverse__class_Odivide(U_171,U_172,U_173),c_Groups_Ozero__class_Ozero(U_171))
| ~ class_Fields_Olinordered__field__inverse__zero(U_171) ),
inference(clausify,[status(thm)],[f_66_2]) ).
cnf(f_66_5,plain,
( c_Orderings_Oord__class_Oless(U_171,U_172,c_Groups_Ozero__class_Ozero(U_171))
| c_Orderings_Oord__class_Oless(U_171,U_173,c_Groups_Ozero__class_Ozero(U_171))
| ~ c_Orderings_Oord__class_Oless(U_171,c_Rings_Oinverse__class_Odivide(U_171,U_172,U_173),c_Groups_Ozero__class_Ozero(U_171))
| ~ class_Fields_Olinordered__field__inverse__zero(U_171) ),
inference(clausify,[status(thm)],[f_66_2]) ).
cnf(f_66_6,plain,
( c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_173)
| c_Orderings_Oord__class_Oless(U_171,U_173,c_Groups_Ozero__class_Ozero(U_171))
| ~ c_Orderings_Oord__class_Oless(U_171,c_Rings_Oinverse__class_Odivide(U_171,U_172,U_173),c_Groups_Ozero__class_Ozero(U_171))
| ~ class_Fields_Olinordered__field__inverse__zero(U_171) ),
inference(clausify,[status(thm)],[f_66_2]) ).
cnf(f_66_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_171,U_173,c_Groups_Ozero__class_Ozero(U_171))
| ~ c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_172)
| c_Orderings_Oord__class_Oless(U_171,c_Rings_Oinverse__class_Odivide(U_171,U_172,U_173),c_Groups_Ozero__class_Ozero(U_171))
| ~ class_Fields_Olinordered__field__inverse__zero(U_171) ),
inference(clausify,[status(thm)],[f_66_2]) ).
cnf(f_66_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_171,c_Groups_Ozero__class_Ozero(U_171),U_173)
| ~ c_Orderings_Oord__class_Oless(U_171,U_172,c_Groups_Ozero__class_Ozero(U_171))
| c_Orderings_Oord__class_Oless(U_171,c_Rings_Oinverse__class_Odivide(U_171,U_172,U_173),c_Groups_Ozero__class_Ozero(U_171))
| ~ class_Fields_Olinordered__field__inverse__zero(U_171) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff]) ).
fof(f_67_2,plain,
! [U_176,U_175,U_174] :
( ( ( c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),c_Rings_Oinverse__class_Odivide(U_174,U_175,U_176))
| ( ( ~ c_Orderings_Oord__class_Oless(U_174,U_176,c_Groups_Ozero__class_Ozero(U_174))
| ~ c_Orderings_Oord__class_Oless(U_174,U_175,c_Groups_Ozero__class_Ozero(U_174)) )
& ( ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_176)
| ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_175) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_174,U_176,c_Groups_Ozero__class_Ozero(U_174))
& c_Orderings_Oord__class_Oless(U_174,U_175,c_Groups_Ozero__class_Ozero(U_174)) )
| ( c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_176)
& c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_175) )
| ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),c_Rings_Oinverse__class_Odivide(U_174,U_175,U_176)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_174) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( c_Orderings_Oord__class_Oless(U_174,U_175,c_Groups_Ozero__class_Ozero(U_174))
| c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_175)
| ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),c_Rings_Oinverse__class_Odivide(U_174,U_175,U_176))
| ~ class_Fields_Olinordered__field__inverse__zero(U_174) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_4,plain,
( c_Orderings_Oord__class_Oless(U_174,U_176,c_Groups_Ozero__class_Ozero(U_174))
| c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_175)
| ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),c_Rings_Oinverse__class_Odivide(U_174,U_175,U_176))
| ~ class_Fields_Olinordered__field__inverse__zero(U_174) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_5,plain,
( c_Orderings_Oord__class_Oless(U_174,U_175,c_Groups_Ozero__class_Ozero(U_174))
| c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_176)
| ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),c_Rings_Oinverse__class_Odivide(U_174,U_175,U_176))
| ~ class_Fields_Olinordered__field__inverse__zero(U_174) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_6,plain,
( c_Orderings_Oord__class_Oless(U_174,U_176,c_Groups_Ozero__class_Ozero(U_174))
| c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_176)
| ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),c_Rings_Oinverse__class_Odivide(U_174,U_175,U_176))
| ~ class_Fields_Olinordered__field__inverse__zero(U_174) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_176)
| ~ c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),U_175)
| c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),c_Rings_Oinverse__class_Odivide(U_174,U_175,U_176))
| ~ class_Fields_Olinordered__field__inverse__zero(U_174) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_174,U_176,c_Groups_Ozero__class_Ozero(U_174))
| ~ c_Orderings_Oord__class_Oless(U_174,U_175,c_Groups_Ozero__class_Ozero(U_174))
| c_Orderings_Oord__class_Oless(U_174,c_Groups_Ozero__class_Ozero(U_174),c_Rings_Oinverse__class_Odivide(U_174,U_175,U_176))
| ~ class_Fields_Olinordered__field__inverse__zero(U_174) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Pls]) ).
fof(f_68_2,plain,
! [U_177] :
( c_Int_Onumber__class_Onumber__of(U_177,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_177)
| ~ class_Int_Onumber__ring(U_177) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( c_Int_Onumber__class_Onumber__of(U_177,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_177)
| ~ class_Int_Onumber__ring(U_177) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__zero]) ).
fof(f_69_2,plain,
! [U_178] :
( c_RealVector_Onorm__class_Onorm(U_178,c_Groups_Ozero__class_Ozero(U_178)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_178) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( c_RealVector_Onorm__class_Onorm(U_178,c_Groups_Ozero__class_Ozero(U_178)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_178) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [V_x_2,T_a] :
( ( ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_RealVector_Onorm__class_Onorm(T_a,V_x_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__eq__zero]) ).
fof(f_70_2,plain,
! [U_180,U_179] :
( ( ( c_RealVector_Onorm__class_Onorm(U_179,U_180) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_180 != c_Groups_Ozero__class_Ozero(U_179) )
& ( U_180 = c_Groups_Ozero__class_Ozero(U_179)
| c_RealVector_Onorm__class_Onorm(U_179,U_180) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(U_179) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( U_180 = c_Groups_Ozero__class_Ozero(U_179)
| c_RealVector_Onorm__class_Onorm(U_179,U_180) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_179) ),
inference(clausify,[status(thm)],[f_70_2]) ).
cnf(f_70_4,plain,
( c_RealVector_Onorm__class_Onorm(U_179,U_180) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_180 != c_Groups_Ozero__class_Ozero(U_179)
| ~ class_RealVector_Oreal__normed__vector(U_179) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [V_a,V_b,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide]) ).
fof(f_71_2,plain,
! [U_183,U_182,U_181] :
( c_Groups_Oabs__class_Oabs(U_181,c_Rings_Oinverse__class_Odivide(U_181,U_183,U_182)) = c_Rings_Oinverse__class_Odivide(U_181,c_Groups_Oabs__class_Oabs(U_181,U_183),c_Groups_Oabs__class_Oabs(U_181,U_182))
| U_182 = c_Groups_Ozero__class_Ozero(U_181)
| ~ class_Fields_Olinordered__field(U_181) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( c_Groups_Oabs__class_Oabs(U_181,c_Rings_Oinverse__class_Odivide(U_181,U_183,U_182)) = c_Rings_Oinverse__class_Odivide(U_181,c_Groups_Oabs__class_Oabs(U_181,U_183),c_Groups_Oabs__class_Oabs(U_181,U_182))
| U_182 = c_Groups_Ozero__class_Ozero(U_181)
| ~ class_Fields_Olinordered__field(U_181) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__not__less__zero]) ).
fof(f_72_2,plain,
! [U_185,U_184] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_184,U_185),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_184) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_184,U_185),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_184) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [V_b,V_a,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))
| ~ class_RealVector_Oreal__normed__field(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__divide]) ).
fof(f_73_2,plain,
! [U_188,U_187,U_186] :
( c_RealVector_Onorm__class_Onorm(U_186,c_Rings_Oinverse__class_Odivide(U_186,U_187,U_188)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_186,U_187),c_RealVector_Onorm__class_Onorm(U_186,U_188))
| ~ class_RealVector_Oreal__normed__field(U_186)
| ~ class_Fields_Ofield__inverse__zero(U_186) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( c_RealVector_Onorm__class_Onorm(U_186,c_Rings_Oinverse__class_Odivide(U_186,U_187,U_188)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_186,U_187),c_RealVector_Onorm__class_Onorm(U_186,U_188))
| ~ class_RealVector_Oreal__normed__field(U_186)
| ~ class_Fields_Ofield__inverse__zero(U_186) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I3_J]) ).
fof(f_74_2,plain,
! [U_190,U_189] :
( ( ( c_Orderings_Oord__class_Oless(U_189,c_Int_Onumber__class_Onumber__of(U_189,U_190),c_Groups_Ozero__class_Ozero(U_189))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_190,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_190,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(U_189,c_Int_Onumber__class_Onumber__of(U_189,U_190),c_Groups_Ozero__class_Ozero(U_189)) ) )
| ~ class_Rings_Olinordered__idom(U_189)
| ~ class_Int_Onumber__ring(U_189) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_190,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(U_189,c_Int_Onumber__class_Onumber__of(U_189,U_190),c_Groups_Ozero__class_Ozero(U_189))
| ~ class_Rings_Olinordered__idom(U_189)
| ~ class_Int_Onumber__ring(U_189) ),
inference(clausify,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
( c_Orderings_Oord__class_Oless(U_189,c_Int_Onumber__class_Onumber__of(U_189,U_190),c_Groups_Ozero__class_Ozero(U_189))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_190,c_Int_OPls)
| ~ class_Rings_Olinordered__idom(U_189)
| ~ class_Int_Onumber__ring(U_189) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).
fof(f_75_2,plain,
! [U_192,U_191] :
( ( ( c_Orderings_Oord__class_Oless(U_191,c_Groups_Ozero__class_Ozero(U_191),c_Int_Onumber__class_Onumber__of(U_191,U_192))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_192) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_192)
| ~ c_Orderings_Oord__class_Oless(U_191,c_Groups_Ozero__class_Ozero(U_191),c_Int_Onumber__class_Onumber__of(U_191,U_192)) ) )
| ~ class_Rings_Olinordered__idom(U_191)
| ~ class_Int_Onumber__ring(U_191) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_192)
| ~ c_Orderings_Oord__class_Oless(U_191,c_Groups_Ozero__class_Ozero(U_191),c_Int_Onumber__class_Onumber__of(U_191,U_192))
| ~ class_Rings_Olinordered__idom(U_191)
| ~ class_Int_Onumber__ring(U_191) ),
inference(clausify,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
( c_Orderings_Oord__class_Oless(U_191,c_Groups_Ozero__class_Ozero(U_191),c_Int_Onumber__class_Onumber__of(U_191,U_192))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_192)
| ~ class_Rings_Olinordered__idom(U_191)
| ~ class_Int_Onumber__ring(U_191) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__neg]) ).
fof(f_76_2,plain,
! [U_194,U_193] :
( c_Groups_Oabs__class_Oabs(U_193,U_194) = c_Groups_Ouminus__class_Ouminus(U_193,U_194)
| ~ c_Orderings_Oord__class_Oless(U_193,U_194,c_Groups_Ozero__class_Ozero(U_193))
| ~ class_Groups_Oordered__ab__group__add__abs(U_193) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( c_Groups_Oabs__class_Oabs(U_193,U_194) = c_Groups_Ouminus__class_Ouminus(U_193,U_194)
| ~ c_Orderings_Oord__class_Oless(U_193,U_194,c_Groups_Ozero__class_Ozero(U_193))
| ~ class_Groups_Oordered__ab__group__add__abs(U_193) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [V_a,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oabs__if(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__if]) ).
fof(f_77_2,plain,
! [U_196,U_195] :
( ( ( c_Groups_Oabs__class_Oabs(U_195,U_196) = U_196
| c_Orderings_Oord__class_Oless(U_195,U_196,c_Groups_Ozero__class_Ozero(U_195)) )
& ( c_Groups_Oabs__class_Oabs(U_195,U_196) = c_Groups_Ouminus__class_Ouminus(U_195,U_196)
| ~ c_Orderings_Oord__class_Oless(U_195,U_196,c_Groups_Ozero__class_Ozero(U_195)) ) )
| ~ class_Groups_Oabs__if(U_195) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( c_Groups_Oabs__class_Oabs(U_195,U_196) = c_Groups_Ouminus__class_Ouminus(U_195,U_196)
| ~ c_Orderings_Oord__class_Oless(U_195,U_196,c_Groups_Ozero__class_Ozero(U_195))
| ~ class_Groups_Oabs__if(U_195) ),
inference(clausify,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
( c_Groups_Oabs__class_Oabs(U_195,U_196) = U_196
| c_Orderings_Oord__class_Oless(U_195,U_196,c_Groups_Ozero__class_Ozero(U_195))
| ~ class_Groups_Oabs__if(U_195) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_pos2]) ).
cnf(f_78_2,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_79_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).
fof(f_79_2,plain,
! [U_199,U_198,U_197] :
( ( ( c_Orderings_Oord__class_Oless(U_197,c_Groups_Oabs__class_Oabs(U_197,U_198),U_199)
| ~ c_Orderings_Oord__class_Oless(U_197,c_Groups_Ouminus__class_Ouminus(U_197,U_198),U_199)
| ~ c_Orderings_Oord__class_Oless(U_197,U_198,U_199) )
& ( ( c_Orderings_Oord__class_Oless(U_197,c_Groups_Ouminus__class_Ouminus(U_197,U_198),U_199)
& c_Orderings_Oord__class_Oless(U_197,U_198,U_199) )
| ~ c_Orderings_Oord__class_Oless(U_197,c_Groups_Oabs__class_Oabs(U_197,U_198),U_199) ) )
| ~ class_Rings_Olinordered__idom(U_197) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( c_Orderings_Oord__class_Oless(U_197,U_198,U_199)
| ~ c_Orderings_Oord__class_Oless(U_197,c_Groups_Oabs__class_Oabs(U_197,U_198),U_199)
| ~ class_Rings_Olinordered__idom(U_197) ),
inference(clausify,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( c_Orderings_Oord__class_Oless(U_197,c_Groups_Ouminus__class_Ouminus(U_197,U_198),U_199)
| ~ c_Orderings_Oord__class_Oless(U_197,c_Groups_Oabs__class_Oabs(U_197,U_198),U_199)
| ~ class_Rings_Olinordered__idom(U_197) ),
inference(clausify,[status(thm)],[f_79_2]) ).
cnf(f_79_5,plain,
( c_Orderings_Oord__class_Oless(U_197,c_Groups_Oabs__class_Oabs(U_197,U_198),U_199)
| ~ c_Orderings_Oord__class_Oless(U_197,c_Groups_Ouminus__class_Ouminus(U_197,U_198),U_199)
| ~ c_Orderings_Oord__class_Oless(U_197,U_198,U_199)
| ~ class_Rings_Olinordered__idom(U_197) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [V_a,V_b,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide]) ).
fof(f_80_2,plain,
! [U_202,U_201,U_200] :
( c_Rings_Oinverse__class_Odivide(U_200,c_Groups_Ouminus__class_Ouminus(U_200,U_202),c_Groups_Ouminus__class_Ouminus(U_200,U_201)) = c_Rings_Oinverse__class_Odivide(U_200,U_202,U_201)
| U_201 = c_Groups_Ozero__class_Ozero(U_200)
| ~ class_Rings_Odivision__ring(U_200) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( c_Rings_Oinverse__class_Odivide(U_200,c_Groups_Ouminus__class_Ouminus(U_200,U_202),c_Groups_Ouminus__class_Ouminus(U_200,U_201)) = c_Rings_Oinverse__class_Odivide(U_200,U_202,U_201)
| U_201 = c_Groups_Ozero__class_Ozero(U_200)
| ~ class_Rings_Odivision__ring(U_200) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [V_a,V_b,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right]) ).
fof(f_81_2,plain,
! [U_205,U_204,U_203] :
( c_Groups_Ouminus__class_Ouminus(U_203,c_Rings_Oinverse__class_Odivide(U_203,U_205,U_204)) = c_Rings_Oinverse__class_Odivide(U_203,U_205,c_Groups_Ouminus__class_Ouminus(U_203,U_204))
| U_204 = c_Groups_Ozero__class_Ozero(U_203)
| ~ class_Rings_Odivision__ring(U_203) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_203,c_Rings_Oinverse__class_Odivide(U_203,U_205,U_204)) = c_Rings_Oinverse__class_Odivide(U_203,U_205,c_Groups_Ouminus__class_Ouminus(U_203,U_204))
| U_204 = c_Groups_Ozero__class_Ozero(U_203)
| ~ class_Rings_Odivision__ring(U_203) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__pos]) ).
fof(f_82_2,plain,
! [U_207,U_206] :
( c_Groups_Oabs__class_Oabs(U_206,U_207) = U_207
| ~ c_Orderings_Oord__class_Oless(U_206,c_Groups_Ozero__class_Ozero(U_206),U_207)
| ~ class_Groups_Oordered__ab__group__add__abs(U_206) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( c_Groups_Oabs__class_Oabs(U_206,U_207) = U_207
| ~ c_Orderings_Oord__class_Oless(U_206,c_Groups_Ozero__class_Ozero(U_206),U_207)
| ~ class_Groups_Oordered__ab__group__add__abs(U_206) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).
fof(f_83_2,plain,
! [U_209,U_208] :
( ( ( c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208),c_Groups_Oabs__class_Oabs(U_208,U_209))
| U_209 = c_Groups_Ozero__class_Ozero(U_208) )
& ( U_209 != c_Groups_Ozero__class_Ozero(U_208)
| ~ c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208),c_Groups_Oabs__class_Oabs(U_208,U_209)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_208) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( U_209 != c_Groups_Ozero__class_Ozero(U_208)
| ~ c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208),c_Groups_Oabs__class_Oabs(U_208,U_209))
| ~ class_Groups_Oordered__ab__group__add__abs(U_208) ),
inference(clausify,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
( c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208),c_Groups_Oabs__class_Oabs(U_208,U_209))
| U_209 = c_Groups_Ozero__class_Ozero(U_208)
| ~ class_Groups_Oordered__ab__group__add__abs(U_208) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__not__less__zero]) ).
fof(f_84_2,plain,
! [U_211,U_210] :
( ~ c_Orderings_Oord__class_Oless(U_210,c_Groups_Oabs__class_Oabs(U_210,U_211),c_Groups_Ozero__class_Ozero(U_210))
| ~ class_Groups_Oordered__ab__group__add__abs(U_210) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_210,c_Groups_Oabs__class_Oabs(U_210,U_211),c_Groups_Ozero__class_Ozero(U_210))
| ~ class_Groups_Oordered__ab__group__add__abs(U_210) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [T_a] :
( c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J]) ).
fof(f_85_2,plain,
! [U_212] :
( c_Groups_Ozero__class_Ozero(U_212) = c_Int_Onumber__class_Onumber__of(U_212,c_Int_OPls)
| ~ class_Int_Onumber__ring(U_212) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( c_Groups_Ozero__class_Ozero(U_212) = c_Int_Onumber__class_Onumber__of(U_212,c_Int_OPls)
| ~ class_Int_Onumber__ring(U_212) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__0]) ).
fof(f_86_2,plain,
! [U_214,U_213] :
( c_Groups_Ominus__class_Ominus(U_213,c_Groups_Ozero__class_Ozero(U_213),U_214) = c_Groups_Ouminus__class_Ouminus(U_213,U_214)
| ~ class_Groups_Ogroup__add(U_213) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( c_Groups_Ominus__class_Ominus(U_213,c_Groups_Ozero__class_Ozero(U_213),U_214) = c_Groups_Ouminus__class_Ouminus(U_213,U_214)
| ~ class_Groups_Ogroup__add(U_213) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).
fof(f_87_2,plain,
! [U_216,U_215] :
( ( ( c_Orderings_Oord__class_Oless(U_215,c_Groups_Ouminus__class_Ouminus(U_215,U_216),U_216)
| ~ c_Orderings_Oord__class_Oless(U_215,c_Groups_Ozero__class_Ozero(U_215),U_216) )
& ( c_Orderings_Oord__class_Oless(U_215,c_Groups_Ozero__class_Ozero(U_215),U_216)
| ~ c_Orderings_Oord__class_Oless(U_215,c_Groups_Ouminus__class_Ouminus(U_215,U_216),U_216) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_215) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( c_Orderings_Oord__class_Oless(U_215,c_Groups_Ozero__class_Ozero(U_215),U_216)
| ~ c_Orderings_Oord__class_Oless(U_215,c_Groups_Ouminus__class_Ouminus(U_215,U_216),U_216)
| ~ class_Groups_Olinordered__ab__group__add(U_215) ),
inference(clausify,[status(thm)],[f_87_2]) ).
cnf(f_87_4,plain,
( c_Orderings_Oord__class_Oless(U_215,c_Groups_Ouminus__class_Ouminus(U_215,U_216),U_216)
| ~ c_Orderings_Oord__class_Oless(U_215,c_Groups_Ozero__class_Ozero(U_215),U_216)
| ~ class_Groups_Olinordered__ab__group__add(U_215) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).
cnf(f_88_2,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_88_1]) ).
fof(f_89_1,plain,
! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k,
inference(fof_nnf,[status(thm)],[fact_number__of__is__id]) ).
fof(f_89_2,plain,
! [U_217] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_217) = U_217,
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_217) = U_217,
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [V_i] :
( ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_zabs__def]) ).
fof(f_90_2,plain,
! [U_218] :
( ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_218) = U_218
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_218,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_218) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_218)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_218,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
( ! [U_220] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_220) = U_220
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_220,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_219] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_219) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_219)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_219,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_219) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_219)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_219,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_5,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_220) = U_220
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_220,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zminus__zminus]) ).
fof(f_91_2,plain,
! [U_221] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_221)) = U_221,
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_221)) = U_221,
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [V_w] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I5_J]) ).
fof(f_92_2,plain,
! [U_222] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_222)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_222)),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_222)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_222)),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__bin__lemma]) ).
fof(f_93_2,plain,
! [U_224,U_223] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_223,U_224)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_223,U_224),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_223,U_224),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_223,U_224) ) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_228,U_226] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_226,U_228)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_226,U_228),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_227,U_225] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_225,U_227),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_225,U_227) ) ),
inference(miniscope,[status(thm)],[f_93_2]) ).
cnf(f_93_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_225,U_227),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_225,U_227) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_226,U_228)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_226,U_228),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_zless__linear]) ).
fof(f_94_2,plain,
! [U_230,U_229] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_230,U_229)
| U_229 = U_230
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_229,U_230) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_230,U_229)
| U_229 = U_230
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_229,U_230) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code]) ).
fof(f_95_2,plain,
! [U_232,U_231] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_231),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_232))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_231,U_232) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_231,U_232)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_231),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_232)) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_236,U_234] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_234),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_236))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_234,U_236) )
& ! [U_235,U_233] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_233,U_235)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_233),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_235)) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_233,U_235)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_233),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_235)) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_234),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_236))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_234,U_236) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
! [V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I1_J]) ).
fof(f_96_2,plain,
! [U_237] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_237,c_Int_OPls) = U_237,
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_237,c_Int_OPls) = U_237,
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I7_J]) ).
fof(f_97_2,plain,
! [U_239,U_238] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(U_238),c_Int_OBit0(U_239)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_238,U_239)),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(U_238),c_Int_OBit0(U_239)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_238,U_239)),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I9_J]) ).
fof(f_98_2,plain,
! [U_241,U_240] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_240),c_Int_OBit0(U_241)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_240,U_241)),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_240),c_Int_OBit0(U_241)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_240,U_241)),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I10_J]) ).
fof(f_99_2,plain,
! [U_243,U_242] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_242),c_Int_OBit1(U_243)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_242,U_243)),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_242),c_Int_OBit1(U_243)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_242,U_243)),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,V_l)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I3_J]) ).
fof(f_100_2,plain,
! [U_244] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_244)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,U_244)),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_244)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,U_244)),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != V_x_2 ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).
fof(f_101_2,plain,
! [U_246,U_245] :
( ( ( c_Groups_Ozero__class_Ozero(U_245) = U_246
| U_246 != c_Groups_Ozero__class_Ozero(U_245) )
& ( U_246 = c_Groups_Ozero__class_Ozero(U_245)
| c_Groups_Ozero__class_Ozero(U_245) != U_246 ) )
| ~ class_Groups_Ozero(U_245) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( U_246 = c_Groups_Ozero__class_Ozero(U_245)
| c_Groups_Ozero__class_Ozero(U_245) != U_246
| ~ class_Groups_Ozero(U_245) ),
inference(clausify,[status(thm)],[f_101_2]) ).
cnf(f_101_4,plain,
( c_Groups_Ozero__class_Ozero(U_245) = U_246
| U_246 != c_Groups_Ozero__class_Ozero(U_245)
| ~ class_Groups_Ozero(U_245) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| V_x = V_y
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(f_102_2,plain,
! [U_249,U_248,U_247] :
( c_Orderings_Oord__class_Oless(U_247,U_249,U_248)
| c_Orderings_Oord__class_Oless(U_247,U_248,U_249)
| U_248 = U_249
| ~ class_Rings_Olinordered__idom(U_247) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( c_Orderings_Oord__class_Oless(U_247,U_249,U_248)
| c_Orderings_Oord__class_Oless(U_247,U_248,U_249)
| U_248 = U_249
| ~ class_Rings_Olinordered__idom(U_247) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = V_b_2
| V_c_2 != V_d_2 )
& ( V_c_2 = V_d_2
| V_a_2 != V_b_2 ) )
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).
fof(f_103_2,plain,
! [U_254,U_253,U_252,U_251,U_250] :
( ( ( U_251 = U_252
| U_253 != U_254 )
& ( U_253 = U_254
| U_251 != U_252 ) )
| c_Groups_Ominus__class_Ominus(U_250,U_251,U_252) != c_Groups_Ominus__class_Ominus(U_250,U_253,U_254)
| ~ class_Groups_Oab__group__add(U_250) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( U_253 = U_254
| U_251 != U_252
| c_Groups_Ominus__class_Ominus(U_250,U_251,U_252) != c_Groups_Ominus__class_Ominus(U_250,U_253,U_254)
| ~ class_Groups_Oab__group__add(U_250) ),
inference(clausify,[status(thm)],[f_103_2]) ).
cnf(f_103_4,plain,
( U_251 = U_252
| U_253 != U_254
| c_Groups_Ominus__class_Ominus(U_250,U_251,U_252) != c_Groups_Ominus__class_Ominus(U_250,U_253,U_254)
| ~ class_Groups_Oab__group__add(U_250) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__minus]) ).
fof(f_104_2,plain,
! [U_256,U_255] :
( c_Groups_Ouminus__class_Ouminus(U_255,c_Groups_Ouminus__class_Ouminus(U_255,U_256)) = U_256
| ~ class_Groups_Ogroup__add(U_255) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_255,c_Groups_Ouminus__class_Ouminus(U_255,U_256)) = U_256
| ~ class_Groups_Ogroup__add(U_255) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_b_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) )
& ( V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).
fof(f_105_2,plain,
! [U_259,U_258,U_257] :
( ( ( U_258 = c_Groups_Ouminus__class_Ouminus(U_257,U_259)
| U_259 != c_Groups_Ouminus__class_Ouminus(U_257,U_258) )
& ( U_259 = c_Groups_Ouminus__class_Ouminus(U_257,U_258)
| U_258 != c_Groups_Ouminus__class_Ouminus(U_257,U_259) ) )
| ~ class_Groups_Ogroup__add(U_257) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
( U_259 = c_Groups_Ouminus__class_Ouminus(U_257,U_258)
| U_258 != c_Groups_Ouminus__class_Ouminus(U_257,U_259)
| ~ class_Groups_Ogroup__add(U_257) ),
inference(clausify,[status(thm)],[f_105_2]) ).
cnf(f_105_4,plain,
( U_258 = c_Groups_Ouminus__class_Ouminus(U_257,U_259)
| U_259 != c_Groups_Ouminus__class_Ouminus(U_257,U_258)
| ~ class_Groups_Ogroup__add(U_257) ),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) != V_a_2 )
& ( c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != V_b_2 ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).
fof(f_106_2,plain,
! [U_262,U_261,U_260] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_260,U_261) = U_262
| c_Groups_Ouminus__class_Ouminus(U_260,U_262) != U_261 )
& ( c_Groups_Ouminus__class_Ouminus(U_260,U_262) = U_261
| c_Groups_Ouminus__class_Ouminus(U_260,U_261) != U_262 ) )
| ~ class_Groups_Ogroup__add(U_260) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_260,U_262) = U_261
| c_Groups_Ouminus__class_Ouminus(U_260,U_261) != U_262
| ~ class_Groups_Ogroup__add(U_260) ),
inference(clausify,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_260,U_261) = U_262
| c_Groups_Ouminus__class_Ouminus(U_260,U_262) != U_261
| ~ class_Groups_Ogroup__add(U_260) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).
fof(f_107_2,plain,
! [U_265,U_264,U_263] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_263,U_264) = c_Groups_Ouminus__class_Ouminus(U_263,U_265)
| U_264 != U_265 )
& ( U_264 = U_265
| c_Groups_Ouminus__class_Ouminus(U_263,U_264) != c_Groups_Ouminus__class_Ouminus(U_263,U_265) ) )
| ~ class_Groups_Ogroup__add(U_263) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( U_264 = U_265
| c_Groups_Ouminus__class_Ouminus(U_263,U_264) != c_Groups_Ouminus__class_Ouminus(U_263,U_265)
| ~ class_Groups_Ogroup__add(U_263) ),
inference(clausify,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_263,U_264) = c_Groups_Ouminus__class_Ouminus(U_263,U_265)
| U_264 != U_265
| ~ class_Groups_Ogroup__add(U_263) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
! [V_v_H_2,V_v_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__nat__number__of]) ).
fof(f_108_2,plain,
! [U_267,U_266] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_266),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_267))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_266,U_267)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_267)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_266,U_267) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_266,U_267)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_267)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_266,U_267) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_266),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_267)) ) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
( ! [U_271,U_269] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_269),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_271))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_269,U_271)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_271)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_269,U_271) ) )
& ! [U_270,U_268] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_268,U_270)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_270)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_268,U_270) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_268),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_270)) ) ),
inference(miniscope,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_270)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_268,U_270)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_268),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_270)) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_268,U_270)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_268),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_270)) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_269,U_271)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_269,U_271)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_269),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_271)) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_271)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_269,U_271)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_269),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_271)) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [V_v_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__0__number__of]) ).
fof(f_109_2,plain,
! [U_272] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_272))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_272) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_272)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_272)) ) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_274] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_274))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_274) )
& ! [U_273] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_273)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_273)) ) ),
inference(miniscope,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_273)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_273)) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_274))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_274) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__Pls]) ).
cnf(f_110_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_110_1]) ).
fof(f_111_1,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I113_J]) ).
cnf(f_111_2,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(clausify,[status(thm)],[f_111_1]) ).
fof(f_112_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__idempotent]) ).
fof(f_112_2,plain,
! [U_276,U_275] :
( c_Groups_Oabs__class_Oabs(U_275,c_Groups_Oabs__class_Oabs(U_275,U_276)) = c_Groups_Oabs__class_Oabs(U_275,U_276)
| ~ class_Groups_Oordered__ab__group__add__abs(U_275) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( c_Groups_Oabs__class_Oabs(U_275,c_Groups_Oabs__class_Oabs(U_275,U_276)) = c_Groups_Oabs__class_Oabs(U_275,U_276)
| ~ class_Groups_Oordered__ab__group__add__abs(U_275) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__0__right]) ).
fof(f_113_2,plain,
! [U_278,U_277] :
( c_Groups_Ominus__class_Ominus(U_277,U_278,c_Groups_Ozero__class_Ozero(U_277)) = U_278
| ~ class_Groups_Ogroup__add(U_277) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( c_Groups_Ominus__class_Ominus(U_277,U_278,c_Groups_Ozero__class_Ozero(U_277)) = U_278
| ~ class_Groups_Ogroup__add(U_277) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
! [V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__self]) ).
fof(f_114_2,plain,
! [U_280,U_279] :
( c_Groups_Ominus__class_Ominus(U_279,U_280,U_280) = c_Groups_Ozero__class_Ozero(U_279)
| ~ class_Groups_Ogroup__add(U_279) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( c_Groups_Ominus__class_Ominus(U_279,U_280,U_280) = c_Groups_Ozero__class_Ozero(U_279)
| ~ class_Groups_Ogroup__add(U_279) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = V_b_2
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != V_b_2 ) )
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).
fof(f_115_2,plain,
! [U_283,U_282,U_281] :
( ( ( U_282 = U_283
| c_Groups_Ominus__class_Ominus(U_281,U_282,U_283) != c_Groups_Ozero__class_Ozero(U_281) )
& ( c_Groups_Ominus__class_Ominus(U_281,U_282,U_283) = c_Groups_Ozero__class_Ozero(U_281)
| U_282 != U_283 ) )
| ~ class_Groups_Oab__group__add(U_281) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( c_Groups_Ominus__class_Ominus(U_281,U_282,U_283) = c_Groups_Ozero__class_Ozero(U_281)
| U_282 != U_283
| ~ class_Groups_Oab__group__add(U_281) ),
inference(clausify,[status(thm)],[f_115_2]) ).
cnf(f_115_4,plain,
( U_282 = U_283
| c_Groups_Ominus__class_Ominus(U_281,U_282,U_283) != c_Groups_Ozero__class_Ozero(U_281)
| ~ class_Groups_Oab__group__add(U_281) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).
fof(f_116_2,plain,
! [U_286,U_285,U_284] :
( ( ( c_Groups_Ominus__class_Ominus(U_284,U_285,U_286) = c_Groups_Ozero__class_Ozero(U_284)
| U_285 != U_286 )
& ( U_285 = U_286
| c_Groups_Ominus__class_Ominus(U_284,U_285,U_286) != c_Groups_Ozero__class_Ozero(U_284) ) )
| ~ class_Groups_Ogroup__add(U_284) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( U_285 = U_286
| c_Groups_Ominus__class_Ominus(U_284,U_285,U_286) != c_Groups_Ozero__class_Ozero(U_284)
| ~ class_Groups_Ogroup__add(U_284) ),
inference(clausify,[status(thm)],[f_116_2]) ).
cnf(f_116_4,plain,
( c_Groups_Ominus__class_Ominus(U_284,U_285,U_286) = c_Groups_Ozero__class_Ozero(U_284)
| U_285 != U_286
| ~ class_Groups_Ogroup__add(U_284) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) )
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).
fof(f_117_2,plain,
! [U_291,U_290,U_289,U_288,U_287] :
( ( ( c_Orderings_Oord__class_Oless(U_287,U_288,U_289)
| ~ c_Orderings_Oord__class_Oless(U_287,U_290,U_291) )
& ( c_Orderings_Oord__class_Oless(U_287,U_290,U_291)
| ~ c_Orderings_Oord__class_Oless(U_287,U_288,U_289) ) )
| c_Groups_Ominus__class_Ominus(U_287,U_288,U_289) != c_Groups_Ominus__class_Ominus(U_287,U_290,U_291)
| ~ class_Groups_Oordered__ab__group__add(U_287) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( c_Orderings_Oord__class_Oless(U_287,U_290,U_291)
| ~ c_Orderings_Oord__class_Oless(U_287,U_288,U_289)
| c_Groups_Ominus__class_Ominus(U_287,U_288,U_289) != c_Groups_Ominus__class_Ominus(U_287,U_290,U_291)
| ~ class_Groups_Oordered__ab__group__add(U_287) ),
inference(clausify,[status(thm)],[f_117_2]) ).
cnf(f_117_4,plain,
( c_Orderings_Oord__class_Oless(U_287,U_288,U_289)
| ~ c_Orderings_Oord__class_Oless(U_287,U_290,U_291)
| c_Groups_Ominus__class_Ominus(U_287,U_288,U_289) != c_Groups_Ominus__class_Ominus(U_287,U_290,U_291)
| ~ class_Groups_Oordered__ab__group__add(U_287) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_1,plain,
! [T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__zero]) ).
fof(f_118_2,plain,
! [U_292] :
( c_Groups_Ouminus__class_Ouminus(U_292,c_Groups_Ozero__class_Ozero(U_292)) = c_Groups_Ozero__class_Ozero(U_292)
| ~ class_Groups_Ogroup__add(U_292) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_292,c_Groups_Ozero__class_Ozero(U_292)) = c_Groups_Ozero__class_Ozero(U_292)
| ~ class_Groups_Ogroup__add(U_292) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| c_Groups_Ozero__class_Ozero(T_a) != V_a_2 )
& ( c_Groups_Ozero__class_Ozero(T_a) = V_a_2
| c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).
fof(f_119_2,plain,
! [U_294,U_293] :
( ( ( c_Groups_Ozero__class_Ozero(U_293) = c_Groups_Ouminus__class_Ouminus(U_293,U_294)
| c_Groups_Ozero__class_Ozero(U_293) != U_294 )
& ( c_Groups_Ozero__class_Ozero(U_293) = U_294
| c_Groups_Ozero__class_Ozero(U_293) != c_Groups_Ouminus__class_Ouminus(U_293,U_294) ) )
| ~ class_Groups_Ogroup__add(U_293) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( c_Groups_Ozero__class_Ozero(U_293) = U_294
| c_Groups_Ozero__class_Ozero(U_293) != c_Groups_Ouminus__class_Ouminus(U_293,U_294)
| ~ class_Groups_Ogroup__add(U_293) ),
inference(clausify,[status(thm)],[f_119_2]) ).
cnf(f_119_4,plain,
( c_Groups_Ozero__class_Ozero(U_293) = c_Groups_Ouminus__class_Ouminus(U_293,U_294)
| c_Groups_Ozero__class_Ozero(U_293) != U_294
| ~ class_Groups_Ogroup__add(U_293) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).
fof(f_120_2,plain,
! [U_296,U_295] :
( ( ( U_296 = c_Groups_Ouminus__class_Ouminus(U_295,U_296)
| U_296 != c_Groups_Ozero__class_Ozero(U_295) )
& ( U_296 = c_Groups_Ozero__class_Ozero(U_295)
| U_296 != c_Groups_Ouminus__class_Ouminus(U_295,U_296) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_295) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( U_296 = c_Groups_Ozero__class_Ozero(U_295)
| U_296 != c_Groups_Ouminus__class_Ouminus(U_295,U_296)
| ~ class_Groups_Olinordered__ab__group__add(U_295) ),
inference(clausify,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( U_296 = c_Groups_Ouminus__class_Ouminus(U_295,U_296)
| U_296 != c_Groups_Ozero__class_Ozero(U_295)
| ~ class_Groups_Olinordered__ab__group__add(U_295) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).
fof(f_121_2,plain,
! [U_298,U_297] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_297,U_298) = c_Groups_Ozero__class_Ozero(U_297)
| U_298 != c_Groups_Ozero__class_Ozero(U_297) )
& ( U_298 = c_Groups_Ozero__class_Ozero(U_297)
| c_Groups_Ouminus__class_Ouminus(U_297,U_298) != c_Groups_Ozero__class_Ozero(U_297) ) )
| ~ class_Groups_Ogroup__add(U_297) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( U_298 = c_Groups_Ozero__class_Ozero(U_297)
| c_Groups_Ouminus__class_Ouminus(U_297,U_298) != c_Groups_Ozero__class_Ozero(U_297)
| ~ class_Groups_Ogroup__add(U_297) ),
inference(clausify,[status(thm)],[f_121_2]) ).
cnf(f_121_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_297,U_298) = c_Groups_Ozero__class_Ozero(U_297)
| U_298 != c_Groups_Ozero__class_Ozero(U_297)
| ~ class_Groups_Ogroup__add(U_297) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != V_a_2 ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).
fof(f_122_2,plain,
! [U_300,U_299] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_299,U_300) = U_300
| U_300 != c_Groups_Ozero__class_Ozero(U_299) )
& ( U_300 = c_Groups_Ozero__class_Ozero(U_299)
| c_Groups_Ouminus__class_Ouminus(U_299,U_300) != U_300 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_299) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( U_300 = c_Groups_Ozero__class_Ozero(U_299)
| c_Groups_Ouminus__class_Ouminus(U_299,U_300) != U_300
| ~ class_Groups_Olinordered__ab__group__add(U_299) ),
inference(clausify,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_299,U_300) = U_300
| U_300 != c_Groups_Ozero__class_Ozero(U_299)
| ~ class_Groups_Olinordered__ab__group__add(U_299) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).
fof(f_123_2,plain,
! [U_303,U_302,U_301] :
( ( ( c_Orderings_Oord__class_Oless(U_301,U_302,c_Groups_Ouminus__class_Ouminus(U_301,U_303))
| ~ c_Orderings_Oord__class_Oless(U_301,U_303,c_Groups_Ouminus__class_Ouminus(U_301,U_302)) )
& ( c_Orderings_Oord__class_Oless(U_301,U_303,c_Groups_Ouminus__class_Ouminus(U_301,U_302))
| ~ c_Orderings_Oord__class_Oless(U_301,U_302,c_Groups_Ouminus__class_Ouminus(U_301,U_303)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_301) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( c_Orderings_Oord__class_Oless(U_301,U_303,c_Groups_Ouminus__class_Ouminus(U_301,U_302))
| ~ c_Orderings_Oord__class_Oless(U_301,U_302,c_Groups_Ouminus__class_Ouminus(U_301,U_303))
| ~ class_Groups_Oordered__ab__group__add(U_301) ),
inference(clausify,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
( c_Orderings_Oord__class_Oless(U_301,U_302,c_Groups_Ouminus__class_Ouminus(U_301,U_303))
| ~ c_Orderings_Oord__class_Oless(U_301,U_303,c_Groups_Ouminus__class_Ouminus(U_301,U_302))
| ~ class_Groups_Oordered__ab__group__add(U_301) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).
fof(f_124_2,plain,
! [U_306,U_305,U_304] :
( ( ( c_Orderings_Oord__class_Oless(U_304,c_Groups_Ouminus__class_Ouminus(U_304,U_305),U_306)
| ~ c_Orderings_Oord__class_Oless(U_304,c_Groups_Ouminus__class_Ouminus(U_304,U_306),U_305) )
& ( c_Orderings_Oord__class_Oless(U_304,c_Groups_Ouminus__class_Ouminus(U_304,U_306),U_305)
| ~ c_Orderings_Oord__class_Oless(U_304,c_Groups_Ouminus__class_Ouminus(U_304,U_305),U_306) ) )
| ~ class_Groups_Oordered__ab__group__add(U_304) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( c_Orderings_Oord__class_Oless(U_304,c_Groups_Ouminus__class_Ouminus(U_304,U_306),U_305)
| ~ c_Orderings_Oord__class_Oless(U_304,c_Groups_Ouminus__class_Ouminus(U_304,U_305),U_306)
| ~ class_Groups_Oordered__ab__group__add(U_304) ),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_4,plain,
( c_Orderings_Oord__class_Oless(U_304,c_Groups_Ouminus__class_Ouminus(U_304,U_305),U_306)
| ~ c_Orderings_Oord__class_Oless(U_304,c_Groups_Ouminus__class_Ouminus(U_304,U_306),U_305)
| ~ class_Groups_Oordered__ab__group__add(U_304) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).
fof(f_125_2,plain,
! [U_309,U_308,U_307] :
( ( ( c_Orderings_Oord__class_Oless(U_307,c_Groups_Ouminus__class_Ouminus(U_307,U_308),c_Groups_Ouminus__class_Ouminus(U_307,U_309))
| ~ c_Orderings_Oord__class_Oless(U_307,U_309,U_308) )
& ( c_Orderings_Oord__class_Oless(U_307,U_309,U_308)
| ~ c_Orderings_Oord__class_Oless(U_307,c_Groups_Ouminus__class_Ouminus(U_307,U_308),c_Groups_Ouminus__class_Ouminus(U_307,U_309)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_307) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( c_Orderings_Oord__class_Oless(U_307,U_309,U_308)
| ~ c_Orderings_Oord__class_Oless(U_307,c_Groups_Ouminus__class_Ouminus(U_307,U_308),c_Groups_Ouminus__class_Ouminus(U_307,U_309))
| ~ class_Groups_Oordered__ab__group__add(U_307) ),
inference(clausify,[status(thm)],[f_125_2]) ).
cnf(f_125_4,plain,
( c_Orderings_Oord__class_Oless(U_307,c_Groups_Ouminus__class_Ouminus(U_307,U_308),c_Groups_Ouminus__class_Ouminus(U_307,U_309))
| ~ c_Orderings_Oord__class_Oless(U_307,U_309,U_308)
| ~ class_Groups_Oordered__ab__group__add(U_307) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__zero__left]) ).
fof(f_126_2,plain,
! [U_311,U_310] :
( c_Rings_Oinverse__class_Odivide(U_310,c_Groups_Ozero__class_Ozero(U_310),U_311) = c_Groups_Ozero__class_Ozero(U_310)
| ~ class_Rings_Odivision__ring(U_310) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( c_Rings_Oinverse__class_Odivide(U_310,c_Groups_Ozero__class_Ozero(U_310),U_311) = c_Groups_Ozero__class_Ozero(U_310)
| ~ class_Rings_Odivision__ring(U_310) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__zero]) ).
fof(f_127_2,plain,
! [U_313,U_312] :
( c_Rings_Oinverse__class_Odivide(U_312,U_313,c_Groups_Ozero__class_Ozero(U_312)) = c_Groups_Ozero__class_Ozero(U_312)
| ~ class_Rings_Odivision__ring__inverse__zero(U_312) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( c_Rings_Oinverse__class_Odivide(U_312,U_313,c_Groups_Ozero__class_Ozero(U_312)) = c_Groups_Ozero__class_Ozero(U_312)
| ~ class_Rings_Odivision__ring__inverse__zero(U_312) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__diff__eq]) ).
fof(f_128_2,plain,
! [U_316,U_315,U_314] :
( c_Groups_Ouminus__class_Ouminus(U_314,c_Groups_Ominus__class_Ominus(U_314,U_315,U_316)) = c_Groups_Ominus__class_Ominus(U_314,U_316,U_315)
| ~ class_Groups_Oab__group__add(U_314) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_314,c_Groups_Ominus__class_Ominus(U_314,U_315,U_316)) = c_Groups_Ominus__class_Ominus(U_314,U_316,U_315)
| ~ class_Groups_Oab__group__add(U_314) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__zero]) ).
fof(f_129_2,plain,
! [U_317] :
( c_Groups_Oabs__class_Oabs(U_317,c_Groups_Ozero__class_Ozero(U_317)) = c_Groups_Ozero__class_Ozero(U_317)
| ~ class_Groups_Oordered__ab__group__add__abs(U_317) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( c_Groups_Oabs__class_Oabs(U_317,c_Groups_Ozero__class_Ozero(U_317)) = c_Groups_Ozero__class_Ozero(U_317)
| ~ class_Groups_Oordered__ab__group__add__abs(U_317) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Oabs__class_Oabs(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).
fof(f_130_2,plain,
! [U_319,U_318] :
( ( ( c_Groups_Oabs__class_Oabs(U_318,U_319) = c_Groups_Ozero__class_Ozero(U_318)
| U_319 != c_Groups_Ozero__class_Ozero(U_318) )
& ( U_319 = c_Groups_Ozero__class_Ozero(U_318)
| c_Groups_Oabs__class_Oabs(U_318,U_319) != c_Groups_Ozero__class_Ozero(U_318) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_318) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( U_319 = c_Groups_Ozero__class_Ozero(U_318)
| c_Groups_Oabs__class_Oabs(U_318,U_319) != c_Groups_Ozero__class_Ozero(U_318)
| ~ class_Groups_Oordered__ab__group__add__abs(U_318) ),
inference(clausify,[status(thm)],[f_130_2]) ).
cnf(f_130_4,plain,
( c_Groups_Oabs__class_Oabs(U_318,U_319) = c_Groups_Ozero__class_Ozero(U_318)
| U_319 != c_Groups_Ozero__class_Ozero(U_318)
| ~ class_Groups_Oordered__ab__group__add__abs(U_318) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib]) ).
fof(f_131_2,plain,
! [U_323,U_322,U_321,U_320] :
( c_Rings_Oinverse__class_Odivide(U_320,c_Groups_Ominus__class_Ominus(U_320,U_321,U_322),U_323) = c_Groups_Ominus__class_Ominus(U_320,c_Rings_Oinverse__class_Odivide(U_320,U_321,U_323),c_Rings_Oinverse__class_Odivide(U_320,U_322,U_323))
| ~ class_Rings_Odivision__ring(U_320) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( c_Rings_Oinverse__class_Odivide(U_320,c_Groups_Ominus__class_Ominus(U_320,U_321,U_322),U_323) = c_Groups_Ominus__class_Ominus(U_320,c_Rings_Oinverse__class_Odivide(U_320,U_321,U_323),c_Rings_Oinverse__class_Odivide(U_320,U_322,U_323))
| ~ class_Rings_Odivision__ring(U_320) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__left]) ).
fof(f_132_2,plain,
! [U_326,U_325,U_324] :
( c_Groups_Ouminus__class_Ouminus(U_324,c_Rings_Oinverse__class_Odivide(U_324,U_325,U_326)) = c_Rings_Oinverse__class_Odivide(U_324,c_Groups_Ouminus__class_Ouminus(U_324,U_325),U_326)
| ~ class_Rings_Odivision__ring(U_324) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_324,c_Rings_Oinverse__class_Odivide(U_324,U_325,U_326)) = c_Rings_Oinverse__class_Odivide(U_324,c_Groups_Ouminus__class_Ouminus(U_324,U_325),U_326)
| ~ class_Rings_Odivision__ring(U_324) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__commute]) ).
fof(f_133_2,plain,
! [U_329,U_328,U_327] :
( c_Groups_Oabs__class_Oabs(U_327,c_Groups_Ominus__class_Ominus(U_327,U_328,U_329)) = c_Groups_Oabs__class_Oabs(U_327,c_Groups_Ominus__class_Ominus(U_327,U_329,U_328))
| ~ class_Groups_Oordered__ab__group__add__abs(U_327) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( c_Groups_Oabs__class_Oabs(U_327,c_Groups_Ominus__class_Ominus(U_327,U_328,U_329)) = c_Groups_Oabs__class_Oabs(U_327,c_Groups_Ominus__class_Ominus(U_327,U_329,U_328))
| ~ class_Groups_Oordered__ab__group__add__abs(U_327) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel]) ).
fof(f_134_2,plain,
! [U_331,U_330] :
( c_Groups_Oabs__class_Oabs(U_330,c_Groups_Ouminus__class_Ouminus(U_330,U_331)) = c_Groups_Oabs__class_Oabs(U_330,U_331)
| ~ class_Groups_Oordered__ab__group__add__abs(U_330) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( c_Groups_Oabs__class_Oabs(U_330,c_Groups_Ouminus__class_Ouminus(U_330,U_331)) = c_Groups_Oabs__class_Oabs(U_330,U_331)
| ~ class_Groups_Oordered__ab__group__add__abs(U_330) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).
fof(f_135_2,plain,
! [U_334,U_333,U_332] :
( ( ( c_Orderings_Oord__class_Oless(U_332,U_333,U_334)
| ~ c_Orderings_Oord__class_Oless(U_332,c_Groups_Ominus__class_Ominus(U_332,U_333,U_334),c_Groups_Ozero__class_Ozero(U_332)) )
& ( c_Orderings_Oord__class_Oless(U_332,c_Groups_Ominus__class_Ominus(U_332,U_333,U_334),c_Groups_Ozero__class_Ozero(U_332))
| ~ c_Orderings_Oord__class_Oless(U_332,U_333,U_334) ) )
| ~ class_Groups_Oordered__ab__group__add(U_332) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( c_Orderings_Oord__class_Oless(U_332,c_Groups_Ominus__class_Ominus(U_332,U_333,U_334),c_Groups_Ozero__class_Ozero(U_332))
| ~ c_Orderings_Oord__class_Oless(U_332,U_333,U_334)
| ~ class_Groups_Oordered__ab__group__add(U_332) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_4,plain,
( c_Orderings_Oord__class_Oless(U_332,U_333,U_334)
| ~ c_Orderings_Oord__class_Oless(U_332,c_Groups_Ominus__class_Ominus(U_332,U_333,U_334),c_Groups_Ozero__class_Ozero(U_332))
| ~ class_Groups_Oordered__ab__group__add(U_332) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).
fof(f_136_2,plain,
! [U_336,U_335] :
( ( ( c_Orderings_Oord__class_Oless(U_335,c_Groups_Ozero__class_Ozero(U_335),c_Groups_Ouminus__class_Ouminus(U_335,U_336))
| ~ c_Orderings_Oord__class_Oless(U_335,U_336,c_Groups_Ozero__class_Ozero(U_335)) )
& ( c_Orderings_Oord__class_Oless(U_335,U_336,c_Groups_Ozero__class_Ozero(U_335))
| ~ c_Orderings_Oord__class_Oless(U_335,c_Groups_Ozero__class_Ozero(U_335),c_Groups_Ouminus__class_Ouminus(U_335,U_336)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_335) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( c_Orderings_Oord__class_Oless(U_335,U_336,c_Groups_Ozero__class_Ozero(U_335))
| ~ c_Orderings_Oord__class_Oless(U_335,c_Groups_Ozero__class_Ozero(U_335),c_Groups_Ouminus__class_Ouminus(U_335,U_336))
| ~ class_Groups_Oordered__ab__group__add(U_335) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_4,plain,
( c_Orderings_Oord__class_Oless(U_335,c_Groups_Ozero__class_Ozero(U_335),c_Groups_Ouminus__class_Ouminus(U_335,U_336))
| ~ c_Orderings_Oord__class_Oless(U_335,U_336,c_Groups_Ozero__class_Ozero(U_335))
| ~ class_Groups_Oordered__ab__group__add(U_335) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).
fof(f_137_2,plain,
! [U_338,U_337] :
( ( ( c_Orderings_Oord__class_Oless(U_337,U_338,c_Groups_Ouminus__class_Ouminus(U_337,U_338))
| ~ c_Orderings_Oord__class_Oless(U_337,U_338,c_Groups_Ozero__class_Ozero(U_337)) )
& ( c_Orderings_Oord__class_Oless(U_337,U_338,c_Groups_Ozero__class_Ozero(U_337))
| ~ c_Orderings_Oord__class_Oless(U_337,U_338,c_Groups_Ouminus__class_Ouminus(U_337,U_338)) ) )
| ~ class_Rings_Olinordered__idom(U_337) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( c_Orderings_Oord__class_Oless(U_337,U_338,c_Groups_Ozero__class_Ozero(U_337))
| ~ c_Orderings_Oord__class_Oless(U_337,U_338,c_Groups_Ouminus__class_Ouminus(U_337,U_338))
| ~ class_Rings_Olinordered__idom(U_337) ),
inference(clausify,[status(thm)],[f_137_2]) ).
cnf(f_137_4,plain,
( c_Orderings_Oord__class_Oless(U_337,U_338,c_Groups_Ouminus__class_Ouminus(U_337,U_338))
| ~ c_Orderings_Oord__class_Oless(U_337,U_338,c_Groups_Ozero__class_Ozero(U_337))
| ~ class_Rings_Olinordered__idom(U_337) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).
fof(f_138_2,plain,
! [U_340,U_339] :
( ( ( c_Orderings_Oord__class_Oless(U_339,c_Groups_Ouminus__class_Ouminus(U_339,U_340),c_Groups_Ozero__class_Ozero(U_339))
| ~ c_Orderings_Oord__class_Oless(U_339,c_Groups_Ozero__class_Ozero(U_339),U_340) )
& ( c_Orderings_Oord__class_Oless(U_339,c_Groups_Ozero__class_Ozero(U_339),U_340)
| ~ c_Orderings_Oord__class_Oless(U_339,c_Groups_Ouminus__class_Ouminus(U_339,U_340),c_Groups_Ozero__class_Ozero(U_339)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_339) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( c_Orderings_Oord__class_Oless(U_339,c_Groups_Ozero__class_Ozero(U_339),U_340)
| ~ c_Orderings_Oord__class_Oless(U_339,c_Groups_Ouminus__class_Ouminus(U_339,U_340),c_Groups_Ozero__class_Ozero(U_339))
| ~ class_Groups_Oordered__ab__group__add(U_339) ),
inference(clausify,[status(thm)],[f_138_2]) ).
cnf(f_138_4,plain,
( c_Orderings_Oord__class_Oless(U_339,c_Groups_Ouminus__class_Ouminus(U_339,U_340),c_Groups_Ozero__class_Ozero(U_339))
| ~ c_Orderings_Oord__class_Oless(U_339,c_Groups_Ozero__class_Ozero(U_339),U_340)
| ~ class_Groups_Oordered__ab__group__add(U_339) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_less__zeroE]) ).
fof(f_139_2,plain,
! [U_341] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_341,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_341,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [V_fa_2] :
( ( c_SEQ_Osubseq(V_fa_2)
| ? [B_m,B_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ) )
& ( ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) )
| ~ c_SEQ_Osubseq(V_fa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_subseq__def]) ).
fof(f_140_2,plain,
! [U_346] :
( ( c_SEQ_Osubseq(U_346)
| ? [U_345,U_344] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_346,U_345),hAPP(U_346,U_344))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_345,U_344) ) )
& ( ! [U_343,U_342] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_346,U_343),hAPP(U_346,U_342))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_343,U_342) )
| ~ c_SEQ_Osubseq(U_346) ) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ! [U_348] :
( c_SEQ_Osubseq(U_348)
| ? [U_345,U_344] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_348,U_345),hAPP(U_348,U_344))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_345,U_344) ) )
& ! [U_347] :
( ! [U_343,U_342] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_347,U_343),hAPP(U_347,U_342))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_343,U_342) )
| ~ c_SEQ_Osubseq(U_347) ) ),
inference(miniscope,[status(thm)],[f_140_2]) ).
fof(f_140_4,plain,
( ! [U_348] :
( c_SEQ_Osubseq(U_348)
| ? [U_344] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_348,sK3(U_348)),hAPP(U_348,U_344))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK3(U_348),U_344) ) )
& ! [U_347] :
( ! [U_343,U_342] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_347,U_343),hAPP(U_347,U_342))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_343,U_342) )
| ~ c_SEQ_Osubseq(U_347) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_345,sK3(U_348))],[f_140_3]) ).
fof(f_140_5,plain,
( ! [U_348] :
( c_SEQ_Osubseq(U_348)
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_348,sK3(U_348)),hAPP(U_348,sK4(U_348)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK3(U_348),sK4(U_348)) ) )
& ! [U_347] :
( ! [U_343,U_342] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_347,U_343),hAPP(U_347,U_342))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_343,U_342) )
| ~ c_SEQ_Osubseq(U_347) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_344,sK4(U_348))],[f_140_4]) ).
cnf(f_140_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_347,U_343),hAPP(U_347,U_342))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_343,U_342)
| ~ c_SEQ_Osubseq(U_347) ),
inference(clausify,[status(thm)],[f_140_5]) ).
cnf(f_140_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK3(U_348),sK4(U_348))
| c_SEQ_Osubseq(U_348) ),
inference(clausify,[status(thm)],[f_140_5]) ).
cnf(f_140_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_348,sK3(U_348)),hAPP(U_348,sK4(U_348)))
| c_SEQ_Osubseq(U_348) ),
inference(clausify,[status(thm)],[f_140_5]) ).
fof(f_141_1,plain,
! [B_e] :
( ? [B_N] :
! [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,B_n)),v_z____)),B_e)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) ),
inference(fof_nnf,[status(thm)],[fact_fz_I2_J]) ).
fof(f_141_2,plain,
! [U_351] :
( ? [U_350] :
! [U_349] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_349)),v_z____)),U_351)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_350,U_349) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_351) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_351] :
( ! [U_349] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_349)),v_z____)),U_351)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK5(U_351),U_349) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_351) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_350,sK5(U_351))],[f_141_2]) ).
cnf(f_141_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,U_349)),v_z____)),U_351)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK5(U_351),U_349)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_351) ),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [V_x,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__minus]) ).
fof(f_142_2,plain,
! [U_354,U_353,U_352] :
( hAPP(c_Polynomial_Opoly(U_352,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_352),U_353)),U_354) = c_Groups_Ouminus__class_Ouminus(U_352,hAPP(c_Polynomial_Opoly(U_352,U_353),U_354))
| ~ class_Rings_Ocomm__ring(U_352) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( hAPP(c_Polynomial_Opoly(U_352,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_352),U_353)),U_354) = c_Groups_Ouminus__class_Ouminus(U_352,hAPP(c_Polynomial_Opoly(U_352,U_353),U_354))
| ~ class_Rings_Ocomm__ring(U_352) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__diff]) ).
fof(f_143_2,plain,
! [U_358,U_357,U_356,U_355] :
( hAPP(c_Polynomial_Opoly(U_355,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_355),U_356,U_357)),U_358) = c_Groups_Ominus__class_Ominus(U_355,hAPP(c_Polynomial_Opoly(U_355,U_356),U_358),hAPP(c_Polynomial_Opoly(U_355,U_357),U_358))
| ~ class_Rings_Ocomm__ring(U_355) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( hAPP(c_Polynomial_Opoly(U_355,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_355),U_356,U_357)),U_358) = c_Groups_Ominus__class_Ominus(U_355,hAPP(c_Polynomial_Opoly(U_355,U_356),U_358),hAPP(c_Polynomial_Opoly(U_355,U_357),U_358))
| ~ class_Rings_Ocomm__ring(U_355) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__0]) ).
fof(f_144_2,plain,
! [U_360,U_359] :
( hAPP(c_Polynomial_Opoly(U_359,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_359))),U_360) = c_Groups_Ozero__class_Ozero(U_359)
| ~ class_Rings_Ocomm__semiring__0(U_359) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( hAPP(c_Polynomial_Opoly(U_359,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_359))),U_360) = c_Groups_Ozero__class_Ozero(U_359)
| ~ class_Rings_Ocomm__semiring__0(U_359) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_not__less0]) ).
fof(f_145_2,plain,
! [U_361] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_361,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_361,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [V_n_2] :
( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).
fof(f_146_2,plain,
! [U_362] :
( ( U_362 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_362) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_362)
| U_362 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
( ! [U_364] :
( U_364 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_364) )
& ! [U_363] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_363)
| U_363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_146_2]) ).
cnf(f_146_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_363)
| U_363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_146_3]) ).
cnf(f_146_5,plain,
( U_364 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_364) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [V_m_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).
fof(f_147_2,plain,
! [U_366,U_365] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_365,U_366))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_366,U_365) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_366,U_365)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_365,U_366)) ) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
( ! [U_370,U_368] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_368,U_370))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_370,U_368) )
& ! [U_369,U_367] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_369,U_367)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_367,U_369)) ) ),
inference(miniscope,[status(thm)],[f_147_2]) ).
cnf(f_147_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_369,U_367)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_367,U_369)) ),
inference(clausify,[status(thm)],[f_147_3]) ).
cnf(f_147_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_368,U_370))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_370,U_368) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_less__nat__zero__code]) ).
fof(f_148_2,plain,
! [U_371] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_371,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_371,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
inference(fof_nnf,[status(thm)],[fact_le0]) ).
fof(f_149_2,plain,
! [U_372] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_372),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_372),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_1,plain,
! [T_a] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J]) ).
fof(f_150_2,plain,
! [U_373] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_373),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_373))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_373))
| ~ class_Groups_Oab__group__add(U_373) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_373),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_373))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_373))
| ~ class_Groups_Oab__group__add(U_373) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_1,plain,
! [V_x,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) )
& ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__poly__def]) ).
fof(f_151_2,plain,
! [U_375,U_374] :
( ( ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_374),U_375) = U_375
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_374),U_375,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_374))) )
& ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_374),U_375) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_374),U_375)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_374),U_375,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_374))) ) )
| ~ class_Rings_Olinordered__idom(U_374) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_374),U_375) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_374),U_375)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_374),U_375,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_374)))
| ~ class_Rings_Olinordered__idom(U_374) ),
inference(clausify,[status(thm)],[f_151_2]) ).
cnf(f_151_4,plain,
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_374),U_375) = U_375
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_374),U_375,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_374)))
| ~ class_Rings_Olinordered__idom(U_374) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_1,plain,
! [V_q,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J]) ).
fof(f_152_2,plain,
! [U_377,U_376] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_376),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_376)),U_377) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_376),U_377)
| ~ class_Groups_Oab__group__add(U_376) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_376),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_376)),U_377) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_376),U_377)
| ~ class_Groups_Oab__group__add(U_376) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [V_p,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J]) ).
fof(f_153_2,plain,
! [U_379,U_378] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_378),U_379,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_378))) = U_379
| ~ class_Groups_Oab__group__add(U_378) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_378),U_379,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_378))) = U_379
| ~ class_Groups_Oab__group__add(U_378) ),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__iff]) ).
fof(f_154_2,plain,
! [U_382,U_381,U_380] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_381,U_380),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_382,U_380))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_381,U_382) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_381,U_382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_381,U_380),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_382,U_380)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_380,U_382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_380,U_381) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_381,U_382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_381,U_380),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_382,U_380))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_380,U_382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_380,U_381) ),
inference(clausify,[status(thm)],[f_154_2]) ).
cnf(f_154_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_381,U_380),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_382,U_380))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_381,U_382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_380,U_382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_380,U_381) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_1,plain,
! [V_n,V_m,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m) ),
inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq]) ).
fof(f_155_2,plain,
! [U_385,U_384,U_383] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_384,U_383),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_385,U_383)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_384,U_385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_383,U_385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_383,U_384) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_384,U_383),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_385,U_383)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_384,U_385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_383,U_385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_383,U_384) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_eq__diff__iff]) ).
fof(f_156_2,plain,
! [U_388,U_387,U_386] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,U_386) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_388,U_386)
| U_387 != U_388 )
& ( U_387 = U_388
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,U_386) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_388,U_386) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_388)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_387) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( U_387 = U_388
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,U_386) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_388,U_386)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_388)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_387) ),
inference(clausify,[status(thm)],[f_156_2]) ).
cnf(f_156_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,U_386) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_388,U_386)
| U_387 != U_388
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_388)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_387) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [V_n,V_i] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel]) ).
fof(f_157_2,plain,
! [U_390,U_389] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_390,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_390,U_389)) = U_389
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_389,U_390) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_390,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_390,U_389)) = U_389
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_389,U_390) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono]) ).
fof(f_158_2,plain,
! [U_393,U_392,U_391] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_391,U_393),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_392,U_393))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_391,U_392) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_391,U_393),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_392,U_393))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_391,U_392) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono2]) ).
fof(f_159_2,plain,
! [U_396,U_395,U_394] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_396,U_395),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_396,U_394))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_394,U_395) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_396,U_395),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_396,U_394))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_394,U_395) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j),
inference(fof_nnf,[status(thm)],[fact_diff__commute]) ).
fof(f_160_2,plain,
! [U_399,U_398,U_397] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_398),U_399) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_399),U_398),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_398),U_399) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_399),U_398),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m),
inference(fof_nnf,[status(thm)],[fact_diff__le__self]) ).
fof(f_161_2,plain,
! [U_401,U_400] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_400,U_401),U_400),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_400,U_401),U_400),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).
fof(f_162_2,plain,
! [U_404,U_403,U_402] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_402,c_Int_Onumber__class_Onumber__of(U_402,U_403),c_Int_Onumber__class_Onumber__of(U_402,U_404))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_403,U_404) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_403,U_404)
| ~ c_Orderings_Oord__class_Oless__eq(U_402,c_Int_Onumber__class_Onumber__of(U_402,U_403),c_Int_Onumber__class_Onumber__of(U_402,U_404)) ) )
| ~ class_Rings_Olinordered__idom(U_402)
| ~ class_Int_Onumber__ring(U_402) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_403,U_404)
| ~ c_Orderings_Oord__class_Oless__eq(U_402,c_Int_Onumber__class_Onumber__of(U_402,U_403),c_Int_Onumber__class_Onumber__of(U_402,U_404))
| ~ class_Rings_Olinordered__idom(U_402)
| ~ class_Int_Onumber__ring(U_402) ),
inference(clausify,[status(thm)],[f_162_2]) ).
cnf(f_162_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_402,c_Int_Onumber__class_Onumber__of(U_402,U_403),c_Int_Onumber__class_Onumber__of(U_402,U_404))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_403,U_404)
| ~ class_Rings_Olinordered__idom(U_402)
| ~ class_Int_Onumber__ring(U_402) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_le__refl]) ).
fof(f_163_2,plain,
! [U_405] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_405,U_405),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_405,U_405),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).
fof(f_164_2,plain,
! [U_407,U_406] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_407,U_406)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_406,U_407) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_407,U_406)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_406,U_407) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| V_m != V_n ),
inference(fof_nnf,[status(thm)],[fact_eq__imp__le]) ).
fof(f_165_2,plain,
! [U_409,U_408] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_408,U_409)
| U_408 != U_409 ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_408,U_409)
| U_408 != U_409 ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_le__trans]) ).
fof(f_166_2,plain,
! [U_412,U_411,U_410] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_410,U_412)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_411,U_412)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_410,U_411) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_410,U_412)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_411,U_412)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_410,U_411) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).
fof(f_167_2,plain,
! [U_414,U_413] :
( U_413 = U_414
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_414,U_413)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_413,U_414) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( U_413 = U_414
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_414,U_413)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_413,U_414) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
! [V_n,V_m] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H]) ).
fof(f_168_2,plain,
! [U_416,U_415] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_415,U_416) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_415,U_416) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_415,U_416) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_415,U_416) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [V_n_2,V_m_2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).
fof(f_169_2,plain,
! [U_418,U_417] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_417,U_418) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_417,U_418) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_417,U_418)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_417,U_418) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
( ! [U_422,U_420] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_420,U_422) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_420,U_422) )
& ! [U_421,U_419] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_419,U_421)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_419,U_421) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_169_2]) ).
cnf(f_169_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_419,U_421)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_419,U_421) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_169_3]) ).
cnf(f_169_5,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_420,U_422) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_420,U_422) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__0__eq]) ).
fof(f_170_2,plain,
! [U_423] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_423,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_423 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_423 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_423,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
( ! [U_425] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_425,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_425 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_424] :
( U_424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_424,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_170_2]) ).
cnf(f_170_4,plain,
( U_424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_424,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_170_3]) ).
cnf(f_170_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_425,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_425 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(f_171_2,plain,
! [U_426] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_426),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_426),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ( V_m != V_n
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le]) ).
fof(f_172_2,plain,
! [U_428,U_427] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_428)
| ( U_427 != U_428
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_427,U_428) ) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_427,U_428)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_428) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_4,plain,
( U_427 != U_428
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_428) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__iff]) ).
fof(f_173_2,plain,
! [U_431,U_430,U_429] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_430,U_429),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_431,U_429))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_430,U_431) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_430,U_431)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_430,U_429),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_431,U_429)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_429,U_431)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_429,U_430) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_430,U_431)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_430,U_429),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_431,U_429))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_429,U_431)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_429,U_430) ),
inference(clausify,[status(thm)],[f_173_2]) ).
cnf(f_173_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_430,U_429),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_431,U_429))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_430,U_431)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_429,U_431)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_429,U_430) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_1,plain,
! [V_c,V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).
fof(f_174_2,plain,
! [U_434,U_433,U_432] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_432,U_434),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_433,U_434))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_434,U_432)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_432,U_433) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_432,U_434),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_433,U_434))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_434,U_432)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_432,U_433) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| V_m = V_n
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less]) ).
fof(f_175_2,plain,
! [U_436,U_435] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_435,U_436)
| U_435 = U_436
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_435,U_436) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_435,U_436)
| U_435 = U_436
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_435,U_436) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).
fof(f_176_2,plain,
! [U_438,U_437] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_437,U_438)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_437,U_438) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_437,U_438)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_437,U_438) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| ( V_m_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) )
& ( V_m_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).
fof(f_177_2,plain,
! [U_440,U_439] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_439,U_440)
| ( U_439 != U_440
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_439,U_440) ) )
& ( U_439 = U_440
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_439,U_440)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_439,U_440) ) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
( ! [U_444,U_442] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_442,U_444)
| ( U_442 != U_444
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_442,U_444) ) )
& ! [U_443,U_441] :
( U_441 = U_443
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_441,U_443)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_441,U_443) ) ),
inference(miniscope,[status(thm)],[f_177_2]) ).
cnf(f_177_4,plain,
( U_441 = U_443
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_441,U_443)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_441,U_443) ),
inference(clausify,[status(thm)],[f_177_3]) ).
cnf(f_177_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_442,U_444)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_442,U_444) ),
inference(clausify,[status(thm)],[f_177_3]) ).
cnf(f_177_6,plain,
( U_442 != U_444
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_442,U_444) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| V_m_2 = V_n_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
& ( ( V_m_2 != V_n_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).
fof(f_178_2,plain,
! [U_446,U_445] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_445,U_446)
| U_445 = U_446
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_445,U_446) )
& ( ( U_445 != U_446
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_445,U_446) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_445,U_446) ) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
( ! [U_450,U_448] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_448,U_450)
| U_448 = U_450
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_448,U_450) )
& ! [U_449,U_447] :
( ( U_447 != U_449
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_447,U_449) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_447,U_449) ) ),
inference(miniscope,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_447,U_449)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_447,U_449) ),
inference(clausify,[status(thm)],[f_178_3]) ).
cnf(f_178_5,plain,
( U_447 != U_449
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_447,U_449) ),
inference(clausify,[status(thm)],[f_178_3]) ).
cnf(f_178_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_448,U_450)
| U_448 = U_450
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_448,U_450) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [V_n_2,V_fa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2))
| ~ c_SEQ_Osubseq(V_fa_2) ),
inference(fof_nnf,[status(thm)],[fact_seq__suble]) ).
fof(f_179_2,plain,
! [U_452,U_451] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_452,hAPP(U_451,U_452))
| ~ c_SEQ_Osubseq(U_451) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_452,hAPP(U_451,U_452))
| ~ c_SEQ_Osubseq(U_451) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).
fof(f_180_2,plain,
! [U_457,U_456,U_455,U_454,U_453] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_453,U_454,U_455)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,U_456,U_457) )
& ( c_Orderings_Oord__class_Oless__eq(U_453,U_456,U_457)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,U_454,U_455) ) )
| c_Groups_Ominus__class_Ominus(U_453,U_454,U_455) != c_Groups_Ominus__class_Ominus(U_453,U_456,U_457)
| ~ class_Groups_Oordered__ab__group__add(U_453) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_453,U_456,U_457)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,U_454,U_455)
| c_Groups_Ominus__class_Ominus(U_453,U_454,U_455) != c_Groups_Ominus__class_Ominus(U_453,U_456,U_457)
| ~ class_Groups_Oordered__ab__group__add(U_453) ),
inference(clausify,[status(thm)],[f_180_2]) ).
cnf(f_180_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_453,U_454,U_455)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,U_456,U_457)
| c_Groups_Ominus__class_Ominus(U_453,U_454,U_455) != c_Groups_Ominus__class_Ominus(U_453,U_456,U_457)
| ~ class_Groups_Oordered__ab__group__add(U_453) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le]) ).
fof(f_181_2,plain,
! [U_460,U_459,U_458] :
( c_Orderings_Oord__class_Oless__eq(U_458,c_Groups_Ouminus__class_Ouminus(U_458,U_460),c_Groups_Ouminus__class_Ouminus(U_458,U_459))
| ~ c_Orderings_Oord__class_Oless__eq(U_458,U_459,U_460)
| ~ class_Groups_Oordered__ab__group__add(U_458) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_458,c_Groups_Ouminus__class_Ouminus(U_458,U_460),c_Groups_Ouminus__class_Ouminus(U_458,U_459))
| ~ c_Orderings_Oord__class_Oless__eq(U_458,U_459,U_460)
| ~ class_Groups_Oordered__ab__group__add(U_458) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).
fof(f_182_2,plain,
! [U_463,U_462,U_461] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_461,c_Groups_Ouminus__class_Ouminus(U_461,U_462),c_Groups_Ouminus__class_Ouminus(U_461,U_463))
| ~ c_Orderings_Oord__class_Oless__eq(U_461,U_463,U_462) )
& ( c_Orderings_Oord__class_Oless__eq(U_461,U_463,U_462)
| ~ c_Orderings_Oord__class_Oless__eq(U_461,c_Groups_Ouminus__class_Ouminus(U_461,U_462),c_Groups_Ouminus__class_Ouminus(U_461,U_463)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_461) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_461,U_463,U_462)
| ~ c_Orderings_Oord__class_Oless__eq(U_461,c_Groups_Ouminus__class_Ouminus(U_461,U_462),c_Groups_Ouminus__class_Ouminus(U_461,U_463))
| ~ class_Groups_Oordered__ab__group__add(U_461) ),
inference(clausify,[status(thm)],[f_182_2]) ).
cnf(f_182_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_461,c_Groups_Ouminus__class_Ouminus(U_461,U_462),c_Groups_Ouminus__class_Ouminus(U_461,U_463))
| ~ c_Orderings_Oord__class_Oless__eq(U_461,U_463,U_462)
| ~ class_Groups_Oordered__ab__group__add(U_461) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).
fof(f_183_2,plain,
! [U_466,U_465,U_464] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_464,c_Groups_Ouminus__class_Ouminus(U_464,U_465),U_466)
| ~ c_Orderings_Oord__class_Oless__eq(U_464,c_Groups_Ouminus__class_Ouminus(U_464,U_466),U_465) )
& ( c_Orderings_Oord__class_Oless__eq(U_464,c_Groups_Ouminus__class_Ouminus(U_464,U_466),U_465)
| ~ c_Orderings_Oord__class_Oless__eq(U_464,c_Groups_Ouminus__class_Ouminus(U_464,U_465),U_466) ) )
| ~ class_Groups_Oordered__ab__group__add(U_464) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
cnf(f_183_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_464,c_Groups_Ouminus__class_Ouminus(U_464,U_466),U_465)
| ~ c_Orderings_Oord__class_Oless__eq(U_464,c_Groups_Ouminus__class_Ouminus(U_464,U_465),U_466)
| ~ class_Groups_Oordered__ab__group__add(U_464) ),
inference(clausify,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_464,c_Groups_Ouminus__class_Ouminus(U_464,U_465),U_466)
| ~ c_Orderings_Oord__class_Oless__eq(U_464,c_Groups_Ouminus__class_Ouminus(U_464,U_466),U_465)
| ~ class_Groups_Oordered__ab__group__add(U_464) ),
inference(clausify,[status(thm)],[f_183_2]) ).
fof(f_184_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).
fof(f_184_2,plain,
! [U_469,U_468,U_467] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_467,U_468,c_Groups_Ouminus__class_Ouminus(U_467,U_469))
| ~ c_Orderings_Oord__class_Oless__eq(U_467,U_469,c_Groups_Ouminus__class_Ouminus(U_467,U_468)) )
& ( c_Orderings_Oord__class_Oless__eq(U_467,U_469,c_Groups_Ouminus__class_Ouminus(U_467,U_468))
| ~ c_Orderings_Oord__class_Oless__eq(U_467,U_468,c_Groups_Ouminus__class_Ouminus(U_467,U_469)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_467) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_467,U_469,c_Groups_Ouminus__class_Ouminus(U_467,U_468))
| ~ c_Orderings_Oord__class_Oless__eq(U_467,U_468,c_Groups_Ouminus__class_Ouminus(U_467,U_469))
| ~ class_Groups_Oordered__ab__group__add(U_467) ),
inference(clausify,[status(thm)],[f_184_2]) ).
cnf(f_184_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_467,U_468,c_Groups_Ouminus__class_Ouminus(U_467,U_469))
| ~ c_Orderings_Oord__class_Oless__eq(U_467,U_469,c_Groups_Ouminus__class_Ouminus(U_467,U_468))
| ~ class_Groups_Oordered__ab__group__add(U_467) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__D1]) ).
fof(f_185_2,plain,
! [U_472,U_471,U_470] :
( c_Orderings_Oord__class_Oless__eq(U_470,U_471,U_472)
| ~ c_Orderings_Oord__class_Oless__eq(U_470,c_Groups_Oabs__class_Oabs(U_470,U_471),U_472)
| ~ class_Groups_Oordered__ab__group__add__abs(U_470) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_470,U_471,U_472)
| ~ c_Orderings_Oord__class_Oless__eq(U_470,c_Groups_Oabs__class_Oabs(U_470,U_471),U_472)
| ~ class_Groups_Oordered__ab__group__add__abs(U_470) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__ge__self]) ).
fof(f_186_2,plain,
! [U_474,U_473] :
( c_Orderings_Oord__class_Oless__eq(U_473,U_474,c_Groups_Oabs__class_Oabs(U_473,U_474))
| ~ class_Groups_Oordered__ab__group__add__abs(U_473) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_473,U_474,c_Groups_Oabs__class_Oabs(U_473,U_474))
| ~ class_Groups_Oordered__ab__group__add__abs(U_473) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I3_J]) ).
fof(f_187_2,plain,
! [U_476,U_475] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_475,c_Int_Onumber__class_Onumber__of(U_475,U_476),c_Groups_Ozero__class_Ozero(U_475))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_476,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_476,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(U_475,c_Int_Onumber__class_Onumber__of(U_475,U_476),c_Groups_Ozero__class_Ozero(U_475)) ) )
| ~ class_Rings_Olinordered__idom(U_475)
| ~ class_Int_Onumber__ring(U_475) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_476,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(U_475,c_Int_Onumber__class_Onumber__of(U_475,U_476),c_Groups_Ozero__class_Ozero(U_475))
| ~ class_Rings_Olinordered__idom(U_475)
| ~ class_Int_Onumber__ring(U_475) ),
inference(clausify,[status(thm)],[f_187_2]) ).
cnf(f_187_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_475,c_Int_Onumber__class_Onumber__of(U_475,U_476),c_Groups_Ozero__class_Ozero(U_475))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_476,c_Int_OPls)
| ~ class_Rings_Olinordered__idom(U_475)
| ~ class_Int_Onumber__ring(U_475) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_1,plain,
! [V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).
fof(f_188_2,plain,
! [U_478,U_477] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_477,c_Groups_Ozero__class_Ozero(U_477),c_Int_Onumber__class_Onumber__of(U_477,U_478))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_478) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_478)
| ~ c_Orderings_Oord__class_Oless__eq(U_477,c_Groups_Ozero__class_Ozero(U_477),c_Int_Onumber__class_Onumber__of(U_477,U_478)) ) )
| ~ class_Rings_Olinordered__idom(U_477)
| ~ class_Int_Onumber__ring(U_477) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_478)
| ~ c_Orderings_Oord__class_Oless__eq(U_477,c_Groups_Ozero__class_Ozero(U_477),c_Int_Onumber__class_Onumber__of(U_477,U_478))
| ~ class_Rings_Olinordered__idom(U_477)
| ~ class_Int_Onumber__ring(U_477) ),
inference(clausify,[status(thm)],[f_188_2]) ).
cnf(f_188_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_477,c_Groups_Ozero__class_Ozero(U_477),c_Int_Onumber__class_Onumber__of(U_477,U_478))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_478)
| ~ class_Rings_Olinordered__idom(U_477)
| ~ class_Int_Onumber__ring(U_477) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).
fof(f_189_2,plain,
! [U_481,U_480,U_479] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_479,U_480,U_481)
| ~ c_Orderings_Oord__class_Oless__eq(U_479,c_Groups_Ominus__class_Ominus(U_479,U_480,U_481),c_Groups_Ozero__class_Ozero(U_479)) )
& ( c_Orderings_Oord__class_Oless__eq(U_479,c_Groups_Ominus__class_Ominus(U_479,U_480,U_481),c_Groups_Ozero__class_Ozero(U_479))
| ~ c_Orderings_Oord__class_Oless__eq(U_479,U_480,U_481) ) )
| ~ class_Groups_Oordered__ab__group__add(U_479) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_479,c_Groups_Ominus__class_Ominus(U_479,U_480,U_481),c_Groups_Ozero__class_Ozero(U_479))
| ~ c_Orderings_Oord__class_Oless__eq(U_479,U_480,U_481)
| ~ class_Groups_Oordered__ab__group__add(U_479) ),
inference(clausify,[status(thm)],[f_189_2]) ).
cnf(f_189_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_479,U_480,U_481)
| ~ c_Orderings_Oord__class_Oless__eq(U_479,c_Groups_Ominus__class_Ominus(U_479,U_480,U_481),c_Groups_Ozero__class_Ozero(U_479))
| ~ class_Groups_Oordered__ab__group__add(U_479) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [V_wa_2,V_v_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ class_Orderings_Olinorder(T_a)
| ~ class_Int_Onumber(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(f_190_2,plain,
! [U_484,U_483,U_482] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_482,c_Int_Onumber__class_Onumber__of(U_482,U_483),c_Int_Onumber__class_Onumber__of(U_482,U_484))
| c_Orderings_Oord__class_Oless(U_482,c_Int_Onumber__class_Onumber__of(U_482,U_484),c_Int_Onumber__class_Onumber__of(U_482,U_483)) )
& ( ~ c_Orderings_Oord__class_Oless(U_482,c_Int_Onumber__class_Onumber__of(U_482,U_484),c_Int_Onumber__class_Onumber__of(U_482,U_483))
| ~ c_Orderings_Oord__class_Oless__eq(U_482,c_Int_Onumber__class_Onumber__of(U_482,U_483),c_Int_Onumber__class_Onumber__of(U_482,U_484)) ) )
| ~ class_Orderings_Olinorder(U_482)
| ~ class_Int_Onumber(U_482) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_482,c_Int_Onumber__class_Onumber__of(U_482,U_484),c_Int_Onumber__class_Onumber__of(U_482,U_483))
| ~ c_Orderings_Oord__class_Oless__eq(U_482,c_Int_Onumber__class_Onumber__of(U_482,U_483),c_Int_Onumber__class_Onumber__of(U_482,U_484))
| ~ class_Orderings_Olinorder(U_482)
| ~ class_Int_Onumber(U_482) ),
inference(clausify,[status(thm)],[f_190_2]) ).
cnf(f_190_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_482,c_Int_Onumber__class_Onumber__of(U_482,U_483),c_Int_Onumber__class_Onumber__of(U_482,U_484))
| c_Orderings_Oord__class_Oless(U_482,c_Int_Onumber__class_Onumber__of(U_482,U_484),c_Int_Onumber__class_Onumber__of(U_482,U_483))
| ~ class_Orderings_Olinorder(U_482)
| ~ class_Int_Onumber(U_482) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).
fof(f_191_2,plain,
! [U_486,U_485] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_485,c_Groups_Ouminus__class_Ouminus(U_485,U_486),U_486)
| ~ c_Orderings_Oord__class_Oless__eq(U_485,c_Groups_Ozero__class_Ozero(U_485),U_486) )
& ( c_Orderings_Oord__class_Oless__eq(U_485,c_Groups_Ozero__class_Ozero(U_485),U_486)
| ~ c_Orderings_Oord__class_Oless__eq(U_485,c_Groups_Ouminus__class_Ouminus(U_485,U_486),U_486) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_485) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_485,c_Groups_Ozero__class_Ozero(U_485),U_486)
| ~ c_Orderings_Oord__class_Oless__eq(U_485,c_Groups_Ouminus__class_Ouminus(U_485,U_486),U_486)
| ~ class_Groups_Olinordered__ab__group__add(U_485) ),
inference(clausify,[status(thm)],[f_191_2]) ).
cnf(f_191_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_485,c_Groups_Ouminus__class_Ouminus(U_485,U_486),U_486)
| ~ c_Orderings_Oord__class_Oless__eq(U_485,c_Groups_Ozero__class_Ozero(U_485),U_486)
| ~ class_Groups_Olinordered__ab__group__add(U_485) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).
fof(f_192_2,plain,
! [U_488,U_487] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ouminus__class_Ouminus(U_487,U_488),c_Groups_Ozero__class_Ozero(U_487))
| ~ c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ozero__class_Ozero(U_487),U_488) )
& ( c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ozero__class_Ozero(U_487),U_488)
| ~ c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ouminus__class_Ouminus(U_487,U_488),c_Groups_Ozero__class_Ozero(U_487)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_487) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ozero__class_Ozero(U_487),U_488)
| ~ c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ouminus__class_Ouminus(U_487,U_488),c_Groups_Ozero__class_Ozero(U_487))
| ~ class_Groups_Oordered__ab__group__add(U_487) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ouminus__class_Ouminus(U_487,U_488),c_Groups_Ozero__class_Ozero(U_487))
| ~ c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ozero__class_Ozero(U_487),U_488)
| ~ class_Groups_Oordered__ab__group__add(U_487) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).
fof(f_193_2,plain,
! [U_490,U_489] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_489,U_490,c_Groups_Ouminus__class_Ouminus(U_489,U_490))
| ~ c_Orderings_Oord__class_Oless__eq(U_489,U_490,c_Groups_Ozero__class_Ozero(U_489)) )
& ( c_Orderings_Oord__class_Oless__eq(U_489,U_490,c_Groups_Ozero__class_Ozero(U_489))
| ~ c_Orderings_Oord__class_Oless__eq(U_489,U_490,c_Groups_Ouminus__class_Ouminus(U_489,U_490)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_489) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_489,U_490,c_Groups_Ozero__class_Ozero(U_489))
| ~ c_Orderings_Oord__class_Oless__eq(U_489,U_490,c_Groups_Ouminus__class_Ouminus(U_489,U_490))
| ~ class_Groups_Olinordered__ab__group__add(U_489) ),
inference(clausify,[status(thm)],[f_193_2]) ).
cnf(f_193_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_489,U_490,c_Groups_Ouminus__class_Ouminus(U_489,U_490))
| ~ c_Orderings_Oord__class_Oless__eq(U_489,U_490,c_Groups_Ozero__class_Ozero(U_489))
| ~ class_Groups_Olinordered__ab__group__add(U_489) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).
fof(f_194_2,plain,
! [U_492,U_491] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_491,c_Groups_Ozero__class_Ozero(U_491),c_Groups_Ouminus__class_Ouminus(U_491,U_492))
| ~ c_Orderings_Oord__class_Oless__eq(U_491,U_492,c_Groups_Ozero__class_Ozero(U_491)) )
& ( c_Orderings_Oord__class_Oless__eq(U_491,U_492,c_Groups_Ozero__class_Ozero(U_491))
| ~ c_Orderings_Oord__class_Oless__eq(U_491,c_Groups_Ozero__class_Ozero(U_491),c_Groups_Ouminus__class_Ouminus(U_491,U_492)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_491) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_491,U_492,c_Groups_Ozero__class_Ozero(U_491))
| ~ c_Orderings_Oord__class_Oless__eq(U_491,c_Groups_Ozero__class_Ozero(U_491),c_Groups_Ouminus__class_Ouminus(U_491,U_492))
| ~ class_Groups_Oordered__ab__group__add(U_491) ),
inference(clausify,[status(thm)],[f_194_2]) ).
cnf(f_194_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_491,c_Groups_Ozero__class_Ozero(U_491),c_Groups_Ouminus__class_Ouminus(U_491,U_492))
| ~ c_Orderings_Oord__class_Oless__eq(U_491,U_492,c_Groups_Ozero__class_Ozero(U_491))
| ~ class_Groups_Oordered__ab__group__add(U_491) ),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg]) ).
fof(f_195_2,plain,
! [U_496,U_495,U_494,U_493] :
( c_Orderings_Oord__class_Oless__eq(U_493,c_Rings_Oinverse__class_Odivide(U_493,U_495,U_496),c_Rings_Oinverse__class_Odivide(U_493,U_494,U_496))
| ~ c_Orderings_Oord__class_Oless__eq(U_493,U_496,c_Groups_Ozero__class_Ozero(U_493))
| ~ c_Orderings_Oord__class_Oless__eq(U_493,U_494,U_495)
| ~ class_Fields_Olinordered__field__inverse__zero(U_493) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_493,c_Rings_Oinverse__class_Odivide(U_493,U_495,U_496),c_Rings_Oinverse__class_Odivide(U_493,U_494,U_496))
| ~ c_Orderings_Oord__class_Oless__eq(U_493,U_496,c_Groups_Ozero__class_Ozero(U_493))
| ~ c_Orderings_Oord__class_Oless__eq(U_493,U_494,U_495)
| ~ class_Fields_Olinordered__field__inverse__zero(U_493) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__right__mono]) ).
fof(f_196_2,plain,
! [U_500,U_499,U_498,U_497] :
( c_Orderings_Oord__class_Oless__eq(U_497,c_Rings_Oinverse__class_Odivide(U_497,U_498,U_500),c_Rings_Oinverse__class_Odivide(U_497,U_499,U_500))
| ~ c_Orderings_Oord__class_Oless__eq(U_497,c_Groups_Ozero__class_Ozero(U_497),U_500)
| ~ c_Orderings_Oord__class_Oless__eq(U_497,U_498,U_499)
| ~ class_Fields_Olinordered__field__inverse__zero(U_497) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_497,c_Rings_Oinverse__class_Odivide(U_497,U_498,U_500),c_Rings_Oinverse__class_Odivide(U_497,U_499,U_500))
| ~ c_Orderings_Oord__class_Oless__eq(U_497,c_Groups_Ozero__class_Ozero(U_497),U_500)
| ~ c_Orderings_Oord__class_Oless__eq(U_497,U_498,U_499)
| ~ class_Fields_Olinordered__field__inverse__zero(U_497) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff]) ).
fof(f_197_2,plain,
! [U_503,U_502,U_501] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_501,c_Rings_Oinverse__class_Odivide(U_501,U_502,U_503),c_Groups_Ozero__class_Ozero(U_501))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_503)
| ~ c_Orderings_Oord__class_Oless__eq(U_501,U_502,c_Groups_Ozero__class_Ozero(U_501)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_501,U_503,c_Groups_Ozero__class_Ozero(U_501))
| ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_502) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_503)
& c_Orderings_Oord__class_Oless__eq(U_501,U_502,c_Groups_Ozero__class_Ozero(U_501)) )
| ( c_Orderings_Oord__class_Oless__eq(U_501,U_503,c_Groups_Ozero__class_Ozero(U_501))
& c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_502) )
| ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Rings_Oinverse__class_Odivide(U_501,U_502,U_503),c_Groups_Ozero__class_Ozero(U_501)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_501) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_501,U_502,c_Groups_Ozero__class_Ozero(U_501))
| c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_502)
| ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Rings_Oinverse__class_Odivide(U_501,U_502,U_503),c_Groups_Ozero__class_Ozero(U_501))
| ~ class_Fields_Olinordered__field__inverse__zero(U_501) ),
inference(clausify,[status(thm)],[f_197_2]) ).
cnf(f_197_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_503)
| c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_502)
| ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Rings_Oinverse__class_Odivide(U_501,U_502,U_503),c_Groups_Ozero__class_Ozero(U_501))
| ~ class_Fields_Olinordered__field__inverse__zero(U_501) ),
inference(clausify,[status(thm)],[f_197_2]) ).
cnf(f_197_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_501,U_502,c_Groups_Ozero__class_Ozero(U_501))
| c_Orderings_Oord__class_Oless__eq(U_501,U_503,c_Groups_Ozero__class_Ozero(U_501))
| ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Rings_Oinverse__class_Odivide(U_501,U_502,U_503),c_Groups_Ozero__class_Ozero(U_501))
| ~ class_Fields_Olinordered__field__inverse__zero(U_501) ),
inference(clausify,[status(thm)],[f_197_2]) ).
cnf(f_197_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_503)
| c_Orderings_Oord__class_Oless__eq(U_501,U_503,c_Groups_Ozero__class_Ozero(U_501))
| ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Rings_Oinverse__class_Odivide(U_501,U_502,U_503),c_Groups_Ozero__class_Ozero(U_501))
| ~ class_Fields_Olinordered__field__inverse__zero(U_501) ),
inference(clausify,[status(thm)],[f_197_2]) ).
cnf(f_197_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_501,U_503,c_Groups_Ozero__class_Ozero(U_501))
| ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_502)
| c_Orderings_Oord__class_Oless__eq(U_501,c_Rings_Oinverse__class_Odivide(U_501,U_502,U_503),c_Groups_Ozero__class_Ozero(U_501))
| ~ class_Fields_Olinordered__field__inverse__zero(U_501) ),
inference(clausify,[status(thm)],[f_197_2]) ).
cnf(f_197_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_501,c_Groups_Ozero__class_Ozero(U_501),U_503)
| ~ c_Orderings_Oord__class_Oless__eq(U_501,U_502,c_Groups_Ozero__class_Ozero(U_501))
| c_Orderings_Oord__class_Oless__eq(U_501,c_Rings_Oinverse__class_Odivide(U_501,U_502,U_503),c_Groups_Ozero__class_Ozero(U_501))
| ~ class_Fields_Olinordered__field__inverse__zero(U_501) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff]) ).
fof(f_198_2,plain,
! [U_506,U_505,U_504] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),c_Rings_Oinverse__class_Odivide(U_504,U_505,U_506))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_504,U_506,c_Groups_Ozero__class_Ozero(U_504))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_506)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_505) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_504,U_506,c_Groups_Ozero__class_Ozero(U_504))
& c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504)) )
| ( c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_506)
& c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_505) )
| ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),c_Rings_Oinverse__class_Odivide(U_504,U_505,U_506)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_505)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),c_Rings_Oinverse__class_Odivide(U_504,U_505,U_506))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_198_2]) ).
cnf(f_198_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_504,U_506,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_505)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),c_Rings_Oinverse__class_Odivide(U_504,U_505,U_506))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_198_2]) ).
cnf(f_198_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_506)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),c_Rings_Oinverse__class_Odivide(U_504,U_505,U_506))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_198_2]) ).
cnf(f_198_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_504,U_506,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_506)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),c_Rings_Oinverse__class_Odivide(U_504,U_505,U_506))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_198_2]) ).
cnf(f_198_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_506)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),U_505)
| c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),c_Rings_Oinverse__class_Odivide(U_504,U_505,U_506))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_198_2]) ).
cnf(f_198_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_504,U_506,c_Groups_Ozero__class_Ozero(U_504))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless__eq(U_504,c_Groups_Ozero__class_Ozero(U_504),c_Rings_Oinverse__class_Odivide(U_504,U_505,U_506))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg]) ).
fof(f_199_2,plain,
! [U_508,U_507] :
( c_Groups_Oabs__class_Oabs(U_507,U_508) = U_508
| ~ c_Orderings_Oord__class_Oless__eq(U_507,c_Groups_Ozero__class_Ozero(U_507),U_508)
| ~ class_Groups_Oordered__ab__group__add__abs(U_507) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( c_Groups_Oabs__class_Oabs(U_507,U_508) = U_508
| ~ c_Orderings_Oord__class_Oless__eq(U_507,c_Groups_Ozero__class_Ozero(U_507),U_508)
| ~ class_Groups_Oordered__ab__group__add__abs(U_507) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).
fof(f_200_2,plain,
! [U_510,U_509] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_509,c_Groups_Oabs__class_Oabs(U_509,U_510),c_Groups_Ozero__class_Ozero(U_509))
| U_510 != c_Groups_Ozero__class_Ozero(U_509) )
& ( U_510 = c_Groups_Ozero__class_Ozero(U_509)
| ~ c_Orderings_Oord__class_Oless__eq(U_509,c_Groups_Oabs__class_Oabs(U_509,U_510),c_Groups_Ozero__class_Ozero(U_509)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_509) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( U_510 = c_Groups_Ozero__class_Ozero(U_509)
| ~ c_Orderings_Oord__class_Oless__eq(U_509,c_Groups_Oabs__class_Oabs(U_509,U_510),c_Groups_Ozero__class_Ozero(U_509))
| ~ class_Groups_Oordered__ab__group__add__abs(U_509) ),
inference(clausify,[status(thm)],[f_200_2]) ).
cnf(f_200_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_509,c_Groups_Oabs__class_Oabs(U_509,U_510),c_Groups_Ozero__class_Ozero(U_509))
| U_510 != c_Groups_Ozero__class_Ozero(U_509)
| ~ class_Groups_Oordered__ab__group__add__abs(U_509) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__ge__zero]) ).
fof(f_201_2,plain,
! [U_512,U_511] :
( c_Orderings_Oord__class_Oless__eq(U_511,c_Groups_Ozero__class_Ozero(U_511),c_Groups_Oabs__class_Oabs(U_511,U_512))
| ~ class_Groups_Oordered__ab__group__add__abs(U_511) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_511,c_Groups_Ozero__class_Ozero(U_511),c_Groups_Oabs__class_Oabs(U_511,U_512))
| ~ class_Groups_Oordered__ab__group__add__abs(U_511) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym]) ).
fof(f_202_2,plain,
! [U_515,U_514,U_513] :
( c_Orderings_Oord__class_Oless__eq(U_513,c_Groups_Ominus__class_Ominus(U_513,c_Groups_Oabs__class_Oabs(U_513,U_514),c_Groups_Oabs__class_Oabs(U_513,U_515)),c_Groups_Oabs__class_Oabs(U_513,c_Groups_Ominus__class_Ominus(U_513,U_515,U_514)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_513) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_513,c_Groups_Ominus__class_Ominus(U_513,c_Groups_Oabs__class_Oabs(U_513,U_514),c_Groups_Oabs__class_Oabs(U_513,U_515)),c_Groups_Oabs__class_Oabs(U_513,c_Groups_Ominus__class_Ominus(U_513,U_515,U_514)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_513) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2]) ).
fof(f_203_2,plain,
! [U_518,U_517,U_516] :
( c_Orderings_Oord__class_Oless__eq(U_516,c_Groups_Ominus__class_Ominus(U_516,c_Groups_Oabs__class_Oabs(U_516,U_517),c_Groups_Oabs__class_Oabs(U_516,U_518)),c_Groups_Oabs__class_Oabs(U_516,c_Groups_Ominus__class_Ominus(U_516,U_517,U_518)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_516) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_516,c_Groups_Ominus__class_Ominus(U_516,c_Groups_Oabs__class_Oabs(U_516,U_517),c_Groups_Oabs__class_Oabs(U_516,U_518)),c_Groups_Oabs__class_Oabs(U_516,c_Groups_Ominus__class_Ominus(U_516,U_517,U_518)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_516) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3]) ).
fof(f_204_2,plain,
! [U_521,U_520,U_519] :
( c_Orderings_Oord__class_Oless__eq(U_519,c_Groups_Oabs__class_Oabs(U_519,c_Groups_Ominus__class_Ominus(U_519,c_Groups_Oabs__class_Oabs(U_519,U_520),c_Groups_Oabs__class_Oabs(U_519,U_521))),c_Groups_Oabs__class_Oabs(U_519,c_Groups_Ominus__class_Ominus(U_519,U_520,U_521)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_519) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_519,c_Groups_Oabs__class_Oabs(U_519,c_Groups_Ominus__class_Ominus(U_519,c_Groups_Oabs__class_Oabs(U_519,U_520),c_Groups_Oabs__class_Oabs(U_519,U_521))),c_Groups_Oabs__class_Oabs(U_519,c_Groups_Ominus__class_Ominus(U_519,U_520,U_521)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_519) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__D2]) ).
fof(f_205_2,plain,
! [U_524,U_523,U_522] :
( c_Orderings_Oord__class_Oless__eq(U_522,c_Groups_Ouminus__class_Ouminus(U_522,U_523),U_524)
| ~ c_Orderings_Oord__class_Oless__eq(U_522,c_Groups_Oabs__class_Oabs(U_522,U_523),U_524)
| ~ class_Groups_Oordered__ab__group__add__abs(U_522) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_522,c_Groups_Ouminus__class_Ouminus(U_522,U_523),U_524)
| ~ c_Orderings_Oord__class_Oless__eq(U_522,c_Groups_Oabs__class_Oabs(U_522,U_523),U_524)
| ~ class_Groups_Oordered__ab__group__add__abs(U_522) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__leI]) ).
fof(f_206_2,plain,
! [U_527,U_526,U_525] :
( c_Orderings_Oord__class_Oless__eq(U_525,c_Groups_Oabs__class_Oabs(U_525,U_526),U_527)
| ~ c_Orderings_Oord__class_Oless__eq(U_525,c_Groups_Ouminus__class_Ouminus(U_525,U_526),U_527)
| ~ c_Orderings_Oord__class_Oless__eq(U_525,U_526,U_527)
| ~ class_Groups_Oordered__ab__group__add__abs(U_525) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_525,c_Groups_Oabs__class_Oabs(U_525,U_526),U_527)
| ~ c_Orderings_Oord__class_Oless__eq(U_525,c_Groups_Ouminus__class_Ouminus(U_525,U_526),U_527)
| ~ c_Orderings_Oord__class_Oless__eq(U_525,U_526,U_527)
| ~ class_Groups_Oordered__ab__group__add__abs(U_525) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).
fof(f_207_2,plain,
! [U_530,U_529,U_528] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Oabs__class_Oabs(U_528,U_529),U_530)
| ~ c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Ouminus__class_Ouminus(U_528,U_529),U_530)
| ~ c_Orderings_Oord__class_Oless__eq(U_528,U_529,U_530) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Ouminus__class_Ouminus(U_528,U_529),U_530)
& c_Orderings_Oord__class_Oless__eq(U_528,U_529,U_530) )
| ~ c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Oabs__class_Oabs(U_528,U_529),U_530) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_528) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_528,U_529,U_530)
| ~ c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Oabs__class_Oabs(U_528,U_529),U_530)
| ~ class_Groups_Oordered__ab__group__add__abs(U_528) ),
inference(clausify,[status(thm)],[f_207_2]) ).
cnf(f_207_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Ouminus__class_Ouminus(U_528,U_529),U_530)
| ~ c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Oabs__class_Oabs(U_528,U_529),U_530)
| ~ class_Groups_Oordered__ab__group__add__abs(U_528) ),
inference(clausify,[status(thm)],[f_207_2]) ).
cnf(f_207_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Oabs__class_Oabs(U_528,U_529),U_530)
| ~ c_Orderings_Oord__class_Oless__eq(U_528,c_Groups_Ouminus__class_Ouminus(U_528,U_529),U_530)
| ~ c_Orderings_Oord__class_Oless__eq(U_528,U_529,U_530)
| ~ class_Groups_Oordered__ab__group__add__abs(U_528) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self]) ).
fof(f_208_2,plain,
! [U_532,U_531] :
( c_Orderings_Oord__class_Oless__eq(U_531,c_Groups_Ouminus__class_Ouminus(U_531,U_532),c_Groups_Oabs__class_Oabs(U_531,U_532))
| ~ class_Groups_Oordered__ab__group__add__abs(U_531) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_531,c_Groups_Ouminus__class_Ouminus(U_531,U_532),c_Groups_Oabs__class_Oabs(U_531,U_532))
| ~ class_Groups_Oordered__ab__group__add__abs(U_531) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg]) ).
fof(f_209_2,plain,
! [U_535,U_534,U_533] :
( c_Orderings_Oord__class_Oless__eq(U_533,c_Groups_Ozero__class_Ozero(U_533),c_Rings_Oinverse__class_Odivide(U_533,U_534,U_535))
| ~ c_Orderings_Oord__class_Oless(U_533,U_535,c_Groups_Ozero__class_Ozero(U_533))
| ~ c_Orderings_Oord__class_Oless__eq(U_533,U_534,c_Groups_Ozero__class_Ozero(U_533))
| ~ class_Fields_Olinordered__field(U_533) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_533,c_Groups_Ozero__class_Ozero(U_533),c_Rings_Oinverse__class_Odivide(U_533,U_534,U_535))
| ~ c_Orderings_Oord__class_Oless(U_533,U_535,c_Groups_Ozero__class_Ozero(U_533))
| ~ c_Orderings_Oord__class_Oless__eq(U_533,U_534,c_Groups_Ozero__class_Ozero(U_533))
| ~ class_Fields_Olinordered__field(U_533) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos]) ).
fof(f_210_2,plain,
! [U_538,U_537,U_536] :
( c_Orderings_Oord__class_Oless__eq(U_536,c_Rings_Oinverse__class_Odivide(U_536,U_537,U_538),c_Groups_Ozero__class_Ozero(U_536))
| ~ c_Orderings_Oord__class_Oless(U_536,c_Groups_Ozero__class_Ozero(U_536),U_538)
| ~ c_Orderings_Oord__class_Oless__eq(U_536,U_537,c_Groups_Ozero__class_Ozero(U_536))
| ~ class_Fields_Olinordered__field(U_536) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_536,c_Rings_Oinverse__class_Odivide(U_536,U_537,U_538),c_Groups_Ozero__class_Ozero(U_536))
| ~ c_Orderings_Oord__class_Oless(U_536,c_Groups_Ozero__class_Ozero(U_536),U_538)
| ~ c_Orderings_Oord__class_Oless__eq(U_536,U_537,c_Groups_Ozero__class_Ozero(U_536))
| ~ class_Fields_Olinordered__field(U_536) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__le]) ).
fof(f_211_2,plain,
! [U_543,U_542,U_541,U_540,U_539] :
( c_Orderings_Oord__class_Oless__eq(U_539,c_Rings_Oinverse__class_Odivide(U_539,U_540,U_543),c_Rings_Oinverse__class_Odivide(U_539,U_541,U_542))
| ~ c_Orderings_Oord__class_Oless__eq(U_539,U_542,U_543)
| ~ c_Orderings_Oord__class_Oless(U_539,c_Groups_Ozero__class_Ozero(U_539),U_542)
| ~ c_Orderings_Oord__class_Oless__eq(U_539,U_540,U_541)
| ~ c_Orderings_Oord__class_Oless__eq(U_539,c_Groups_Ozero__class_Ozero(U_539),U_540)
| ~ class_Fields_Olinordered__field(U_539) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_539,c_Rings_Oinverse__class_Odivide(U_539,U_540,U_543),c_Rings_Oinverse__class_Odivide(U_539,U_541,U_542))
| ~ c_Orderings_Oord__class_Oless__eq(U_539,U_542,U_543)
| ~ c_Orderings_Oord__class_Oless(U_539,c_Groups_Ozero__class_Ozero(U_539),U_542)
| ~ c_Orderings_Oord__class_Oless__eq(U_539,U_540,U_541)
| ~ c_Orderings_Oord__class_Oless__eq(U_539,c_Groups_Ozero__class_Ozero(U_539),U_540)
| ~ class_Fields_Olinordered__field(U_539) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__less]) ).
fof(f_212_2,plain,
! [U_548,U_547,U_546,U_545,U_544] :
( c_Orderings_Oord__class_Oless(U_544,c_Rings_Oinverse__class_Odivide(U_544,U_545,U_548),c_Rings_Oinverse__class_Odivide(U_544,U_546,U_547))
| ~ c_Orderings_Oord__class_Oless__eq(U_544,U_547,U_548)
| ~ c_Orderings_Oord__class_Oless(U_544,c_Groups_Ozero__class_Ozero(U_544),U_547)
| ~ c_Orderings_Oord__class_Oless(U_544,U_545,U_546)
| ~ c_Orderings_Oord__class_Oless__eq(U_544,c_Groups_Ozero__class_Ozero(U_544),U_545)
| ~ class_Fields_Olinordered__field(U_544) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( c_Orderings_Oord__class_Oless(U_544,c_Rings_Oinverse__class_Odivide(U_544,U_545,U_548),c_Rings_Oinverse__class_Odivide(U_544,U_546,U_547))
| ~ c_Orderings_Oord__class_Oless__eq(U_544,U_547,U_548)
| ~ c_Orderings_Oord__class_Oless(U_544,c_Groups_Ozero__class_Ozero(U_544),U_547)
| ~ c_Orderings_Oord__class_Oless(U_544,U_545,U_546)
| ~ c_Orderings_Oord__class_Oless__eq(U_544,c_Groups_Ozero__class_Ozero(U_544),U_545)
| ~ class_Fields_Olinordered__field(U_544) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))
| ~ c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__less2]) ).
fof(f_213_2,plain,
! [U_553,U_552,U_551,U_550,U_549] :
( c_Orderings_Oord__class_Oless(U_549,c_Rings_Oinverse__class_Odivide(U_549,U_550,U_553),c_Rings_Oinverse__class_Odivide(U_549,U_551,U_552))
| ~ c_Orderings_Oord__class_Oless(U_549,U_552,U_553)
| ~ c_Orderings_Oord__class_Oless(U_549,c_Groups_Ozero__class_Ozero(U_549),U_552)
| ~ c_Orderings_Oord__class_Oless__eq(U_549,U_550,U_551)
| ~ c_Orderings_Oord__class_Oless(U_549,c_Groups_Ozero__class_Ozero(U_549),U_550)
| ~ class_Fields_Olinordered__field(U_549) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( c_Orderings_Oord__class_Oless(U_549,c_Rings_Oinverse__class_Odivide(U_549,U_550,U_553),c_Rings_Oinverse__class_Odivide(U_549,U_551,U_552))
| ~ c_Orderings_Oord__class_Oless(U_549,U_552,U_553)
| ~ c_Orderings_Oord__class_Oless(U_549,c_Groups_Ozero__class_Ozero(U_549),U_552)
| ~ c_Orderings_Oord__class_Oless__eq(U_549,U_550,U_551)
| ~ c_Orderings_Oord__class_Oless(U_549,c_Groups_Ozero__class_Ozero(U_549),U_550)
| ~ class_Fields_Olinordered__field(U_549) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg]) ).
fof(f_214_2,plain,
! [U_556,U_555,U_554] :
( c_Orderings_Oord__class_Oless__eq(U_554,c_Rings_Oinverse__class_Odivide(U_554,U_555,U_556),c_Groups_Ozero__class_Ozero(U_554))
| ~ c_Orderings_Oord__class_Oless(U_554,U_556,c_Groups_Ozero__class_Ozero(U_554))
| ~ c_Orderings_Oord__class_Oless__eq(U_554,c_Groups_Ozero__class_Ozero(U_554),U_555)
| ~ class_Fields_Olinordered__field(U_554) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_554,c_Rings_Oinverse__class_Odivide(U_554,U_555,U_556),c_Groups_Ozero__class_Ozero(U_554))
| ~ c_Orderings_Oord__class_Oless(U_554,U_556,c_Groups_Ozero__class_Ozero(U_554))
| ~ c_Orderings_Oord__class_Oless__eq(U_554,c_Groups_Ozero__class_Ozero(U_554),U_555)
| ~ class_Fields_Olinordered__field(U_554) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos]) ).
fof(f_215_2,plain,
! [U_559,U_558,U_557] :
( c_Orderings_Oord__class_Oless__eq(U_557,c_Groups_Ozero__class_Ozero(U_557),c_Rings_Oinverse__class_Odivide(U_557,U_558,U_559))
| ~ c_Orderings_Oord__class_Oless(U_557,c_Groups_Ozero__class_Ozero(U_557),U_559)
| ~ c_Orderings_Oord__class_Oless__eq(U_557,c_Groups_Ozero__class_Ozero(U_557),U_558)
| ~ class_Fields_Olinordered__field(U_557) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_557,c_Groups_Ozero__class_Ozero(U_557),c_Rings_Oinverse__class_Odivide(U_557,U_558,U_559))
| ~ c_Orderings_Oord__class_Oless(U_557,c_Groups_Ozero__class_Ozero(U_557),U_559)
| ~ c_Orderings_Oord__class_Oless__eq(U_557,c_Groups_Ozero__class_Ozero(U_557),U_558)
| ~ class_Fields_Olinordered__field(U_557) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos]) ).
fof(f_216_2,plain,
! [U_561,U_560] :
( c_Groups_Oabs__class_Oabs(U_560,U_561) = c_Groups_Ouminus__class_Ouminus(U_560,U_561)
| ~ c_Orderings_Oord__class_Oless__eq(U_560,U_561,c_Groups_Ozero__class_Ozero(U_560))
| ~ class_Groups_Oordered__ab__group__add__abs(U_560) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( c_Groups_Oabs__class_Oabs(U_560,U_561) = c_Groups_Ouminus__class_Ouminus(U_560,U_561)
| ~ c_Orderings_Oord__class_Oless__eq(U_560,U_561,c_Groups_Ozero__class_Ozero(U_560))
| ~ class_Groups_Oordered__ab__group__add__abs(U_560) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero]) ).
fof(f_217_2,plain,
! [U_563,U_562] :
( c_Orderings_Oord__class_Oless__eq(U_562,c_Groups_Ouminus__class_Ouminus(U_562,c_Groups_Oabs__class_Oabs(U_562,U_563)),c_Groups_Ozero__class_Ozero(U_562))
| ~ class_Groups_Oordered__ab__group__add__abs(U_562) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_562,c_Groups_Ouminus__class_Ouminus(U_562,c_Groups_Oabs__class_Oabs(U_562,U_563)),c_Groups_Ozero__class_Ozero(U_562))
| ~ class_Groups_Oordered__ab__group__add__abs(U_562) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [V_n,V_m] :
( V_m = V_n
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal]) ).
fof(f_218_2,plain,
! [U_565,U_564] :
( U_564 = U_565
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_565,U_564) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_564,U_565) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( U_564 = U_565
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_565,U_564) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_564,U_565) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_1,plain,
! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_diff__self__eq__0]) ).
fof(f_219_2,plain,
! [U_566] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_566,U_566) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_566,U_566) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
inference(fof_nnf,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(f_220_2,plain,
! [U_567] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_567,
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_567,
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_1,plain,
! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_diff__0__eq__0]) ).
fof(f_221_2,plain,
! [U_568] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_568) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_568) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_1,plain,
! [V_P_2,V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& V_m_2 = V_n_2 )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).
fof(f_222_2,plain,
! [U_571,U_570,U_569] :
( hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| ( ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_570,U_569) )
| ( ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
& U_569 = U_570 )
| ( ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_569,U_570) ) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_570,U_569)
| hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| U_569 = U_570
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_569,U_570) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_4,plain,
( ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| U_569 = U_570
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_569,U_570) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_570,U_569)
| hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_569,U_570) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_6,plain,
( ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_569,U_570) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_570,U_569)
| hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| U_569 = U_570
| ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569)) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_8,plain,
( ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| U_569 = U_570
| ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569)) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_570,U_569)
| hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569)) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_10,plain,
( ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569))
| ~ hBOOL(hAPP(hAPP(U_571,U_570),U_569)) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono2]) ).
fof(f_223_2,plain,
! [U_574,U_573,U_572] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_574,U_573),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_574,U_572))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_572,U_574)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_572,U_573) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_574,U_573),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_574,U_572))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_572,U_574)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_572,U_573) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_1,plain,
! [V_n,V_k,V_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less]) ).
fof(f_224_2,plain,
! [U_577,U_576,U_575] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_575,U_577),U_576)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_575,U_576) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_575,U_577),U_576)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_575,U_576) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_1,plain,
! [V_t,V_s] :
( V_s != V_t
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).
fof(f_225_2,plain,
! [U_579,U_578] :
( U_578 != U_579
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_578,U_579) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( U_578 != U_579
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_578,U_579) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_1,plain,
! [V_m,V_n] :
( V_m != V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).
fof(f_226_2,plain,
! [U_581,U_580] :
( U_581 != U_580
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_580,U_581) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( U_581 != U_580
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_580,U_581) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).
fof(f_227_2,plain,
! [U_582] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_582,U_582),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_582,U_582),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
| V_x = V_y ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(f_228_2,plain,
! [U_584,U_583] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_584,U_583)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_583,U_584)
| U_583 = U_584 ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_584,U_583)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_583,U_584)
| U_583 = U_584 ),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_1,plain,
! [V_n_2,V_m_2] :
( ( V_m_2 != V_n_2
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| V_m_2 = V_n_2 ) ),
inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).
fof(f_229_2,plain,
! [U_586,U_585] :
( ( U_585 != U_586
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_586,U_585)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_585,U_586) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_586,U_585)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_585,U_586)
| U_585 = U_586 ) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
( ! [U_590,U_588] :
( U_588 != U_590
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_590,U_588)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_588,U_590) ) )
& ! [U_589,U_587] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_589,U_587)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_587,U_589)
| U_587 = U_589 ) ),
inference(miniscope,[status(thm)],[f_229_2]) ).
cnf(f_229_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_589,U_587)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_587,U_589)
| U_587 = U_589 ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_588,U_590)
| U_588 != U_590 ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_590,U_588)
| U_588 != U_590 ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).
fof(f_230_2,plain,
! [U_591] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_591,U_591),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_591,U_591),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_1,plain,
! [V_pa_2,T_a] :
( ( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__zero]) ).
fof(f_231_2,plain,
! [U_593,U_592] :
( ( ( c_Polynomial_Opoly(U_592,U_593) = c_Polynomial_Opoly(U_592,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_592)))
| U_593 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_592)) )
& ( U_593 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_592))
| c_Polynomial_Opoly(U_592,U_593) != c_Polynomial_Opoly(U_592,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_592))) ) )
| ~ class_Rings_Oidom(U_592)
| ~ class_Int_Oring__char__0(U_592) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( U_593 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_592))
| c_Polynomial_Opoly(U_592,U_593) != c_Polynomial_Opoly(U_592,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_592)))
| ~ class_Rings_Oidom(U_592)
| ~ class_Int_Oring__char__0(U_592) ),
inference(clausify,[status(thm)],[f_231_2]) ).
cnf(f_231_4,plain,
( c_Polynomial_Opoly(U_592,U_593) = c_Polynomial_Opoly(U_592,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_592)))
| U_593 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_592))
| ~ class_Rings_Oidom(U_592)
| ~ class_Int_Oring__char__0(U_592) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_1,plain,
! [V_q_2,V_pa_2,T_a] :
( ( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
| V_pa_2 != V_q_2 )
& ( V_pa_2 = V_q_2
| c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,V_q_2) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__eq__iff]) ).
fof(f_232_2,plain,
! [U_596,U_595,U_594] :
( ( ( c_Polynomial_Opoly(U_594,U_595) = c_Polynomial_Opoly(U_594,U_596)
| U_595 != U_596 )
& ( U_595 = U_596
| c_Polynomial_Opoly(U_594,U_595) != c_Polynomial_Opoly(U_594,U_596) ) )
| ~ class_Rings_Oidom(U_594)
| ~ class_Int_Oring__char__0(U_594) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
( U_595 = U_596
| c_Polynomial_Opoly(U_594,U_595) != c_Polynomial_Opoly(U_594,U_596)
| ~ class_Rings_Oidom(U_594)
| ~ class_Int_Oring__char__0(U_594) ),
inference(clausify,[status(thm)],[f_232_2]) ).
cnf(f_232_4,plain,
( c_Polynomial_Opoly(U_594,U_595) = c_Polynomial_Opoly(U_594,U_596)
| U_595 != U_596
| ~ class_Rings_Oidom(U_594)
| ~ class_Int_Oring__char__0(U_594) ),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_1,plain,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_gr0I]) ).
fof(f_233_2,plain,
! [U_597] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_597)
| U_597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_597)
| U_597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [V_n,V_m] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_gr__implies__not0]) ).
fof(f_234_2,plain,
! [U_599,U_598] :
( U_599 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_598,U_599) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_599] :
( ! [U_598] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_598,U_599)
| U_599 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_234_2]) ).
cnf(f_234_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_598,U_599)
| U_599 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__less]) ).
fof(f_235_2,plain,
! [U_601,U_600] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_601,U_600),U_601)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_601)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_600) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_601,U_600),U_601)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_601)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_600) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_1,plain,
! [V_pa_2,T_a] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff]) ).
fof(f_236_2,plain,
! [U_603,U_602] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_602,U_603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_603 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_602)) )
& ( U_603 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_602))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_602,U_603) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(U_602) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
( U_603 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_602))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_602,U_603) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(U_602) ),
inference(clausify,[status(thm)],[f_236_2]) ).
cnf(f_236_4,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_602,U_603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_603 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_602))
| ~ class_Groups_Ozero(U_602) ),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_1,plain,
! [V_a_2,V_pa_2,T_a] :
( ( ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
& ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__root]) ).
fof(f_237_2,plain,
! [U_606,U_605,U_604] :
( ( ( hAPP(c_Polynomial_Opoly(U_604,U_605),U_606) = c_Groups_Ozero__class_Ozero(U_604)
| ( c_Polynomial_Oorder(U_604,U_606,U_605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_605 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_604)) ) )
& ( c_Polynomial_Oorder(U_604,U_606,U_605) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_605 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_604))
| hAPP(c_Polynomial_Opoly(U_604,U_605),U_606) != c_Groups_Ozero__class_Ozero(U_604) ) )
| ~ class_Rings_Oidom(U_604) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( c_Polynomial_Oorder(U_604,U_606,U_605) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_605 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_604))
| hAPP(c_Polynomial_Opoly(U_604,U_605),U_606) != c_Groups_Ozero__class_Ozero(U_604)
| ~ class_Rings_Oidom(U_604) ),
inference(clausify,[status(thm)],[f_237_2]) ).
cnf(f_237_4,plain,
( U_605 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_604))
| hAPP(c_Polynomial_Opoly(U_604,U_605),U_606) = c_Groups_Ozero__class_Ozero(U_604)
| ~ class_Rings_Oidom(U_604) ),
inference(clausify,[status(thm)],[f_237_2]) ).
cnf(f_237_5,plain,
( c_Polynomial_Oorder(U_604,U_606,U_605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(U_604,U_605),U_606) = c_Groups_Ozero__class_Ozero(U_604)
| ~ class_Rings_Oidom(U_604) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_1,plain,
! [V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__refl]) ).
fof(f_238_2,plain,
! [U_608,U_607] :
( c_Orderings_Oord__class_Oless__eq(U_607,U_608,U_608)
| ~ class_Orderings_Opreorder(U_607) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_607,U_608,U_608)
| ~ class_Orderings_Opreorder(U_607) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J]) ).
fof(f_239_2,plain,
! [U_610,U_609] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_609,U_610)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_609,U_610) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_609,U_610)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_609,U_610) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_1,plain,
! [V_p,V_z,V_e] :
( ? [B_d] :
( ! [B_w] :
( 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))),V_e)
| ~ 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_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_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),V_e) ),
inference(fof_nnf,[status(thm)],[fact_poly__cont]) ).
fof(f_240_2,plain,
! [U_615,U_614,U_613] :
( ? [U_612] :
( ! [U_611] :
( 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,U_615),U_611),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_615),U_614))),U_613)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_611,U_614)),U_612)
| ~ 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,U_611,U_614))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_612) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_613) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_615,U_614,U_613] :
( ( ! [U_611] :
( 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,U_615),U_611),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_615),U_614))),U_613)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_611,U_614)),sK6(U_615,U_614,U_613))
| ~ 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,U_611,U_614))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK6(U_615,U_614,U_613)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_613) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_612,sK6(U_615,U_614,U_613))],[f_240_2]) ).
cnf(f_240_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK6(U_615,U_614,U_613))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_613) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_615),U_611),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_615),U_614))),U_613)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_611,U_614)),sK6(U_615,U_614,U_613))
| ~ 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,U_611,U_614)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_613) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus]) ).
fof(f_241_2,plain,
! [U_618,U_617,U_616] :
( c_Groups_Ominus__class_Ominus(U_616,c_Groups_Ouminus__class_Ouminus(U_616,U_617),c_Groups_Ouminus__class_Ouminus(U_616,U_618)) = c_Groups_Ouminus__class_Ouminus(U_616,c_Groups_Ominus__class_Ominus(U_616,U_617,U_618))
| ~ class_Groups_Oab__group__add(U_616) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( c_Groups_Ominus__class_Ominus(U_616,c_Groups_Ouminus__class_Ouminus(U_616,U_617),c_Groups_Ouminus__class_Ouminus(U_616,U_618)) = c_Groups_Ouminus__class_Ouminus(U_616,c_Groups_Ominus__class_Ominus(U_616,U_617,U_618))
| ~ class_Groups_Oab__group__add(U_616) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Odecseq(T_a,V_X_2)
| ? [B_m,B_n] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) ) )
& ( ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
| ~ c_SEQ_Odecseq(T_a,V_X_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_decseq__def]) ).
fof(f_242_2,plain,
! [U_624,U_623] :
( ( ( c_SEQ_Odecseq(U_623,U_624)
| ? [U_622,U_621] :
( ~ c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_624,U_621),hAPP(U_624,U_622))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_622,U_621) ) )
& ( ! [U_620,U_619] :
( c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_624,U_619),hAPP(U_624,U_620))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_620,U_619) )
| ~ c_SEQ_Odecseq(U_623,U_624) ) )
| ~ class_Orderings_Oorder(U_623) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_624,U_623] :
( ( ( c_SEQ_Odecseq(U_623,U_624)
| ? [U_621] :
( ~ c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_624,U_621),hAPP(U_624,sK7(U_624,U_623)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK7(U_624,U_623),U_621) ) )
& ( ! [U_620,U_619] :
( c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_624,U_619),hAPP(U_624,U_620))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_620,U_619) )
| ~ c_SEQ_Odecseq(U_623,U_624) ) )
| ~ class_Orderings_Oorder(U_623) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_622,sK7(U_624,U_623))],[f_242_2]) ).
fof(f_242_4,plain,
! [U_624,U_623] :
( ( ( c_SEQ_Odecseq(U_623,U_624)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_624,sK8(U_624,U_623)),hAPP(U_624,sK7(U_624,U_623)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK7(U_624,U_623),sK8(U_624,U_623)) ) )
& ( ! [U_620,U_619] :
( c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_624,U_619),hAPP(U_624,U_620))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_620,U_619) )
| ~ c_SEQ_Odecseq(U_623,U_624) ) )
| ~ class_Orderings_Oorder(U_623) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_621,sK8(U_624,U_623))],[f_242_3]) ).
cnf(f_242_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_624,U_619),hAPP(U_624,U_620))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_620,U_619)
| ~ c_SEQ_Odecseq(U_623,U_624)
| ~ class_Orderings_Oorder(U_623) ),
inference(clausify,[status(thm)],[f_242_4]) ).
cnf(f_242_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK7(U_624,U_623),sK8(U_624,U_623))
| c_SEQ_Odecseq(U_623,U_624)
| ~ class_Orderings_Oorder(U_623) ),
inference(clausify,[status(thm)],[f_242_4]) ).
cnf(f_242_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_624,sK8(U_624,U_623)),hAPP(U_624,sK7(U_624,U_623)))
| c_SEQ_Odecseq(U_623,U_624)
| ~ class_Orderings_Oorder(U_623) ),
inference(clausify,[status(thm)],[f_242_4]) ).
fof(f_243_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__mono]) ).
fof(f_243_2,plain,
! [U_627,U_626,U_625] :
( c_Orderings_Oord__class_Oless__eq(U_625,c_Groups_Ouminus__class_Ouminus(U_625,U_627),c_Groups_Ouminus__class_Ouminus(U_625,U_626))
| ~ c_Orderings_Oord__class_Oless__eq(U_625,U_626,U_627)
| ~ class_Lattices_Oboolean__algebra(U_625) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_625,c_Groups_Ouminus__class_Ouminus(U_625,U_627),c_Groups_Ouminus__class_Ouminus(U_625,U_626))
| ~ c_Orderings_Oord__class_Oless__eq(U_625,U_626,U_627)
| ~ class_Lattices_Oboolean__algebra(U_625) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
inference(fof_nnf,[status(thm)],[fact_rp]) ).
cnf(f_244_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
inference(clausify,[status(thm)],[f_244_1]) ).
fof(f_245_1,plain,
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(B_n)),v_r),
inference(fof_nnf,[status(thm)],[fact_g_I1_J]) ).
fof(f_245_2,plain,
! [U_628] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(U_628)),v_r),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(U_628)),v_r),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_1,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zle__antisym]) ).
fof(f_246_2,plain,
! [U_630,U_629] :
( U_629 = U_630
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_630,U_629)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_629,U_630) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( U_629 = U_630
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_630,U_629)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_629,U_630) ),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zle__trans]) ).
fof(f_247_2,plain,
! [U_633,U_632,U_631] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_631,U_633)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_632,U_633)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_631,U_632) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_631,U_633)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_632,U_633)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_631,U_632) ),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_1,plain,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zle__linear]) ).
fof(f_248_2,plain,
! [U_635,U_634] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_635,U_634)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_634,U_635) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
cnf(f_248_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_635,U_634)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_634,U_635) ),
inference(clausify,[status(thm)],[f_248_2]) ).
fof(f_249_1,plain,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w),
inference(fof_nnf,[status(thm)],[fact_zle__refl]) ).
fof(f_249_2,plain,
! [U_636] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_636,U_636),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_636,U_636),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J]) ).
fof(f_250_2,plain,
! [U_638,U_637] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_637),c_Int_OBit1(U_638))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_637,U_638) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_637,U_638)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_637),c_Int_OBit1(U_638)) ) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
( ! [U_642,U_640] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_640),c_Int_OBit1(U_642))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_640,U_642) )
& ! [U_641,U_639] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_639,U_641)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_639),c_Int_OBit1(U_641)) ) ),
inference(miniscope,[status(thm)],[f_250_2]) ).
cnf(f_250_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_639,U_641)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_639),c_Int_OBit1(U_641)) ),
inference(clausify,[status(thm)],[f_250_3]) ).
cnf(f_250_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_640),c_Int_OBit1(U_642))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_640,U_642) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J]) ).
fof(f_251_2,plain,
! [U_644,U_643] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_643),c_Int_OBit1(U_644))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_643,U_644) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_643,U_644)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_643),c_Int_OBit1(U_644)) ) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_648,U_646] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_646),c_Int_OBit1(U_648))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_646,U_648) )
& ! [U_647,U_645] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_645,U_647)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_645),c_Int_OBit1(U_647)) ) ),
inference(miniscope,[status(thm)],[f_251_2]) ).
cnf(f_251_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_645,U_647)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_645),c_Int_OBit1(U_647)) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_646),c_Int_OBit1(U_648))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_646,U_648) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I19_J]) ).
cnf(f_252_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(clausify,[status(thm)],[f_252_1]) ).
fof(f_253_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J]) ).
fof(f_253_2,plain,
! [U_650,U_649] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_649),c_Int_OBit0(U_650))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_649,U_650) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_649,U_650)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_649),c_Int_OBit0(U_650)) ) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ! [U_654,U_652] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_652),c_Int_OBit0(U_654))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_652,U_654) )
& ! [U_653,U_651] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_651,U_653)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_651),c_Int_OBit0(U_653)) ) ),
inference(miniscope,[status(thm)],[f_253_2]) ).
cnf(f_253_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_651,U_653)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_651),c_Int_OBit0(U_653)) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_652),c_Int_OBit0(U_654))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_652,U_654) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J]) ).
fof(f_254_2,plain,
! [U_656,U_655] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_655),c_Int_OBit0(U_656))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_655,U_656) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_655,U_656)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_655),c_Int_OBit0(U_656)) ) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
( ! [U_660,U_658] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_658),c_Int_OBit0(U_660))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_658,U_660) )
& ! [U_659,U_657] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_657,U_659)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_657),c_Int_OBit0(U_659)) ) ),
inference(miniscope,[status(thm)],[f_254_2]) ).
cnf(f_254_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_657,U_659)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_657),c_Int_OBit0(U_659)) ),
inference(clausify,[status(thm)],[f_254_3]) ).
cnf(f_254_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_658),c_Int_OBit0(U_660))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_658,U_660) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__less__def]) ).
fof(f_255_2,plain,
! [U_662,U_661] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_661,U_662)
| U_661 = U_662
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_661,U_662) )
& ( ( U_661 != U_662
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_661,U_662) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_661,U_662) ) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
( ! [U_666,U_664] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_664,U_666)
| U_664 = U_666
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_664,U_666) )
& ! [U_665,U_663] :
( ( U_663 != U_665
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_663,U_665) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_663,U_665) ) ),
inference(miniscope,[status(thm)],[f_255_2]) ).
cnf(f_255_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_663,U_665)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_663,U_665) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_5,plain,
( U_663 != U_665
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_663,U_665) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_664,U_666)
| U_664 = U_666
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_664,U_666) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__real__def]) ).
fof(f_256_2,plain,
! [U_668,U_667] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_667,U_668)
| ( U_667 != U_668
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_667,U_668) ) )
& ( U_667 = U_668
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_667,U_668)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_667,U_668) ) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
( ! [U_672,U_670] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_670,U_672)
| ( U_670 != U_672
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_670,U_672) ) )
& ! [U_671,U_669] :
( U_669 = U_671
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_669,U_671)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_669,U_671) ) ),
inference(miniscope,[status(thm)],[f_256_2]) ).
cnf(f_256_4,plain,
( U_669 = U_671
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_669,U_671)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_669,U_671) ),
inference(clausify,[status(thm)],[f_256_3]) ).
cnf(f_256_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_670,U_672)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_670,U_672) ),
inference(clausify,[status(thm)],[f_256_3]) ).
cnf(f_256_6,plain,
( U_670 != U_672
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_670,U_672) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_1,plain,
! [V_wa_2,V_za_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
| V_za_2 = V_wa_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) )
& ( ( V_za_2 != V_wa_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__le]) ).
fof(f_257_2,plain,
! [U_674,U_673] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_673,U_674)
| U_673 = U_674
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_673,U_674) )
& ( ( U_673 != U_674
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_673,U_674) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_673,U_674) ) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
( ! [U_678,U_676] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_676,U_678)
| U_676 = U_678
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_676,U_678) )
& ! [U_677,U_675] :
( ( U_675 != U_677
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_675,U_677) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_675,U_677) ) ),
inference(miniscope,[status(thm)],[f_257_2]) ).
cnf(f_257_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_675,U_677)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_675,U_677) ),
inference(clausify,[status(thm)],[f_257_3]) ).
cnf(f_257_5,plain,
( U_675 != U_677
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_675,U_677) ),
inference(clausify,[status(thm)],[f_257_3]) ).
cnf(f_257_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_676,U_678)
| U_676 = U_678
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_676,U_678) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code]) ).
fof(f_258_2,plain,
! [U_680,U_679] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_679),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_680))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_679,U_680) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_679,U_680)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_679),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_680)) ) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
( ! [U_684,U_682] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_682),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_684))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_682,U_684) )
& ! [U_683,U_681] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_681,U_683)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_681),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_683)) ) ),
inference(miniscope,[status(thm)],[f_258_2]) ).
cnf(f_258_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_681,U_683)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_681),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_683)) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_682),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_684))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_682,U_684) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J]) ).
fof(f_259_2,plain,
! [U_685] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_685))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_685) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_685)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_685)) ) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
( ! [U_687] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_687))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_687) )
& ! [U_686] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_686)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_686)) ) ),
inference(miniscope,[status(thm)],[f_259_2]) ).
cnf(f_259_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_686)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_686)) ),
inference(clausify,[status(thm)],[f_259_3]) ).
cnf(f_259_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_687))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_687) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J]) ).
fof(f_260_2,plain,
! [U_689,U_688] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_688),c_Int_OBit1(U_689))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_688,U_689) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_688,U_689)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_688),c_Int_OBit1(U_689)) ) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ! [U_693,U_691] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_691),c_Int_OBit1(U_693))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_691,U_693) )
& ! [U_692,U_690] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_690,U_692)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_690),c_Int_OBit1(U_692)) ) ),
inference(miniscope,[status(thm)],[f_260_2]) ).
cnf(f_260_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_690,U_692)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_690),c_Int_OBit1(U_692)) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_691),c_Int_OBit1(U_693))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_691,U_693) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J]) ).
fof(f_261_2,plain,
! [U_695,U_694] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_694),c_Int_OBit1(U_695))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_694,U_695) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_694,U_695)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_694),c_Int_OBit1(U_695)) ) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
( ! [U_699,U_697] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_697),c_Int_OBit1(U_699))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_697,U_699) )
& ! [U_698,U_696] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_696,U_698)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_696),c_Int_OBit1(U_698)) ) ),
inference(miniscope,[status(thm)],[f_261_2]) ).
cnf(f_261_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_696,U_698)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_696),c_Int_OBit1(U_698)) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_697),c_Int_OBit1(U_699))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_697,U_699) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J]) ).
fof(f_262_2,plain,
! [U_700] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_700))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_700) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_700)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_700)) ) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
( ! [U_702] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_702))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_702) )
& ! [U_701] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_701)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_701)) ) ),
inference(miniscope,[status(thm)],[f_262_2]) ).
cnf(f_262_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_701)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_701)) ),
inference(clausify,[status(thm)],[f_262_3]) ).
cnf(f_262_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_702))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_702) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J]) ).
fof(f_263_2,plain,
! [U_703] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_703),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_703,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_703,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_703),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
( ! [U_705] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_705),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_705,c_Int_OPls) )
& ! [U_704] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_704,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_704),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_263_2]) ).
cnf(f_263_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_704,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_704),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_263_3]) ).
cnf(f_263_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_705),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_705,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
! [V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__ge__zero]) ).
fof(f_264_2,plain,
! [U_707,U_706] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_706,U_707))
| ~ class_RealVector_Oreal__normed__vector(U_706) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_706,U_707))
| ~ class_RealVector_Oreal__normed__vector(U_706) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__le__divide__iff]) ).
fof(f_265_2,plain,
! [U_709,U_708] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_708,U_709))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_709,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_708) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_709)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_708,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_709,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_708) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_709)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_708,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_708,U_709)) ) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
( ! [U_713,U_711] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_711,U_713))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_713,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_711) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_713)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_711,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ! [U_712,U_710] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_712,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_710) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_712)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_710,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_710,U_712)) ) ),
inference(miniscope,[status(thm)],[f_265_2]) ).
cnf(f_265_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_712)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_710,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_710,U_712)) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_712,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_710)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_710,U_712)) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_711)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_711,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_711,U_713)) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_713,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_711,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_711,U_713)) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_711)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_713)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_711,U_713)) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_9,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_713,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_713)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_711,U_713)) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff]) ).
fof(f_266_2,plain,
! [U_715,U_714] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_714,U_715)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_714,U_715),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_714,U_715),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_714,U_715) ) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
( ! [U_719,U_717] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_717,U_719)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_717,U_719),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_718,U_716] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_716,U_718),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_716,U_718) ) ),
inference(miniscope,[status(thm)],[f_266_2]) ).
cnf(f_266_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_716,U_718),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_716,U_718) ),
inference(clausify,[status(thm)],[f_266_3]) ).
cnf(f_266_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_717,U_719)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_717,U_719),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [V_ra_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2) ) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff]) ).
fof(f_267_2,plain,
! [U_721,U_720] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_720),U_721)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_720,U_721)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_721),U_720) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_720,U_721)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_721),U_720) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_720),U_721) ) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
( ! [U_725,U_723] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_723),U_725)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_723,U_725)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_725),U_723) )
& ! [U_724,U_722] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_722,U_724)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_724),U_722) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_722),U_724) ) ),
inference(miniscope,[status(thm)],[f_267_2]) ).
cnf(f_267_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_724),U_722)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_722),U_724) ),
inference(clausify,[status(thm)],[f_267_3]) ).
cnf(f_267_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_722,U_724)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_722),U_724) ),
inference(clausify,[status(thm)],[f_267_3]) ).
cnf(f_267_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_723),U_725)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_723,U_725)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_725),U_723) ),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff]) ).
fof(f_268_2,plain,
! [U_727,U_726] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_726,U_727),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_727 != c_Groups_Ozero__class_Ozero(U_726) )
& ( U_727 = c_Groups_Ozero__class_Ozero(U_726)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_726,U_727),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(U_726) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( U_727 = c_Groups_Ozero__class_Ozero(U_726)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_726,U_727),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_726) ),
inference(clausify,[status(thm)],[f_268_2]) ).
cnf(f_268_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_726,U_727),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_727 != c_Groups_Ozero__class_Ozero(U_726)
| ~ class_RealVector_Oreal__normed__vector(U_726) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_1,plain,
! [V_v_2] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__0]) ).
fof(f_269_2,plain,
! [U_728] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_728) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_728,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_728,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_728) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
( ! [U_730] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_730) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_730,c_Int_OPls) )
& ! [U_729] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_729,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_729) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_269_2]) ).
cnf(f_269_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_729,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_729) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_5,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_730) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_730,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [V_v_2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__0__number__of]) ).
fof(f_270_2,plain,
! [U_731] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_731)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_731,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_731,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_731) ) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
( ! [U_733] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_733)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_733,c_Int_OPls) )
& ! [U_732] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_732,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_732) ) ),
inference(miniscope,[status(thm)],[f_270_2]) ).
cnf(f_270_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_732,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_732) ),
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(f_270_5,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_733)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_733,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J]) ).
fof(f_271_2,plain,
! [U_734] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_734))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_734) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_734)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_734)) ) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
( ! [U_736] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_736))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_736) )
& ! [U_735] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_735)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_735)) ) ),
inference(miniscope,[status(thm)],[f_271_2]) ).
cnf(f_271_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_735)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_735)) ),
inference(clausify,[status(thm)],[f_271_3]) ).
cnf(f_271_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_736))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_736) ),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J]) ).
fof(f_272_2,plain,
! [U_737] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_737),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_737,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_737,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_737),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
( ! [U_739] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_739),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_739,c_Int_OPls) )
& ! [U_738] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_738,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_738),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_272_2]) ).
cnf(f_272_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_738,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_738),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_272_3]) ).
cnf(f_272_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_739),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_739,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_272_3]) ).
fof(f_273_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J]) ).
fof(f_273_2,plain,
! [U_741,U_740] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_740),c_Int_OBit1(U_741))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_740,U_741) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_740,U_741)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_740),c_Int_OBit1(U_741)) ) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
( ! [U_745,U_743] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_743),c_Int_OBit1(U_745))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_743,U_745) )
& ! [U_744,U_742] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_742,U_744)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_742),c_Int_OBit1(U_744)) ) ),
inference(miniscope,[status(thm)],[f_273_2]) ).
cnf(f_273_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_742,U_744)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_742),c_Int_OBit1(U_744)) ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_743),c_Int_OBit1(U_745))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_743,U_745) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J]) ).
fof(f_274_2,plain,
! [U_747,U_746] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_746),c_Int_OBit1(U_747))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_746,U_747) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_746,U_747)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_746),c_Int_OBit1(U_747)) ) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
( ! [U_751,U_749] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_749),c_Int_OBit1(U_751))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_749,U_751) )
& ! [U_750,U_748] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_748,U_750)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_748),c_Int_OBit1(U_750)) ) ),
inference(miniscope,[status(thm)],[f_274_2]) ).
cnf(f_274_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_748,U_750)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_748),c_Int_OBit1(U_750)) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_749),c_Int_OBit1(U_751))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_749,U_751) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J]) ).
fof(f_275_2,plain,
! [U_753,U_752] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_752),c_Int_OBit0(U_753))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_752,U_753) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_752,U_753)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_752),c_Int_OBit0(U_753)) ) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_757,U_755] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_755),c_Int_OBit0(U_757))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_755,U_757) )
& ! [U_756,U_754] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_754,U_756)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_754),c_Int_OBit0(U_756)) ) ),
inference(miniscope,[status(thm)],[f_275_2]) ).
cnf(f_275_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_754,U_756)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_754),c_Int_OBit0(U_756)) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_755),c_Int_OBit0(U_757))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_755,U_757) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J]) ).
fof(f_276_2,plain,
! [U_759,U_758] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_758),c_Int_OBit0(U_759))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_758,U_759) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_758,U_759)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_758),c_Int_OBit0(U_759)) ) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
( ! [U_763,U_761] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_761),c_Int_OBit0(U_763))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_761,U_763) )
& ! [U_762,U_760] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_760,U_762)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_760),c_Int_OBit0(U_762)) ) ),
inference(miniscope,[status(thm)],[f_276_2]) ).
cnf(f_276_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_760,U_762)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_760),c_Int_OBit0(U_762)) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_761),c_Int_OBit0(U_763))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_761,U_763) ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__le__cases]) ).
fof(f_277_2,plain,
! [U_766,U_765,U_764] :
( c_Orderings_Oord__class_Oless__eq(U_764,U_766,U_765)
| c_Orderings_Oord__class_Oless__eq(U_764,U_765,U_766)
| ~ class_Orderings_Olinorder(U_764) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_764,U_766,U_765)
| c_Orderings_Oord__class_Oless__eq(U_764,U_765,U_766)
| ~ class_Orderings_Olinorder(U_764) ),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_1,plain,
! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_278_2,plain,
! [U_771,U_770,U_769,U_768,U_767] :
( c_Orderings_Oord__class_Oless__eq(U_767,hAPP(U_769,U_771),hAPP(U_770,U_771))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_768,U_767),U_769,U_770)
| ~ class_Orderings_Oord(U_767) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_767,hAPP(U_769,U_771),hAPP(U_770,U_771))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_768,U_767),U_769,U_770)
| ~ class_Orderings_Oord(U_767) ),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I6_J]) ).
fof(f_279_2,plain,
! [U_775,U_774,U_773,U_772] :
( c_Orderings_Oord__class_Oless__eq(U_772,U_775,U_774)
| ~ c_Orderings_Oord__class_Oless__eq(U_772,U_775,U_773)
| ~ c_Orderings_Oord__class_Oless__eq(U_772,U_773,U_774)
| ~ class_Orderings_Oorder(U_772) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_772,U_775,U_774)
| ~ c_Orderings_Oord__class_Oless__eq(U_772,U_775,U_773)
| ~ c_Orderings_Oord__class_Oless__eq(U_772,U_773,U_774)
| ~ class_Orderings_Oorder(U_772) ),
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_1,plain,
! [V_x,V_y,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I5_J]) ).
fof(f_280_2,plain,
! [U_778,U_777,U_776] :
( U_778 = U_777
| ~ c_Orderings_Oord__class_Oless__eq(U_776,U_778,U_777)
| ~ c_Orderings_Oord__class_Oless__eq(U_776,U_777,U_778)
| ~ class_Orderings_Oorder(U_776) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( U_778 = U_777
| ~ c_Orderings_Oord__class_Oless__eq(U_776,U_778,U_777)
| ~ c_Orderings_Oord__class_Oless__eq(U_776,U_777,U_778)
| ~ class_Orderings_Oorder(U_776) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__trans]) ).
fof(f_281_2,plain,
! [U_782,U_781,U_780,U_779] :
( c_Orderings_Oord__class_Oless__eq(U_779,U_780,U_782)
| ~ c_Orderings_Oord__class_Oless__eq(U_779,U_781,U_782)
| ~ c_Orderings_Oord__class_Oless__eq(U_779,U_780,U_781)
| ~ class_Orderings_Opreorder(U_779) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_779,U_780,U_782)
| ~ c_Orderings_Oord__class_Oless__eq(U_779,U_781,U_782)
| ~ c_Orderings_Oord__class_Oless__eq(U_779,U_780,U_781)
| ~ class_Orderings_Opreorder(U_779) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym]) ).
fof(f_282_2,plain,
! [U_785,U_784,U_783] :
( U_784 = U_785
| ~ c_Orderings_Oord__class_Oless__eq(U_783,U_785,U_784)
| ~ c_Orderings_Oord__class_Oless__eq(U_783,U_784,U_785)
| ~ class_Orderings_Oorder(U_783) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( U_784 = U_785
| ~ c_Orderings_Oord__class_Oless__eq(U_783,U_785,U_784)
| ~ c_Orderings_Oord__class_Oless__eq(U_783,U_784,U_785)
| ~ class_Orderings_Oorder(U_783) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| V_b != V_c
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I4_J]) ).
fof(f_283_2,plain,
! [U_789,U_788,U_787,U_786] :
( c_Orderings_Oord__class_Oless__eq(U_786,U_789,U_788)
| U_787 != U_789
| ~ c_Orderings_Oord__class_Oless__eq(U_786,U_787,U_788)
| ~ class_Orderings_Oorder(U_786) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_786,U_789,U_788)
| U_787 != U_789
| ~ c_Orderings_Oord__class_Oless__eq(U_786,U_787,U_788)
| ~ class_Orderings_Oorder(U_786) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| V_b != V_c
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__le__eq__trans]) ).
fof(f_284_2,plain,
! [U_793,U_792,U_791,U_790] :
( c_Orderings_Oord__class_Oless__eq(U_790,U_791,U_793)
| U_792 != U_793
| ~ c_Orderings_Oord__class_Oless__eq(U_790,U_791,U_792)
| ~ class_Orderings_Oord(U_790) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_790,U_791,U_793)
| U_792 != U_793
| ~ c_Orderings_Oord__class_Oless__eq(U_790,U_791,U_792)
| ~ class_Orderings_Oord(U_790) ),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
| V_a != V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I3_J]) ).
fof(f_285_2,plain,
! [U_797,U_796,U_795,U_794] :
( c_Orderings_Oord__class_Oless__eq(U_794,U_797,U_795)
| ~ c_Orderings_Oord__class_Oless__eq(U_794,U_797,U_796)
| U_795 != U_796
| ~ class_Orderings_Oorder(U_794) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
cnf(f_285_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_794,U_797,U_795)
| ~ c_Orderings_Oord__class_Oless__eq(U_794,U_797,U_796)
| U_795 != U_796
| ~ class_Orderings_Oorder(U_794) ),
inference(clausify,[status(thm)],[f_285_2]) ).
fof(f_286_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| V_a != V_b
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__eq__le__trans]) ).
fof(f_286_2,plain,
! [U_801,U_800,U_799,U_798] :
( c_Orderings_Oord__class_Oless__eq(U_798,U_799,U_801)
| ~ c_Orderings_Oord__class_Oless__eq(U_798,U_800,U_801)
| U_799 != U_800
| ~ class_Orderings_Oord(U_798) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_798,U_799,U_801)
| ~ c_Orderings_Oord__class_Oless__eq(U_798,U_800,U_801)
| U_799 != U_800
| ~ class_Orderings_Oord(U_798) ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_287_2,plain,
! [U_804,U_803,U_802] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_802,U_804,U_803)
| U_804 != U_803 )
& ( U_804 = U_803
| ~ c_Orderings_Oord__class_Oless__eq(U_802,U_804,U_803) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_802,U_803,U_804)
| ~ class_Orderings_Oorder(U_802) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
( U_804 = U_803
| ~ c_Orderings_Oord__class_Oless__eq(U_802,U_804,U_803)
| ~ c_Orderings_Oord__class_Oless__eq(U_802,U_803,U_804)
| ~ class_Orderings_Oorder(U_802) ),
inference(clausify,[status(thm)],[f_287_2]) ).
cnf(f_287_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_802,U_804,U_803)
| U_804 != U_803
| ~ c_Orderings_Oord__class_Oless__eq(U_802,U_803,U_804)
| ~ class_Orderings_Oorder(U_802) ),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_1,plain,
! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_288_2,plain,
! [U_809,U_808,U_807,U_806,U_805] :
( c_Orderings_Oord__class_Oless__eq(U_805,hAPP(U_807,U_809),hAPP(U_808,U_809))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_806,U_805),U_807,U_808)
| ~ class_Orderings_Oord(U_805) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_805,hAPP(U_807,U_809),hAPP(U_808,U_809))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_806,U_805),U_807,U_808)
| ~ class_Orderings_Oord(U_805) ),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| V_x != V_y
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__refl]) ).
fof(f_289_2,plain,
! [U_812,U_811,U_810] :
( c_Orderings_Oord__class_Oless__eq(U_810,U_811,U_812)
| U_811 != U_812
| ~ class_Orderings_Opreorder(U_810) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_810,U_811,U_812)
| U_811 != U_812
| ~ class_Orderings_Opreorder(U_810) ),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| V_x_2 != V_y_2 ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_290_2,plain,
! [U_815,U_814,U_813] :
( ( ( U_814 = U_815
| ~ c_Orderings_Oord__class_Oless__eq(U_813,U_815,U_814)
| ~ c_Orderings_Oord__class_Oless__eq(U_813,U_814,U_815) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_813,U_815,U_814)
& c_Orderings_Oord__class_Oless__eq(U_813,U_814,U_815) )
| U_814 != U_815 ) )
| ~ class_Orderings_Oorder(U_813) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_813,U_814,U_815)
| U_814 != U_815
| ~ class_Orderings_Oorder(U_813) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_813,U_815,U_814)
| U_814 != U_815
| ~ class_Orderings_Oorder(U_813) ),
inference(clausify,[status(thm)],[f_290_2]) ).
cnf(f_290_5,plain,
( U_814 = U_815
| ~ c_Orderings_Oord__class_Oless__eq(U_813,U_815,U_814)
| ~ c_Orderings_Oord__class_Oless__eq(U_813,U_814,U_815)
| ~ class_Orderings_Oorder(U_813) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__linear]) ).
fof(f_291_2,plain,
! [U_818,U_817,U_816] :
( c_Orderings_Oord__class_Oless__eq(U_816,U_818,U_817)
| c_Orderings_Oord__class_Oless__eq(U_816,U_817,U_818)
| ~ class_Orderings_Olinorder(U_816) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_816,U_818,U_817)
| c_Orderings_Oord__class_Oless__eq(U_816,U_817,U_818)
| ~ class_Orderings_Olinorder(U_816) ),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_1,plain,
! [V_ga_2,V_fa_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
| ? [B_x] : ~ c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_ga_2,B_x)) )
& ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_ga_2,B_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_292_2,plain,
! [U_824,U_823,U_822,U_821] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,U_821),U_823,U_824)
| ? [U_820] : ~ c_Orderings_Oord__class_Oless__eq(U_821,hAPP(U_823,U_820),hAPP(U_824,U_820)) )
& ( ! [U_819] : c_Orderings_Oord__class_Oless__eq(U_821,hAPP(U_823,U_819),hAPP(U_824,U_819))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,U_821),U_823,U_824) ) )
| ~ class_Orderings_Oord(U_821) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_824,U_823,U_822,U_821] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,U_821),U_823,U_824)
| ~ c_Orderings_Oord__class_Oless__eq(U_821,hAPP(U_823,sK9(U_824,U_823,U_822,U_821)),hAPP(U_824,sK9(U_824,U_823,U_822,U_821))) )
& ( ! [U_819] : c_Orderings_Oord__class_Oless__eq(U_821,hAPP(U_823,U_819),hAPP(U_824,U_819))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,U_821),U_823,U_824) ) )
| ~ class_Orderings_Oord(U_821) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_820,sK9(U_824,U_823,U_822,U_821))],[f_292_2]) ).
cnf(f_292_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_821,hAPP(U_823,U_819),hAPP(U_824,U_819))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,U_821),U_823,U_824)
| ~ class_Orderings_Oord(U_821) ),
inference(clausify,[status(thm)],[f_292_3]) ).
cnf(f_292_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,U_821),U_823,U_824)
| ~ c_Orderings_Oord__class_Oless__eq(U_821,hAPP(U_823,sK9(U_824,U_823,U_822,U_821)),hAPP(U_824,sK9(U_824,U_823,U_822,U_821)))
| ~ class_Orderings_Oord(U_821) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_1,plain,
! [V_v_H_2,V_v_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__nat__number__of]) ).
fof(f_293_2,plain,
! [U_826,U_825] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_825),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_826))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_825,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_825,U_826) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_825,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_825,U_826)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_825),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_826)) ) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
( ! [U_830,U_828] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_828),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_830))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_828,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_828,U_830) ) )
& ! [U_829,U_827] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_827,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_827,U_829)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_827),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_829)) ) ),
inference(miniscope,[status(thm)],[f_293_2]) ).
cnf(f_293_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_827,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_827,U_829)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_827),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_829)) ),
inference(clausify,[status(thm)],[f_293_3]) ).
cnf(f_293_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_828,U_830)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_828),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_830)) ),
inference(clausify,[status(thm)],[f_293_3]) ).
cnf(f_293_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_828,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_828),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_830)) ),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_1,plain,
! [V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__irrefl]) ).
fof(f_294_2,plain,
! [U_832,U_831] :
( ~ c_Orderings_Oord__class_Oless(U_831,U_832,U_832)
| ~ class_Orderings_Opreorder(U_831) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_831,U_832,U_832)
| ~ class_Orderings_Opreorder(U_831) ),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 != V_y_2
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2 ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_295_2,plain,
! [U_835,U_834,U_833] :
( ( ( U_834 != U_835
| ( ~ c_Orderings_Oord__class_Oless(U_833,U_835,U_834)
& ~ c_Orderings_Oord__class_Oless(U_833,U_834,U_835) ) )
& ( c_Orderings_Oord__class_Oless(U_833,U_835,U_834)
| c_Orderings_Oord__class_Oless(U_833,U_834,U_835)
| U_834 = U_835 ) )
| ~ class_Orderings_Olinorder(U_833) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
( c_Orderings_Oord__class_Oless(U_833,U_835,U_834)
| c_Orderings_Oord__class_Oless(U_833,U_834,U_835)
| U_834 = U_835
| ~ class_Orderings_Olinorder(U_833) ),
inference(clausify,[status(thm)],[f_295_2]) ).
cnf(f_295_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_833,U_834,U_835)
| U_834 != U_835
| ~ class_Orderings_Olinorder(U_833) ),
inference(clausify,[status(thm)],[f_295_2]) ).
cnf(f_295_5,plain,
( ~ c_Orderings_Oord__class_Oless(U_833,U_835,U_834)
| U_834 != U_835
| ~ class_Orderings_Olinorder(U_833) ),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_296_2,plain,
! [U_838,U_837,U_836] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_836,U_837,U_838)
| ( U_837 != U_838
& ~ c_Orderings_Oord__class_Oless(U_836,U_838,U_837) ) )
& ( U_837 = U_838
| c_Orderings_Oord__class_Oless(U_836,U_838,U_837)
| c_Orderings_Oord__class_Oless(U_836,U_837,U_838) ) )
| ~ class_Orderings_Olinorder(U_836) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
( U_837 = U_838
| c_Orderings_Oord__class_Oless(U_836,U_838,U_837)
| c_Orderings_Oord__class_Oless(U_836,U_837,U_838)
| ~ class_Orderings_Olinorder(U_836) ),
inference(clausify,[status(thm)],[f_296_2]) ).
cnf(f_296_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_836,U_838,U_837)
| ~ c_Orderings_Oord__class_Oless(U_836,U_837,U_838)
| ~ class_Orderings_Olinorder(U_836) ),
inference(clausify,[status(thm)],[f_296_2]) ).
cnf(f_296_5,plain,
( U_837 != U_838
| ~ c_Orderings_Oord__class_Oless(U_836,U_837,U_838)
| ~ class_Orderings_Olinorder(U_836) ),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__less__linear]) ).
fof(f_297_2,plain,
! [U_841,U_840,U_839] :
( c_Orderings_Oord__class_Oless(U_839,U_841,U_840)
| U_840 = U_841
| c_Orderings_Oord__class_Oless(U_839,U_840,U_841)
| ~ class_Orderings_Olinorder(U_839) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
( c_Orderings_Oord__class_Oless(U_839,U_841,U_840)
| U_840 = U_841
| c_Orderings_Oord__class_Oless(U_839,U_840,U_841)
| ~ class_Orderings_Olinorder(U_839) ),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_298_2,plain,
! [U_844,U_843,U_842] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_842,U_844,U_843)
| U_844 != U_843 )
& ( U_844 = U_843
| c_Orderings_Oord__class_Oless(U_842,U_844,U_843) ) )
| c_Orderings_Oord__class_Oless(U_842,U_843,U_844)
| ~ class_Orderings_Olinorder(U_842) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
( U_844 = U_843
| c_Orderings_Oord__class_Oless(U_842,U_844,U_843)
| c_Orderings_Oord__class_Oless(U_842,U_843,U_844)
| ~ class_Orderings_Olinorder(U_842) ),
inference(clausify,[status(thm)],[f_298_2]) ).
cnf(f_298_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_842,U_844,U_843)
| U_844 != U_843
| c_Orderings_Oord__class_Oless(U_842,U_843,U_844)
| ~ class_Orderings_Olinorder(U_842) ),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE]) ).
fof(f_299_2,plain,
! [U_847,U_846,U_845] :
( c_Orderings_Oord__class_Oless(U_845,U_847,U_846)
| c_Orderings_Oord__class_Oless(U_845,U_846,U_847)
| U_846 = U_847
| ~ class_Orderings_Olinorder(U_845) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( c_Orderings_Oord__class_Oless(U_845,U_847,U_846)
| c_Orderings_Oord__class_Oless(U_845,U_846,U_847)
| U_846 = U_847
| ~ class_Orderings_Olinorder(U_845) ),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__neq]) ).
fof(f_300_2,plain,
! [U_850,U_849,U_848] :
( U_849 != U_850
| ~ c_Orderings_Oord__class_Oless(U_848,U_849,U_850)
| ~ class_Orderings_Oorder(U_848) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
cnf(f_300_3,plain,
( U_849 != U_850
| ~ c_Orderings_Oord__class_Oless(U_848,U_849,U_850)
| ~ class_Orderings_Oorder(U_848) ),
inference(clausify,[status(thm)],[f_300_2]) ).
fof(f_301_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__not__sym]) ).
fof(f_301_2,plain,
! [U_853,U_852,U_851] :
( ~ c_Orderings_Oord__class_Oless(U_851,U_853,U_852)
| ~ c_Orderings_Oord__class_Oless(U_851,U_852,U_853)
| ~ class_Orderings_Opreorder(U_851) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
cnf(f_301_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_851,U_853,U_852)
| ~ c_Orderings_Oord__class_Oless(U_851,U_852,U_853)
| ~ class_Orderings_Opreorder(U_851) ),
inference(clausify,[status(thm)],[f_301_2]) ).
fof(f_302_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(f_302_2,plain,
! [U_856,U_855,U_854] :
( ~ c_Orderings_Oord__class_Oless(U_854,U_856,U_855)
| ~ c_Orderings_Oord__class_Oless(U_854,U_855,U_856)
| ~ class_Orderings_Opreorder(U_854) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_854,U_856,U_855)
| ~ c_Orderings_Oord__class_Oless(U_854,U_855,U_856)
| ~ class_Orderings_Opreorder(U_854) ),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq]) ).
fof(f_303_2,plain,
! [U_859,U_858,U_857] :
( U_858 != U_859
| ~ c_Orderings_Oord__class_Oless(U_857,U_858,U_859)
| ~ class_Orderings_Oorder(U_857) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
( U_858 != U_859
| ~ c_Orderings_Oord__class_Oless(U_857,U_858,U_859)
| ~ class_Orderings_Oorder(U_857) ),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
! [V_y,V_x,T_a] :
( V_y != V_x
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2]) ).
fof(f_304_2,plain,
! [U_862,U_861,U_860] :
( U_862 != U_861
| ~ c_Orderings_Oord__class_Oless(U_860,U_861,U_862)
| ~ class_Orderings_Oorder(U_860) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
cnf(f_304_3,plain,
( U_862 != U_861
| ~ c_Orderings_Oord__class_Oless(U_860,U_861,U_862)
| ~ class_Orderings_Oorder(U_860) ),
inference(clausify,[status(thm)],[f_304_2]) ).
fof(f_305_1,plain,
! [V_b,V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__asym_H]) ).
fof(f_305_2,plain,
! [U_865,U_864,U_863] :
( ~ c_Orderings_Oord__class_Oless(U_863,U_865,U_864)
| ~ c_Orderings_Oord__class_Oless(U_863,U_864,U_865)
| ~ class_Orderings_Opreorder(U_863) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
cnf(f_305_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_863,U_865,U_864)
| ~ c_Orderings_Oord__class_Oless(U_863,U_864,U_865)
| ~ class_Orderings_Opreorder(U_863) ),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_1,plain,
! [V_a,V_b,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I9_J]) ).
fof(f_306_2,plain,
! [U_868,U_867,U_866] :
( ~ c_Orderings_Oord__class_Oless(U_866,U_868,U_867)
| ~ c_Orderings_Oord__class_Oless(U_866,U_867,U_868)
| ~ class_Orderings_Oorder(U_866) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_866,U_868,U_867)
| ~ c_Orderings_Oord__class_Oless(U_866,U_867,U_868)
| ~ class_Orderings_Oorder(U_866) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
| V_a != V_b
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__eq__less__trans]) ).
fof(f_307_2,plain,
! [U_872,U_871,U_870,U_869] :
( c_Orderings_Oord__class_Oless(U_869,U_870,U_872)
| ~ c_Orderings_Oord__class_Oless(U_869,U_871,U_872)
| U_870 != U_871
| ~ class_Orderings_Oord(U_869) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( c_Orderings_Oord__class_Oless(U_869,U_870,U_872)
| ~ c_Orderings_Oord__class_Oless(U_869,U_871,U_872)
| U_870 != U_871
| ~ class_Orderings_Oord(U_869) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
| V_a != V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I1_J]) ).
fof(f_308_2,plain,
! [U_876,U_875,U_874,U_873] :
( c_Orderings_Oord__class_Oless(U_873,U_876,U_874)
| ~ c_Orderings_Oord__class_Oless(U_873,U_876,U_875)
| U_874 != U_875
| ~ class_Orderings_Oorder(U_873) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
cnf(f_308_3,plain,
( c_Orderings_Oord__class_Oless(U_873,U_876,U_874)
| ~ c_Orderings_Oord__class_Oless(U_873,U_876,U_875)
| U_874 != U_875
| ~ class_Orderings_Oorder(U_873) ),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
| V_b != V_c
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__less__eq__trans]) ).
fof(f_309_2,plain,
! [U_880,U_879,U_878,U_877] :
( c_Orderings_Oord__class_Oless(U_877,U_878,U_880)
| U_879 != U_880
| ~ c_Orderings_Oord__class_Oless(U_877,U_878,U_879)
| ~ class_Orderings_Oord(U_877) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_3,plain,
( c_Orderings_Oord__class_Oless(U_877,U_878,U_880)
| U_879 != U_880
| ~ c_Orderings_Oord__class_Oless(U_877,U_878,U_879)
| ~ class_Orderings_Oord(U_877) ),
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| V_b != V_c
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I2_J]) ).
fof(f_310_2,plain,
! [U_884,U_883,U_882,U_881] :
( c_Orderings_Oord__class_Oless(U_881,U_884,U_883)
| U_882 != U_884
| ~ c_Orderings_Oord__class_Oless(U_881,U_882,U_883)
| ~ class_Orderings_Oorder(U_881) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
( c_Orderings_Oord__class_Oless(U_881,U_884,U_883)
| U_882 != U_884
| ~ c_Orderings_Oord__class_Oless(U_881,U_882,U_883)
| ~ class_Orderings_Oorder(U_881) ),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__trans]) ).
fof(f_311_2,plain,
! [U_888,U_887,U_886,U_885] :
( c_Orderings_Oord__class_Oless(U_885,U_886,U_888)
| ~ c_Orderings_Oord__class_Oless(U_885,U_887,U_888)
| ~ c_Orderings_Oord__class_Oless(U_885,U_886,U_887)
| ~ class_Orderings_Opreorder(U_885) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( c_Orderings_Oord__class_Oless(U_885,U_886,U_888)
| ~ c_Orderings_Oord__class_Oless(U_885,U_887,U_888)
| ~ c_Orderings_Oord__class_Oless(U_885,U_886,U_887)
| ~ class_Orderings_Opreorder(U_885) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I10_J]) ).
fof(f_312_2,plain,
! [U_892,U_891,U_890,U_889] :
( c_Orderings_Oord__class_Oless(U_889,U_892,U_891)
| ~ c_Orderings_Oord__class_Oless(U_889,U_892,U_890)
| ~ c_Orderings_Oord__class_Oless(U_889,U_890,U_891)
| ~ class_Orderings_Oorder(U_889) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
cnf(f_312_3,plain,
( c_Orderings_Oord__class_Oless(U_889,U_892,U_891)
| ~ c_Orderings_Oord__class_Oless(U_889,U_892,U_890)
| ~ c_Orderings_Oord__class_Oless(U_889,U_890,U_891)
| ~ class_Orderings_Oorder(U_889) ),
inference(clausify,[status(thm)],[f_312_2]) ).
fof(f_313_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__asym]) ).
fof(f_313_2,plain,
! [U_895,U_894,U_893] :
( ~ c_Orderings_Oord__class_Oless(U_893,U_895,U_894)
| ~ c_Orderings_Oord__class_Oless(U_893,U_894,U_895)
| ~ class_Orderings_Opreorder(U_893) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
cnf(f_313_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_893,U_895,U_894)
| ~ c_Orderings_Oord__class_Oless(U_893,U_894,U_895)
| ~ class_Orderings_Opreorder(U_893) ),
inference(clausify,[status(thm)],[f_313_2]) ).
fof(f_314_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__cases]) ).
fof(f_314_2,plain,
! [U_898,U_897,U_896] :
( c_Orderings_Oord__class_Oless(U_896,U_898,U_897)
| U_897 = U_898
| c_Orderings_Oord__class_Oless(U_896,U_897,U_898)
| ~ class_Orderings_Olinorder(U_896) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
cnf(f_314_3,plain,
( c_Orderings_Oord__class_Oless(U_896,U_898,U_897)
| U_897 = U_898
| c_Orderings_Oord__class_Oless(U_896,U_897,U_898)
| ~ class_Orderings_Olinorder(U_896) ),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2]) ).
fof(f_315_2,plain,
! [U_901,U_900,U_899] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_899,U_900),c_RealVector_Onorm__class_Onorm(U_899,U_901)),c_RealVector_Onorm__class_Onorm(U_899,c_Groups_Ominus__class_Ominus(U_899,U_900,U_901)))
| ~ class_RealVector_Oreal__normed__vector(U_899) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_899,U_900),c_RealVector_Onorm__class_Onorm(U_899,U_901)),c_RealVector_Onorm__class_Onorm(U_899,c_Groups_Ominus__class_Ominus(U_899,U_900,U_901)))
| ~ class_RealVector_Oreal__normed__vector(U_899) ),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))
| ~ class_Groups_Ominus(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).
fof(f_316_2,plain,
! [U_906,U_905,U_904,U_903,U_902] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_903,U_902),U_904,U_905),U_906) = c_Groups_Ominus__class_Ominus(U_902,hAPP(U_904,U_906),hAPP(U_905,U_906))
| ~ class_Groups_Ominus(U_902) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_903,U_902),U_904,U_905),U_906) = c_Groups_Ominus__class_Ominus(U_902,hAPP(U_904,U_906),hAPP(U_905,U_906))
| ~ class_Groups_Ominus(U_902) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__compl]) ).
fof(f_317_2,plain,
! [U_908,U_907] :
( c_Groups_Ouminus__class_Ouminus(U_907,c_Groups_Ouminus__class_Ouminus(U_907,U_908)) = U_908
| ~ class_Lattices_Oboolean__algebra(U_907) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
cnf(f_317_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_907,c_Groups_Ouminus__class_Ouminus(U_907,U_908)) = U_908
| ~ class_Lattices_Oboolean__algebra(U_907) ),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_1,plain,
! [V_x_2,V_A_2,T_b,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2))
| ~ class_Groups_Ouminus(T_a) ),
inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).
fof(f_318_2,plain,
! [U_912,U_911,U_910,U_909] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_910,U_909),U_911),U_912) = c_Groups_Ouminus__class_Ouminus(U_909,hAPP(U_911,U_912))
| ~ class_Groups_Ouminus(U_909) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
cnf(f_318_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_910,U_909),U_911),U_912) = c_Groups_Ouminus__class_Ouminus(U_909,hAPP(U_911,U_912))
| ~ class_Groups_Ouminus(U_909) ),
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) ) )
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).
fof(f_319_2,plain,
! [U_915,U_914,U_913] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_913,U_914) = c_Groups_Ouminus__class_Ouminus(U_913,U_915)
| U_914 != U_915 )
& ( U_914 = U_915
| c_Groups_Ouminus__class_Ouminus(U_913,U_914) != c_Groups_Ouminus__class_Ouminus(U_913,U_915) ) )
| ~ class_Lattices_Oboolean__algebra(U_913) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
cnf(f_319_3,plain,
( U_914 = U_915
| c_Groups_Ouminus__class_Ouminus(U_913,U_914) != c_Groups_Ouminus__class_Ouminus(U_913,U_915)
| ~ class_Lattices_Oboolean__algebra(U_913) ),
inference(clausify,[status(thm)],[f_319_2]) ).
cnf(f_319_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_913,U_914) = c_Groups_Ouminus__class_Ouminus(U_913,U_915)
| U_914 != U_915
| ~ class_Lattices_Oboolean__algebra(U_913) ),
inference(clausify,[status(thm)],[f_319_2]) ).
fof(f_320_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq3]) ).
fof(f_320_2,plain,
! [U_918,U_917,U_916] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_916,U_917),c_RealVector_Onorm__class_Onorm(U_916,U_918))),c_RealVector_Onorm__class_Onorm(U_916,c_Groups_Ominus__class_Ominus(U_916,U_917,U_918)))
| ~ class_RealVector_Oreal__normed__vector(U_916) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_916,U_917),c_RealVector_Onorm__class_Onorm(U_916,U_918))),c_RealVector_Onorm__class_Onorm(U_916,c_Groups_Ominus__class_Ominus(U_916,U_917,U_918)))
| ~ class_RealVector_Oreal__normed__vector(U_916) ),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_321_2,plain,
! [U_921,U_920,U_919] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_919,U_920,U_921)
| ~ c_Orderings_Oord__class_Oless__eq(U_919,U_921,U_920) )
& ( c_Orderings_Oord__class_Oless__eq(U_919,U_921,U_920)
| c_Orderings_Oord__class_Oless(U_919,U_920,U_921) ) )
| ~ class_Orderings_Olinorder(U_919) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_919,U_921,U_920)
| c_Orderings_Oord__class_Oless(U_919,U_920,U_921)
| ~ class_Orderings_Olinorder(U_919) ),
inference(clausify,[status(thm)],[f_321_2]) ).
cnf(f_321_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_919,U_920,U_921)
| ~ c_Orderings_Oord__class_Oless__eq(U_919,U_921,U_920)
| ~ class_Orderings_Olinorder(U_919) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_322_2,plain,
! [U_924,U_923,U_922] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_922,U_923,U_924)
| ~ c_Orderings_Oord__class_Oless(U_922,U_924,U_923) )
& ( c_Orderings_Oord__class_Oless(U_922,U_924,U_923)
| c_Orderings_Oord__class_Oless__eq(U_922,U_923,U_924) ) )
| ~ class_Orderings_Olinorder(U_922) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( c_Orderings_Oord__class_Oless(U_922,U_924,U_923)
| c_Orderings_Oord__class_Oless__eq(U_922,U_923,U_924)
| ~ class_Orderings_Olinorder(U_922) ),
inference(clausify,[status(thm)],[f_322_2]) ).
cnf(f_322_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_922,U_923,U_924)
| ~ c_Orderings_Oord__class_Oless(U_922,U_924,U_923)
| ~ class_Orderings_Olinorder(U_922) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear]) ).
fof(f_323_2,plain,
! [U_927,U_926,U_925] :
( c_Orderings_Oord__class_Oless(U_925,U_927,U_926)
| c_Orderings_Oord__class_Oless__eq(U_925,U_926,U_927)
| ~ class_Orderings_Olinorder(U_925) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_3,plain,
( c_Orderings_Oord__class_Oless(U_925,U_927,U_926)
| c_Orderings_Oord__class_Oless__eq(U_925,U_926,U_927)
| ~ class_Orderings_Olinorder(U_925) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_324_2,plain,
! [U_930,U_929,U_928] :
( ( ( c_Orderings_Oord__class_Oless(U_928,U_929,U_930)
| U_929 = U_930
| ~ c_Orderings_Oord__class_Oless__eq(U_928,U_929,U_930) )
& ( ( U_929 != U_930
& c_Orderings_Oord__class_Oless__eq(U_928,U_929,U_930) )
| ~ c_Orderings_Oord__class_Oless(U_928,U_929,U_930) ) )
| ~ class_Orderings_Oorder(U_928) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
cnf(f_324_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_928,U_929,U_930)
| ~ c_Orderings_Oord__class_Oless(U_928,U_929,U_930)
| ~ class_Orderings_Oorder(U_928) ),
inference(clausify,[status(thm)],[f_324_2]) ).
cnf(f_324_4,plain,
( U_929 != U_930
| ~ c_Orderings_Oord__class_Oless(U_928,U_929,U_930)
| ~ class_Orderings_Oorder(U_928) ),
inference(clausify,[status(thm)],[f_324_2]) ).
cnf(f_324_5,plain,
( c_Orderings_Oord__class_Oless(U_928,U_929,U_930)
| U_929 = U_930
| ~ c_Orderings_Oord__class_Oless__eq(U_928,U_929,U_930)
| ~ class_Orderings_Oorder(U_928) ),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_325_2,plain,
! [U_933,U_932,U_931] :
( ( ( c_Orderings_Oord__class_Oless(U_931,U_932,U_933)
| c_Orderings_Oord__class_Oless__eq(U_931,U_933,U_932)
| ~ c_Orderings_Oord__class_Oless__eq(U_931,U_932,U_933) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(U_931,U_933,U_932)
& c_Orderings_Oord__class_Oless__eq(U_931,U_932,U_933) )
| ~ c_Orderings_Oord__class_Oless(U_931,U_932,U_933) ) )
| ~ class_Orderings_Opreorder(U_931) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_931,U_932,U_933)
| ~ c_Orderings_Oord__class_Oless(U_931,U_932,U_933)
| ~ class_Orderings_Opreorder(U_931) ),
inference(clausify,[status(thm)],[f_325_2]) ).
cnf(f_325_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_931,U_933,U_932)
| ~ c_Orderings_Oord__class_Oless(U_931,U_932,U_933)
| ~ class_Orderings_Opreorder(U_931) ),
inference(clausify,[status(thm)],[f_325_2]) ).
cnf(f_325_5,plain,
( c_Orderings_Oord__class_Oless(U_931,U_932,U_933)
| c_Orderings_Oord__class_Oless__eq(U_931,U_933,U_932)
| ~ c_Orderings_Oord__class_Oless__eq(U_931,U_932,U_933)
| ~ class_Orderings_Opreorder(U_931) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_326_2,plain,
! [U_936,U_935,U_934] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_934,U_935,U_936)
| ( U_935 != U_936
& ~ c_Orderings_Oord__class_Oless(U_934,U_935,U_936) ) )
& ( U_935 = U_936
| c_Orderings_Oord__class_Oless(U_934,U_935,U_936)
| ~ c_Orderings_Oord__class_Oless__eq(U_934,U_935,U_936) ) )
| ~ class_Orderings_Oorder(U_934) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
cnf(f_326_3,plain,
( U_935 = U_936
| c_Orderings_Oord__class_Oless(U_934,U_935,U_936)
| ~ c_Orderings_Oord__class_Oless__eq(U_934,U_935,U_936)
| ~ class_Orderings_Oorder(U_934) ),
inference(clausify,[status(thm)],[f_326_2]) ).
cnf(f_326_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_934,U_935,U_936)
| c_Orderings_Oord__class_Oless__eq(U_934,U_935,U_936)
| ~ class_Orderings_Oorder(U_934) ),
inference(clausify,[status(thm)],[f_326_2]) ).
cnf(f_326_5,plain,
( U_935 != U_936
| c_Orderings_Oord__class_Oless__eq(U_934,U_935,U_936)
| ~ class_Orderings_Oorder(U_934) ),
inference(clausify,[status(thm)],[f_326_2]) ).
fof(f_327_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leI]) ).
fof(f_327_2,plain,
! [U_939,U_938,U_937] :
( c_Orderings_Oord__class_Oless__eq(U_937,U_939,U_938)
| c_Orderings_Oord__class_Oless(U_937,U_938,U_939)
| ~ class_Orderings_Olinorder(U_937) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_937,U_939,U_938)
| c_Orderings_Oord__class_Oless(U_937,U_938,U_939)
| ~ class_Orderings_Olinorder(U_937) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_1,plain,
! [V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__leE]) ).
fof(f_328_2,plain,
! [U_942,U_941,U_940] :
( c_Orderings_Oord__class_Oless(U_940,U_942,U_941)
| c_Orderings_Oord__class_Oless__eq(U_940,U_941,U_942)
| ~ class_Orderings_Olinorder(U_940) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( c_Orderings_Oord__class_Oless(U_940,U_942,U_941)
| c_Orderings_Oord__class_Oless__eq(U_940,U_941,U_942)
| ~ class_Orderings_Olinorder(U_940) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_329_2,plain,
! [U_945,U_944,U_943] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_943,U_944,U_945)
| U_944 != U_945 )
& ( U_944 = U_945
| ~ c_Orderings_Oord__class_Oless__eq(U_943,U_944,U_945) ) )
| c_Orderings_Oord__class_Oless(U_943,U_944,U_945)
| ~ class_Orderings_Olinorder(U_943) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
cnf(f_329_3,plain,
( U_944 = U_945
| ~ c_Orderings_Oord__class_Oless__eq(U_943,U_944,U_945)
| c_Orderings_Oord__class_Oless(U_943,U_944,U_945)
| ~ class_Orderings_Olinorder(U_943) ),
inference(clausify,[status(thm)],[f_329_2]) ).
cnf(f_329_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_943,U_944,U_945)
| U_944 != U_945
| c_Orderings_Oord__class_Oless(U_943,U_944,U_945)
| ~ class_Orderings_Olinorder(U_943) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| V_a = V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans]) ).
fof(f_330_2,plain,
! [U_948,U_947,U_946] :
( c_Orderings_Oord__class_Oless(U_946,U_947,U_948)
| ~ c_Orderings_Oord__class_Oless__eq(U_946,U_947,U_948)
| U_947 = U_948
| ~ class_Orderings_Oorder(U_946) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
cnf(f_330_3,plain,
( c_Orderings_Oord__class_Oless(U_946,U_947,U_948)
| ~ c_Orderings_Oord__class_Oless__eq(U_946,U_947,U_948)
| U_947 = U_948
| ~ class_Orderings_Oorder(U_946) ),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| V_a = V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I12_J]) ).
fof(f_331_2,plain,
! [U_951,U_950,U_949] :
( c_Orderings_Oord__class_Oless(U_949,U_951,U_950)
| ~ c_Orderings_Oord__class_Oless__eq(U_949,U_951,U_950)
| U_950 = U_951
| ~ class_Orderings_Oorder(U_949) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
( c_Orderings_Oord__class_Oless(U_949,U_951,U_950)
| ~ c_Orderings_Oord__class_Oless__eq(U_949,U_951,U_950)
| U_950 = U_951
| ~ class_Orderings_Oorder(U_949) ),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_1,plain,
! [V_x,V_y,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leD]) ).
fof(f_332_2,plain,
! [U_954,U_953,U_952] :
( ~ c_Orderings_Oord__class_Oless(U_952,U_954,U_953)
| ~ c_Orderings_Oord__class_Oless__eq(U_952,U_953,U_954)
| ~ class_Orderings_Olinorder(U_952) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
cnf(f_332_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_952,U_954,U_953)
| ~ c_Orderings_Oord__class_Oless__eq(U_952,U_953,U_954)
| ~ class_Orderings_Olinorder(U_952) ),
inference(clausify,[status(thm)],[f_332_2]) ).
fof(f_333_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__le]) ).
fof(f_333_2,plain,
! [U_957,U_956,U_955] :
( c_Orderings_Oord__class_Oless__eq(U_955,U_956,U_957)
| ~ c_Orderings_Oord__class_Oless(U_955,U_956,U_957)
| ~ class_Orderings_Opreorder(U_955) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_955,U_956,U_957)
| ~ c_Orderings_Oord__class_Oless(U_955,U_956,U_957)
| ~ class_Orderings_Opreorder(U_955) ),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_334_2,plain,
! [U_960,U_959,U_958] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_958,U_959,U_960)
| U_959 != U_960 )
& ( U_959 = U_960
| c_Orderings_Oord__class_Oless(U_958,U_959,U_960) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_958,U_959,U_960)
| ~ class_Orderings_Olinorder(U_958) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
cnf(f_334_3,plain,
( U_959 = U_960
| c_Orderings_Oord__class_Oless(U_958,U_959,U_960)
| ~ c_Orderings_Oord__class_Oless__eq(U_958,U_959,U_960)
| ~ class_Orderings_Olinorder(U_958) ),
inference(clausify,[status(thm)],[f_334_2]) ).
cnf(f_334_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_958,U_959,U_960)
| U_959 != U_960
| ~ c_Orderings_Oord__class_Oless__eq(U_958,U_959,U_960)
| ~ class_Orderings_Olinorder(U_958) ),
inference(clausify,[status(thm)],[f_334_2]) ).
fof(f_335_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq]) ).
fof(f_335_2,plain,
! [U_963,U_962,U_961] :
( U_962 = U_963
| c_Orderings_Oord__class_Oless(U_961,U_962,U_963)
| ~ c_Orderings_Oord__class_Oless__eq(U_961,U_962,U_963)
| ~ class_Orderings_Oorder(U_961) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
( U_962 = U_963
| c_Orderings_Oord__class_Oless(U_961,U_962,U_963)
| ~ c_Orderings_Oord__class_Oless__eq(U_961,U_962,U_963)
| ~ class_Orderings_Oorder(U_961) ),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| V_a = V_b
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans]) ).
fof(f_336_2,plain,
! [U_966,U_965,U_964] :
( c_Orderings_Oord__class_Oless(U_964,U_965,U_966)
| U_965 = U_966
| ~ c_Orderings_Oord__class_Oless__eq(U_964,U_965,U_966)
| ~ class_Orderings_Oorder(U_964) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
( c_Orderings_Oord__class_Oless(U_964,U_965,U_966)
| U_965 = U_966
| ~ c_Orderings_Oord__class_Oless__eq(U_964,U_965,U_966)
| ~ class_Orderings_Oorder(U_964) ),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_1,plain,
! [V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| V_a = V_b
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I11_J]) ).
fof(f_337_2,plain,
! [U_969,U_968,U_967] :
( c_Orderings_Oord__class_Oless(U_967,U_968,U_969)
| U_969 = U_968
| ~ c_Orderings_Oord__class_Oless__eq(U_967,U_968,U_969)
| ~ class_Orderings_Oorder(U_967) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
( c_Orderings_Oord__class_Oless(U_967,U_968,U_969)
| U_969 = U_968
| ~ c_Orderings_Oord__class_Oless__eq(U_967,U_968,U_969)
| ~ class_Orderings_Oorder(U_967) ),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le__trans]) ).
fof(f_338_2,plain,
! [U_973,U_972,U_971,U_970] :
( c_Orderings_Oord__class_Oless(U_970,U_971,U_973)
| ~ c_Orderings_Oord__class_Oless__eq(U_970,U_972,U_973)
| ~ c_Orderings_Oord__class_Oless(U_970,U_971,U_972)
| ~ class_Orderings_Opreorder(U_970) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
cnf(f_338_3,plain,
( c_Orderings_Oord__class_Oless(U_970,U_971,U_973)
| ~ c_Orderings_Oord__class_Oless__eq(U_970,U_972,U_973)
| ~ c_Orderings_Oord__class_Oless(U_970,U_971,U_972)
| ~ class_Orderings_Opreorder(U_970) ),
inference(clausify,[status(thm)],[f_338_2]) ).
fof(f_339_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I7_J]) ).
fof(f_339_2,plain,
! [U_977,U_976,U_975,U_974] :
( c_Orderings_Oord__class_Oless(U_974,U_977,U_976)
| ~ c_Orderings_Oord__class_Oless__eq(U_974,U_977,U_975)
| ~ c_Orderings_Oord__class_Oless(U_974,U_975,U_976)
| ~ class_Orderings_Oorder(U_974) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
cnf(f_339_3,plain,
( c_Orderings_Oord__class_Oless(U_974,U_977,U_976)
| ~ c_Orderings_Oord__class_Oless__eq(U_974,U_977,U_975)
| ~ c_Orderings_Oord__class_Oless(U_974,U_975,U_976)
| ~ class_Orderings_Oorder(U_974) ),
inference(clausify,[status(thm)],[f_339_2]) ).
fof(f_340_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less__trans]) ).
fof(f_340_2,plain,
! [U_981,U_980,U_979,U_978] :
( c_Orderings_Oord__class_Oless(U_978,U_979,U_981)
| ~ c_Orderings_Oord__class_Oless(U_978,U_980,U_981)
| ~ c_Orderings_Oord__class_Oless__eq(U_978,U_979,U_980)
| ~ class_Orderings_Opreorder(U_978) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
( c_Orderings_Oord__class_Oless(U_978,U_979,U_981)
| ~ c_Orderings_Oord__class_Oless(U_978,U_980,U_981)
| ~ c_Orderings_Oord__class_Oless__eq(U_978,U_979,U_980)
| ~ class_Orderings_Opreorder(U_978) ),
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I8_J]) ).
fof(f_341_2,plain,
! [U_985,U_984,U_983,U_982] :
( c_Orderings_Oord__class_Oless(U_982,U_985,U_984)
| ~ c_Orderings_Oord__class_Oless(U_982,U_985,U_983)
| ~ c_Orderings_Oord__class_Oless__eq(U_982,U_983,U_984)
| ~ class_Orderings_Oorder(U_982) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( c_Orderings_Oord__class_Oless(U_982,U_985,U_984)
| ~ c_Orderings_Oord__class_Oless(U_982,U_985,U_983)
| ~ c_Orderings_Oord__class_Oless__eq(U_982,U_983,U_984)
| ~ class_Orderings_Oorder(U_982) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) ) )
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).
fof(f_342_2,plain,
! [U_988,U_987,U_986] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_986,c_Groups_Ouminus__class_Ouminus(U_986,U_987),c_Groups_Ouminus__class_Ouminus(U_986,U_988))
| ~ c_Orderings_Oord__class_Oless__eq(U_986,U_988,U_987) )
& ( c_Orderings_Oord__class_Oless__eq(U_986,U_988,U_987)
| ~ c_Orderings_Oord__class_Oless__eq(U_986,c_Groups_Ouminus__class_Ouminus(U_986,U_987),c_Groups_Ouminus__class_Ouminus(U_986,U_988)) ) )
| ~ class_Lattices_Oboolean__algebra(U_986) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_986,U_988,U_987)
| ~ c_Orderings_Oord__class_Oless__eq(U_986,c_Groups_Ouminus__class_Ouminus(U_986,U_987),c_Groups_Ouminus__class_Ouminus(U_986,U_988))
| ~ class_Lattices_Oboolean__algebra(U_986) ),
inference(clausify,[status(thm)],[f_342_2]) ).
cnf(f_342_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_986,c_Groups_Ouminus__class_Ouminus(U_986,U_987),c_Groups_Ouminus__class_Ouminus(U_986,U_988))
| ~ c_Orderings_Oord__class_Oless__eq(U_986,U_988,U_987)
| ~ class_Lattices_Oboolean__algebra(U_986) ),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).
cnf(f_343_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_343_1]) ).
fof(f_344_1,plain,
! [V_n] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_n)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_n))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n)) ),
inference(fof_nnf,[status(thm)],[fact_number__of1]) ).
fof(f_344_2,plain,
! [U_989] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(U_989)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(U_989))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_989)) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(U_989)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_989)) ),
inference(clausify,[status(thm)],[f_344_2]) ).
cnf(f_344_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(U_989)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_989)) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).
cnf(f_345_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_345_1]) ).
fof(f_346_1,plain,
! [V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_z)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z),v_r) ),
inference(fof_nnf,[status(thm)],[fact_s1m]) ).
fof(f_346_2,plain,
! [U_990] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_990)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_990),v_r) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_990)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_990),v_r) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_number__of2]) ).
cnf(f_347_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(clausify,[status(thm)],[f_347_1]) ).
fof(f_348_1,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r) ),
inference(fof_nnf,[status(thm)],[fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096]) ).
cnf(f_348_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r),
inference(clausify,[status(thm)],[f_348_1]) ).
cnf(f_348_3,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
inference(clausify,[status(thm)],[f_348_1]) ).
fof(f_349_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
inference(fof_nnf,[status(thm)],[fact_wr]) ).
cnf(f_349_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
inference(clausify,[status(thm)],[f_349_1]) ).
fof(f_350_1,plain,
! [B_y] :
( ( ? [B_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
& ? [B_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,v_s____) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,v_s____)
| ! [B_x] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
| ! [B_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ) ),
inference(fof_nnf,[status(thm)],[fact_s]) ).
fof(f_350_2,plain,
! [U_995] :
( ( ? [U_994] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_995,U_994)
& ? [U_993] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_993)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_994)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_993),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_995,v_s____) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_995,v_s____)
| ! [U_992] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_995,U_992)
| ! [U_991] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_991)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_991),v_r) ) ) ) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
( ! [U_997] :
( ? [U_994] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,U_994)
& ? [U_993] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_993)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_994)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_993),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,v_s____) )
& ! [U_996] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_996,v_s____)
| ! [U_992] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_996,U_992)
| ! [U_991] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_991)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_991),v_r) ) ) ) ),
inference(miniscope,[status(thm)],[f_350_2]) ).
fof(f_350_4,plain,
( ! [U_997] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,sK10(U_997))
& ? [U_993] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_993)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK10(U_997))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_993),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,v_s____) )
& ! [U_996] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_996,v_s____)
| ! [U_992] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_996,U_992)
| ! [U_991] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_991)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_991),v_r) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_994,sK10(U_997))],[f_350_3]) ).
fof(f_350_5,plain,
( ! [U_997] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,sK10(U_997))
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK11(U_997))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK10(U_997))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK11(U_997)),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,v_s____) )
& ! [U_996] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_996,v_s____)
| ! [U_992] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_996,U_992)
| ! [U_991] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_991)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_991),v_r) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_993,sK11(U_997))],[f_350_4]) ).
cnf(f_350_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_996,v_s____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_996,U_992)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_991)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_991),v_r) ),
inference(clausify,[status(thm)],[f_350_5]) ).
cnf(f_350_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK11(U_997)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,v_s____) ),
inference(clausify,[status(thm)],[f_350_5]) ).
cnf(f_350_8,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK11(U_997))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK10(U_997))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,v_s____) ),
inference(clausify,[status(thm)],[f_350_5]) ).
cnf(f_350_9,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,sK10(U_997))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_997,v_s____) ),
inference(clausify,[status(thm)],[f_350_5]) ).
fof(f_351_1,plain,
! [V_ga_2,V_fa_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
| c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2,V_fa_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2,V_fa_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_ga_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_351_2,plain,
! [U_1001,U_1000,U_999,U_998] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_999,U_998),U_1000,U_1001)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_999,U_998),U_1001,U_1000)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_999,U_998),U_1000,U_1001) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_999,U_998),U_1001,U_1000)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_999,U_998),U_1000,U_1001) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_999,U_998),U_1000,U_1001) ) )
| ~ class_Orderings_Oord(U_998) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
cnf(f_351_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_999,U_998),U_1000,U_1001)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_999,U_998),U_1000,U_1001)
| ~ class_Orderings_Oord(U_998) ),
inference(clausify,[status(thm)],[f_351_2]) ).
cnf(f_351_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_999,U_998),U_1001,U_1000)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_999,U_998),U_1000,U_1001)
| ~ class_Orderings_Oord(U_998) ),
inference(clausify,[status(thm)],[f_351_2]) ).
cnf(f_351_5,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_999,U_998),U_1000,U_1001)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_999,U_998),U_1001,U_1000)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_999,U_998),U_1000,U_1001)
| ~ class_Orderings_Oord(U_998) ),
inference(clausify,[status(thm)],[f_351_2]) ).
fof(f_352_1,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_real__le__antisym]) ).
fof(f_352_2,plain,
! [U_1003,U_1002] :
( U_1002 = U_1003
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1003,U_1002)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1002,U_1003) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,plain,
( U_1002 = U_1003
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1003,U_1002)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1002,U_1003) ),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_real__le__trans]) ).
fof(f_353_2,plain,
! [U_1006,U_1005,U_1004] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1004,U_1006)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1005,U_1006)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1004,U_1005) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1004,U_1006)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1005,U_1006)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1004,U_1005) ),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_1,plain,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_real__le__linear]) ).
fof(f_354_2,plain,
! [U_1008,U_1007] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1008,U_1007)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1007,U_1008) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1008,U_1007)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1007,U_1008) ),
inference(clausify,[status(thm)],[f_354_2]) ).
fof(f_355_1,plain,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
inference(fof_nnf,[status(thm)],[fact_real__le__refl]) ).
fof(f_355_2,plain,
! [U_1009] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1009,U_1009),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1009,U_1009),
inference(clausify,[status(thm)],[f_355_2]) ).
fof(f_356_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).
cnf(f_356_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_356_1]) ).
fof(f_357_1,plain,
( ( ? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ! [B_z] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ),
inference(fof_nnf,[status(thm)],[fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096]) ).
fof(f_357_2,plain,
( ( ? [U_1011] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1011)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1011),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ! [U_1010] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1010)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1010),v_r) ) ) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK12)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK12),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ! [U_1010] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1010)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1010),v_r) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_1011,sK12)],[f_357_2]) ).
cnf(f_357_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1010)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1010),v_r) ),
inference(clausify,[status(thm)],[f_357_3]) ).
cnf(f_357_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK12),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
inference(clausify,[status(thm)],[f_357_3]) ).
cnf(f_357_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK12)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_1,plain,
! [V_y_2] :
( ( ? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),V_y_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2)
| ! [B_z] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ),
inference(fof_nnf,[status(thm)],[fact_s1]) ).
fof(f_358_2,plain,
! [U_1014] :
( ( ? [U_1013] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1013)),U_1014)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1013),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1014) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1014)
| ! [U_1012] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1012)),U_1014)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1012),v_r) ) ) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
( ! [U_1016] :
( ? [U_1013] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1013)),U_1016)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1013),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1016) )
& ! [U_1015] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1015)
| ! [U_1012] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1012)),U_1015)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1012),v_r) ) ) ),
inference(miniscope,[status(thm)],[f_358_2]) ).
fof(f_358_4,plain,
( ! [U_1016] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK13(U_1016))),U_1016)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK13(U_1016)),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1016) )
& ! [U_1015] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1015)
| ! [U_1012] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1012)),U_1015)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1012),v_r) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_1013,sK13(U_1016))],[f_358_3]) ).
cnf(f_358_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1015)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1012)),U_1015)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1012),v_r) ),
inference(clausify,[status(thm)],[f_358_4]) ).
cnf(f_358_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK13(U_1016)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1016) ),
inference(clausify,[status(thm)],[f_358_4]) ).
cnf(f_358_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK13(U_1016))),U_1016)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1016) ),
inference(clausify,[status(thm)],[f_358_4]) ).
fof(f_359_1,plain,
! [V_y_2] :
( ( ? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)))),V_y_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2)
| ! [B_z] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)))),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ),
inference(fof_nnf,[status(thm)],[fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096]) ).
fof(f_359_2,plain,
! [U_1019] :
( ( ? [U_1018] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1018)))),U_1019)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1018),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1019) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1019)
| ! [U_1017] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1017)))),U_1019)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1017),v_r) ) ) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
( ! [U_1021] :
( ? [U_1018] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1018)))),U_1021)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1018),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1021) )
& ! [U_1020] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1020)
| ! [U_1017] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1017)))),U_1020)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1017),v_r) ) ) ),
inference(miniscope,[status(thm)],[f_359_2]) ).
fof(f_359_4,plain,
( ! [U_1021] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK14(U_1021))))),U_1021)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK14(U_1021)),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1021) )
& ! [U_1020] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1020)
| ! [U_1017] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1017)))),U_1020)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1017),v_r) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_1018,sK14(U_1021))],[f_359_3]) ).
cnf(f_359_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1020)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1017)))),U_1020)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1017),v_r) ),
inference(clausify,[status(thm)],[f_359_4]) ).
cnf(f_359_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK14(U_1021)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1021) ),
inference(clausify,[status(thm)],[f_359_4]) ).
cnf(f_359_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK14(U_1021))))),U_1021)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),U_1021) ),
inference(clausify,[status(thm)],[f_359_4]) ).
fof(f_360_1,plain,
? [B_z] :
! [B_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_z)
| ! [B_za] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_za)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_za),v_r) ) ),
inference(fof_nnf,[status(thm)],[fact_mth2]) ).
fof(f_360_2,plain,
? [U_1024] :
! [U_1023] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1023,U_1024)
| ! [U_1022] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1022)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1023)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1022),v_r) ) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_1023] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1023,sK15)
| ! [U_1022] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1022)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1023)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1022),v_r) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_1024,sK15)],[f_360_2]) ).
cnf(f_360_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1023,sK15)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1022)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1023)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1022),v_r) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
( ? [B_z] :
! [B_w] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_w)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_w),v_r) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
inference(fof_nnf,[status(thm)],[fact_calculation]) ).
fof(f_361_2,plain,
( ? [U_1026] :
! [U_1025] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1026)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1025)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1025),v_r) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
( ! [U_1025] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK16)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1025)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1025),v_r) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_1026,sK16)],[f_361_2]) ).
cnf(f_361_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK16)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1025)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1025),v_r)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [V_x_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_z_2)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r) ),
inference(fof_nnf,[status(thm)],[fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096]) ).
fof(f_362_2,plain,
! [U_1028,U_1027] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1028,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1027)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1028)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1027),v_r) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
cnf(f_362_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1028,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1027)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1028)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1027),v_r) ),
inference(clausify,[status(thm)],[f_362_2]) ).
fof(f_363_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),
inference(fof_nnf,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(f_363_2,plain,
! [U_1029] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1029)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1029)),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1029)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1029)),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_1,plain,
? [B_s] :
! [B_y] :
( ( ? [B_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
& ? [B_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s)
| ! [B_x] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
| ! [B_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ) ),
inference(fof_nnf,[status(thm)],[fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096]) ).
fof(f_364_2,plain,
? [U_1035] :
! [U_1034] :
( ( ? [U_1033] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1034,U_1033)
& ? [U_1032] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1032)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1033)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1032),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1034,U_1035) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1034,U_1035)
| ! [U_1031] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1034,U_1031)
| ! [U_1030] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1030)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1031)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1030),v_r) ) ) ) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
? [U_1035] :
( ! [U_1037] :
( ? [U_1033] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,U_1033)
& ? [U_1032] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1032)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1033)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1032),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,U_1035) )
& ! [U_1036] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,U_1035)
| ! [U_1031] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,U_1031)
| ! [U_1030] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1030)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1031)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1030),v_r) ) ) ) ),
inference(miniscope,[status(thm)],[f_364_2]) ).
fof(f_364_4,plain,
( ! [U_1037] :
( ? [U_1033] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,U_1033)
& ? [U_1032] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1032)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1033)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1032),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK17) )
& ! [U_1036] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,sK17)
| ! [U_1031] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,U_1031)
| ! [U_1030] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1030)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1031)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1030),v_r) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_1035,sK17)],[f_364_3]) ).
fof(f_364_5,plain,
( ! [U_1037] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK18(U_1037))
& ? [U_1032] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1032)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK18(U_1037))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1032),v_r) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK17) )
& ! [U_1036] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,sK17)
| ! [U_1031] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,U_1031)
| ! [U_1030] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1030)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1031)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1030),v_r) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_1033,sK18(U_1037))],[f_364_4]) ).
fof(f_364_6,plain,
( ! [U_1037] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK18(U_1037))
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19(U_1037))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK18(U_1037))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK19(U_1037)),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK17) )
& ! [U_1036] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,sK17)
| ! [U_1031] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,U_1031)
| ! [U_1030] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1030)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1031)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1030),v_r) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1032,sK19(U_1037))],[f_364_5]) ).
cnf(f_364_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,sK17)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1036,U_1031)
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1030)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1031)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1030),v_r) ),
inference(clausify,[status(thm)],[f_364_6]) ).
cnf(f_364_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK19(U_1037)),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK17) ),
inference(clausify,[status(thm)],[f_364_6]) ).
cnf(f_364_9,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19(U_1037))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK18(U_1037))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK17) ),
inference(clausify,[status(thm)],[f_364_6]) ).
cnf(f_364_10,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK18(U_1037))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1037,sK17) ),
inference(clausify,[status(thm)],[f_364_6]) ).
fof(f_365_1,plain,
? [B_x,B_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
inference(fof_nnf,[status(thm)],[fact_mth1]) ).
fof(f_365_2,plain,
? [U_1039,U_1038] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1038)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1039)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1038),v_r) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
? [U_1038] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1038)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK20)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1038),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1039,sK20)],[f_365_2]) ).
fof(f_365_4,plain,
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK20)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK21),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_1038,sK21)],[f_365_3]) ).
cnf(f_365_5,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK21),v_r),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_6,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK21)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,sK20),
inference(clausify,[status(thm)],[f_365_4]) ).
fof(f_366_1,plain,
! [V_x,V_y] :
( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) )
& ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ) ),
inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).
fof(f_366_2,plain,
! [U_1041,U_1040] :
( ( c_Nat__Transfer_Otsub(U_1041,U_1040) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1040,U_1041) )
& ( c_Nat__Transfer_Otsub(U_1041,U_1040) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1041,U_1040)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1040,U_1041) ) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
( ! [U_1045,U_1043] :
( c_Nat__Transfer_Otsub(U_1045,U_1043) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1043,U_1045) )
& ! [U_1044,U_1042] :
( c_Nat__Transfer_Otsub(U_1044,U_1042) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1044,U_1042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1042,U_1044) ) ),
inference(miniscope,[status(thm)],[f_366_2]) ).
cnf(f_366_4,plain,
( c_Nat__Transfer_Otsub(U_1044,U_1042) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1044,U_1042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1042,U_1044) ),
inference(clausify,[status(thm)],[f_366_3]) ).
cnf(f_366_5,plain,
( c_Nat__Transfer_Otsub(U_1045,U_1043) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1043,U_1045) ),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Oone__class_Oone(T_a) = V_x_2
| V_x_2 != c_Groups_Oone__class_Oone(T_a) )
& ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
| c_Groups_Oone__class_Oone(T_a) != V_x_2 ) )
| ~ class_Groups_Oone(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).
fof(f_367_2,plain,
! [U_1047,U_1046] :
( ( ( c_Groups_Oone__class_Oone(U_1046) = U_1047
| U_1047 != c_Groups_Oone__class_Oone(U_1046) )
& ( U_1047 = c_Groups_Oone__class_Oone(U_1046)
| c_Groups_Oone__class_Oone(U_1046) != U_1047 ) )
| ~ class_Groups_Oone(U_1046) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
cnf(f_367_3,plain,
( U_1047 = c_Groups_Oone__class_Oone(U_1046)
| c_Groups_Oone__class_Oone(U_1046) != U_1047
| ~ class_Groups_Oone(U_1046) ),
inference(clausify,[status(thm)],[f_367_2]) ).
cnf(f_367_4,plain,
( c_Groups_Oone__class_Oone(U_1046) = U_1047
| U_1047 != c_Groups_Oone__class_Oone(U_1046)
| ~ class_Groups_Oone(U_1046) ),
inference(clausify,[status(thm)],[f_367_2]) ).
fof(f_368_1,plain,
! [T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__one]) ).
fof(f_368_2,plain,
! [U_1048] :
( c_RealVector_Onorm__class_Onorm(U_1048,c_Groups_Oone__class_Oone(U_1048)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1048) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
cnf(f_368_3,plain,
( c_RealVector_Onorm__class_Onorm(U_1048,c_Groups_Oone__class_Oone(U_1048)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1048) ),
inference(clausify,[status(thm)],[f_368_2]) ).
fof(f_369_1,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__1]) ).
fof(f_369_2,plain,
! [U_1050,U_1049] :
( hAPP(c_Polynomial_Opoly(U_1049,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1049))),U_1050) = c_Groups_Oone__class_Oone(U_1049)
| ~ class_Rings_Ocomm__semiring__1(U_1049) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
( hAPP(c_Polynomial_Opoly(U_1049,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1049))),U_1050) = c_Groups_Oone__class_Oone(U_1049)
| ~ class_Rings_Ocomm__semiring__1(U_1049) ),
inference(clausify,[status(thm)],[f_369_2]) ).
fof(f_370_1,plain,
! [T_a] :
( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__neq__one]) ).
fof(f_370_2,plain,
! [U_1051] :
( c_Groups_Ozero__class_Ozero(U_1051) != c_Groups_Oone__class_Oone(U_1051)
| ~ class_Rings_Ozero__neq__one(U_1051) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
( c_Groups_Ozero__class_Ozero(U_1051) != c_Groups_Oone__class_Oone(U_1051)
| ~ class_Rings_Ozero__neq__one(U_1051) ),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_1,plain,
! [T_a] :
( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ozero__neq__one(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__neq__zero]) ).
fof(f_371_2,plain,
! [U_1052] :
( c_Groups_Oone__class_Oone(U_1052) != c_Groups_Ozero__class_Ozero(U_1052)
| ~ class_Rings_Ozero__neq__one(U_1052) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
( c_Groups_Oone__class_Oone(U_1052) != c_Groups_Ozero__class_Ozero(U_1052)
| ~ class_Rings_Ozero__neq__one(U_1052) ),
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__1]) ).
fof(f_372_2,plain,
! [U_1054,U_1053] :
( c_Rings_Oinverse__class_Odivide(U_1053,U_1054,c_Groups_Oone__class_Oone(U_1053)) = U_1054
| ~ class_Rings_Odivision__ring(U_1053) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1053,U_1054,c_Groups_Oone__class_Oone(U_1053)) = U_1054
| ~ class_Rings_Odivision__ring(U_1053) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_1,plain,
! [T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__one]) ).
fof(f_373_2,plain,
! [U_1055] :
( c_Groups_Oabs__class_Oabs(U_1055,c_Groups_Oone__class_Oone(U_1055)) = c_Groups_Oone__class_Oone(U_1055)
| ~ class_Rings_Olinordered__idom(U_1055) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
cnf(f_373_3,plain,
( c_Groups_Oabs__class_Oabs(U_1055,c_Groups_Oone__class_Oone(U_1055)) = c_Groups_Oone__class_Oone(U_1055)
| ~ class_Rings_Olinordered__idom(U_1055) ),
inference(clausify,[status(thm)],[f_373_2]) ).
fof(f_374_1,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__zero__not__eq__one]) ).
cnf(f_374_2,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_374_1]) ).
fof(f_375_1,plain,
! [T_a] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__one__le__zero]) ).
fof(f_375_2,plain,
! [U_1056] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1056,c_Groups_Oone__class_Oone(U_1056),c_Groups_Ozero__class_Ozero(U_1056))
| ~ class_Rings_Olinordered__semidom(U_1056) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
cnf(f_375_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1056,c_Groups_Oone__class_Oone(U_1056),c_Groups_Ozero__class_Ozero(U_1056))
| ~ class_Rings_Olinordered__semidom(U_1056) ),
inference(clausify,[status(thm)],[f_375_2]) ).
fof(f_376_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__one]) ).
fof(f_376_2,plain,
! [U_1057] :
( c_Orderings_Oord__class_Oless__eq(U_1057,c_Groups_Ozero__class_Ozero(U_1057),c_Groups_Oone__class_Oone(U_1057))
| ~ class_Rings_Olinordered__semidom(U_1057) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
cnf(f_376_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1057,c_Groups_Ozero__class_Ozero(U_1057),c_Groups_Oone__class_Oone(U_1057))
| ~ class_Rings_Olinordered__semidom(U_1057) ),
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__one]) ).
fof(f_377_2,plain,
! [U_1058] :
( c_Orderings_Oord__class_Oless(U_1058,c_Groups_Ozero__class_Ozero(U_1058),c_Groups_Oone__class_Oone(U_1058))
| ~ class_Rings_Olinordered__semidom(U_1058) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
cnf(f_377_3,plain,
( c_Orderings_Oord__class_Oless(U_1058,c_Groups_Ozero__class_Ozero(U_1058),c_Groups_Oone__class_Oone(U_1058))
| ~ class_Rings_Olinordered__semidom(U_1058) ),
inference(clausify,[status(thm)],[f_377_2]) ).
fof(f_378_1,plain,
! [T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__one__less__zero]) ).
fof(f_378_2,plain,
! [U_1059] :
( ~ c_Orderings_Oord__class_Oless(U_1059,c_Groups_Oone__class_Oone(U_1059),c_Groups_Ozero__class_Ozero(U_1059))
| ~ class_Rings_Olinordered__semidom(U_1059) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
cnf(f_378_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1059,c_Groups_Oone__class_Oone(U_1059),c_Groups_Ozero__class_Ozero(U_1059))
| ~ class_Rings_Olinordered__semidom(U_1059) ),
inference(clausify,[status(thm)],[f_378_2]) ).
fof(f_379_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) != c_Groups_Oone__class_Oone(T_a) ) )
| V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).
fof(f_379_2,plain,
! [U_1062,U_1061,U_1060] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1060,U_1062,U_1061) = c_Groups_Oone__class_Oone(U_1060)
| U_1062 != U_1061 )
& ( U_1062 = U_1061
| c_Rings_Oinverse__class_Odivide(U_1060,U_1062,U_1061) != c_Groups_Oone__class_Oone(U_1060) ) )
| U_1061 = c_Groups_Ozero__class_Ozero(U_1060)
| ~ class_Rings_Odivision__ring(U_1060) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
cnf(f_379_3,plain,
( U_1062 = U_1061
| c_Rings_Oinverse__class_Odivide(U_1060,U_1062,U_1061) != c_Groups_Oone__class_Oone(U_1060)
| U_1061 = c_Groups_Ozero__class_Ozero(U_1060)
| ~ class_Rings_Odivision__ring(U_1060) ),
inference(clausify,[status(thm)],[f_379_2]) ).
cnf(f_379_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1060,U_1062,U_1061) = c_Groups_Oone__class_Oone(U_1060)
| U_1062 != U_1061
| U_1061 = c_Groups_Ozero__class_Ozero(U_1060)
| ~ class_Rings_Odivision__ring(U_1060) ),
inference(clausify,[status(thm)],[f_379_2]) ).
fof(f_380_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__self]) ).
fof(f_380_2,plain,
! [U_1064,U_1063] :
( c_Rings_Oinverse__class_Odivide(U_1063,U_1064,U_1064) = c_Groups_Oone__class_Oone(U_1063)
| U_1064 = c_Groups_Ozero__class_Ozero(U_1063)
| ~ class_Rings_Odivision__ring(U_1063) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
cnf(f_380_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1063,U_1064,U_1064) = c_Groups_Oone__class_Oone(U_1063)
| U_1064 = c_Groups_Ozero__class_Ozero(U_1063)
| ~ class_Rings_Odivision__ring(U_1063) ),
inference(clausify,[status(thm)],[f_380_2]) ).
fof(f_381_1,plain,
! [V_a,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
| V_a != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__self__if]) ).
fof(f_381_2,plain,
! [U_1066,U_1065] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1065,U_1066,U_1066) = c_Groups_Oone__class_Oone(U_1065)
| U_1066 = c_Groups_Ozero__class_Ozero(U_1065) )
& ( c_Rings_Oinverse__class_Odivide(U_1065,U_1066,U_1066) = c_Groups_Ozero__class_Ozero(U_1065)
| U_1066 != c_Groups_Ozero__class_Ozero(U_1065) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_1065) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1065,U_1066,U_1066) = c_Groups_Ozero__class_Ozero(U_1065)
| U_1066 != c_Groups_Ozero__class_Ozero(U_1065)
| ~ class_Rings_Odivision__ring__inverse__zero(U_1065) ),
inference(clausify,[status(thm)],[f_381_2]) ).
cnf(f_381_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1065,U_1066,U_1066) = c_Groups_Oone__class_Oone(U_1065)
| U_1066 = c_Groups_Ozero__class_Ozero(U_1065)
| ~ class_Rings_Odivision__ring__inverse__zero(U_1065) ),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_1,plain,
! [T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1]) ).
fof(f_382_2,plain,
! [U_1067] :
( c_Int_Onumber__class_Onumber__of(U_1067,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_1067)
| ~ class_Int_Onumber__ring(U_1067) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1067,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_1067)
| ~ class_Int_Onumber__ring(U_1067) ),
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_1,plain,
! [T_a] :
( c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J]) ).
fof(f_383_2,plain,
! [U_1068] :
( c_Groups_Oone__class_Oone(U_1068) = c_Int_Onumber__class_Onumber__of(U_1068,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_1068) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
cnf(f_383_3,plain,
( c_Groups_Oone__class_Oone(U_1068) = c_Int_Onumber__class_Onumber__of(U_1068,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_1068) ),
inference(clausify,[status(thm)],[f_383_2]) ).
fof(f_384_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).
fof(f_384_2,plain,
! [U_1070,U_1069] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_1069,U_1070))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1070)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1069) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
cnf(f_384_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_1069,U_1070))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1070)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1069) ),
inference(clausify,[status(thm)],[f_384_2]) ).
fof(f_385_1,plain,
! [V_x,V_y] :
( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ),
inference(fof_nnf,[status(thm)],[fact_tsub__eq]) ).
fof(f_385_2,plain,
! [U_1072,U_1071] :
( c_Nat__Transfer_Otsub(U_1072,U_1071) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1072,U_1071)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1071,U_1072) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
cnf(f_385_3,plain,
( c_Nat__Transfer_Otsub(U_1072,U_1071) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1072,U_1071)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1071,U_1072) ),
inference(clausify,[status(thm)],[f_385_2]) ).
fof(f_386_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I4_J]) ).
fof(f_386_2,plain,
! [U_1074,U_1073] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1073,c_Int_Onumber__class_Onumber__of(U_1073,U_1074),c_Groups_Oone__class_Oone(U_1073))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1074,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1074,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(U_1073,c_Int_Onumber__class_Onumber__of(U_1073,U_1074),c_Groups_Oone__class_Oone(U_1073)) ) )
| ~ class_Rings_Olinordered__idom(U_1073)
| ~ class_Int_Onumber__ring(U_1073) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
cnf(f_386_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1074,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(U_1073,c_Int_Onumber__class_Onumber__of(U_1073,U_1074),c_Groups_Oone__class_Oone(U_1073))
| ~ class_Rings_Olinordered__idom(U_1073)
| ~ class_Int_Onumber__ring(U_1073) ),
inference(clausify,[status(thm)],[f_386_2]) ).
cnf(f_386_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1073,c_Int_Onumber__class_Onumber__of(U_1073,U_1074),c_Groups_Oone__class_Oone(U_1073))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1074,c_Int_OBit1(c_Int_OPls))
| ~ class_Rings_Olinordered__idom(U_1073)
| ~ class_Int_Onumber__ring(U_1073) ),
inference(clausify,[status(thm)],[f_386_2]) ).
fof(f_387_1,plain,
! [V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I2_J]) ).
fof(f_387_2,plain,
! [U_1076,U_1075] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1075,c_Groups_Oone__class_Oone(U_1075),c_Int_Onumber__class_Onumber__of(U_1075,U_1076))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1076) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1076)
| ~ c_Orderings_Oord__class_Oless__eq(U_1075,c_Groups_Oone__class_Oone(U_1075),c_Int_Onumber__class_Onumber__of(U_1075,U_1076)) ) )
| ~ class_Rings_Olinordered__idom(U_1075)
| ~ class_Int_Onumber__ring(U_1075) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
cnf(f_387_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1076)
| ~ c_Orderings_Oord__class_Oless__eq(U_1075,c_Groups_Oone__class_Oone(U_1075),c_Int_Onumber__class_Onumber__of(U_1075,U_1076))
| ~ class_Rings_Olinordered__idom(U_1075)
| ~ class_Int_Onumber__ring(U_1075) ),
inference(clausify,[status(thm)],[f_387_2]) ).
cnf(f_387_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1075,c_Groups_Oone__class_Oone(U_1075),c_Int_Onumber__class_Onumber__of(U_1075,U_1076))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1076)
| ~ class_Rings_Olinordered__idom(U_1075)
| ~ class_Int_Onumber__ring(U_1075) ),
inference(clausify,[status(thm)],[f_387_2]) ).
fof(f_388_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I4_J]) ).
fof(f_388_2,plain,
! [U_1078,U_1077] :
( ( ( c_Orderings_Oord__class_Oless(U_1077,c_Int_Onumber__class_Onumber__of(U_1077,U_1078),c_Groups_Oone__class_Oone(U_1077))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1078,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1078,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(U_1077,c_Int_Onumber__class_Onumber__of(U_1077,U_1078),c_Groups_Oone__class_Oone(U_1077)) ) )
| ~ class_Rings_Olinordered__idom(U_1077)
| ~ class_Int_Onumber__ring(U_1077) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
cnf(f_388_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1078,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(U_1077,c_Int_Onumber__class_Onumber__of(U_1077,U_1078),c_Groups_Oone__class_Oone(U_1077))
| ~ class_Rings_Olinordered__idom(U_1077)
| ~ class_Int_Onumber__ring(U_1077) ),
inference(clausify,[status(thm)],[f_388_2]) ).
cnf(f_388_4,plain,
( c_Orderings_Oord__class_Oless(U_1077,c_Int_Onumber__class_Onumber__of(U_1077,U_1078),c_Groups_Oone__class_Oone(U_1077))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1078,c_Int_OBit1(c_Int_OPls))
| ~ class_Rings_Olinordered__idom(U_1077)
| ~ class_Int_Onumber__ring(U_1077) ),
inference(clausify,[status(thm)],[f_388_2]) ).
fof(f_389_1,plain,
! [V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I2_J]) ).
fof(f_389_2,plain,
! [U_1080,U_1079] :
( ( ( c_Orderings_Oord__class_Oless(U_1079,c_Groups_Oone__class_Oone(U_1079),c_Int_Onumber__class_Onumber__of(U_1079,U_1080))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1080) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1080)
| ~ c_Orderings_Oord__class_Oless(U_1079,c_Groups_Oone__class_Oone(U_1079),c_Int_Onumber__class_Onumber__of(U_1079,U_1080)) ) )
| ~ class_Rings_Olinordered__idom(U_1079)
| ~ class_Int_Onumber__ring(U_1079) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1080)
| ~ c_Orderings_Oord__class_Oless(U_1079,c_Groups_Oone__class_Oone(U_1079),c_Int_Onumber__class_Onumber__of(U_1079,U_1080))
| ~ class_Rings_Olinordered__idom(U_1079)
| ~ class_Int_Onumber__ring(U_1079) ),
inference(clausify,[status(thm)],[f_389_2]) ).
cnf(f_389_4,plain,
( c_Orderings_Oord__class_Oless(U_1079,c_Groups_Oone__class_Oone(U_1079),c_Int_Onumber__class_Onumber__of(U_1079,U_1080))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1080)
| ~ class_Rings_Olinordered__idom(U_1079)
| ~ class_Int_Onumber__ring(U_1079) ),
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_half]) ).
fof(f_390_2,plain,
! [U_1081] :
( c_Orderings_Oord__class_Oless(U_1081,c_Groups_Ozero__class_Ozero(U_1081),c_Rings_Oinverse__class_Odivide(U_1081,c_Groups_Oone__class_Oone(U_1081),c_Int_Onumber__class_Onumber__of(U_1081,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_1081)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1081) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
cnf(f_390_3,plain,
( c_Orderings_Oord__class_Oless(U_1081,c_Groups_Ozero__class_Ozero(U_1081),c_Rings_Oinverse__class_Odivide(U_1081,c_Groups_Oone__class_Oone(U_1081),c_Int_Onumber__class_Onumber__of(U_1081,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_1081)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1081) ),
inference(clausify,[status(thm)],[f_390_2]) ).
fof(f_391_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less]) ).
fof(f_391_2,plain,
! [U_1084,U_1083,U_1082] :
( c_Orderings_Oord__class_Oless(U_1082,U_1083,U_1084)
| ~ c_Orderings_Oord__class_Oless__eq(U_1082,c_Groups_Ozero__class_Ozero(U_1082),U_1084)
| ~ c_Orderings_Oord__class_Oless(U_1082,c_Power_Opower__class_Opower(U_1082,U_1083,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1082,U_1084,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_1082) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
( c_Orderings_Oord__class_Oless(U_1082,U_1083,U_1084)
| ~ c_Orderings_Oord__class_Oless__eq(U_1082,c_Groups_Ozero__class_Ozero(U_1082),U_1084)
| ~ c_Orderings_Oord__class_Oless(U_1082,c_Power_Opower__class_Opower(U_1082,U_1083,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1082,U_1084,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_1082) ),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_1,plain,
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(B_n))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))),
inference(fof_nnf,[status(thm)],[fact_g_I2_J]) ).
fof(f_392_2,plain,
! [U_1085] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(U_1085))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1085))))),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(U_1085))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1085))))),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_1,plain,
! [V_p,V_r] :
? [B_m] :
( ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_z)),B_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),V_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
inference(fof_nnf,[status(thm)],[fact_poly__bound__exists]) ).
fof(f_393_2,plain,
! [U_1089,U_1088] :
? [U_1087] :
( ! [U_1086] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_1089),U_1086)),U_1087)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1086),U_1088) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1087) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
! [U_1089,U_1088] :
( ! [U_1086] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_1089),U_1086)),sK22(U_1089,U_1088))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1086),U_1088) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(U_1089,U_1088)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_1087,sK22(U_1089,U_1088))],[f_393_2]) ).
cnf(f_393_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(U_1089,U_1088)),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_1089),U_1086)),sK22(U_1089,U_1088))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1086),U_1088) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_1,plain,
! [V_u] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u) ),
inference(fof_nnf,[status(thm)],[fact_lemma__real__divide__sqrt__less]) ).
fof(f_394_2,plain,
! [U_1090] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1090,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),U_1090)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1090) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
cnf(f_394_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1090,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),U_1090)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1090) ),
inference(clausify,[status(thm)],[f_394_2]) ).
fof(f_395_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_lessI]) ).
fof(f_395_2,plain,
! [U_1091] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1091,c_Nat_OSuc(U_1091)),
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1091,c_Nat_OSuc(U_1091)),
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mono]) ).
fof(f_396_2,plain,
! [U_1093,U_1092] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1092),c_Nat_OSuc(U_1093))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1092,U_1093) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
cnf(f_396_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1092),c_Nat_OSuc(U_1093))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1092,U_1093) ),
inference(clausify,[status(thm)],[f_396_2]) ).
fof(f_397_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_zero__less__Suc]) ).
fof(f_397_2,plain,
! [U_1094] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_1094)),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_1094)),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(f_398_2,plain,
! [U_1095] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1095)),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1095)),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_1,plain,
! [V_x_2] :
( ( c_NthRoot_Osqrt(V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(V_x_2) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__1__iff]) ).
fof(f_399_2,plain,
! [U_1096] :
( ( c_NthRoot_Osqrt(U_1096) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1096 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( U_1096 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_1096) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
( ! [U_1098] :
( c_NthRoot_Osqrt(U_1098) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1098 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ! [U_1097] :
( U_1097 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_1097) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_399_2]) ).
cnf(f_399_4,plain,
( U_1097 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_1097) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_399_3]) ).
cnf(f_399_5,plain,
( c_NthRoot_Osqrt(U_1098) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1098 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_1,plain,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__one]) ).
cnf(f_400_2,plain,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_400_1]) ).
fof(f_401_1,plain,
! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(f_401_2,plain,
! [U_1099] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1099)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1099),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_401_1]) ).
cnf(f_401_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1099)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1099),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_401_2]) ).
fof(f_402_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__1]) ).
cnf(f_402_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_402_1]) ).
fof(f_403_1,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_One__nat__def]) ).
cnf(f_403_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_403_1]) ).
fof(f_404_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__one]) ).
cnf(f_404_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_404_1]) ).
fof(f_405_1,plain,
! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
inference(fof_nnf,[status(thm)],[fact_diff__Suc__1]) ).
fof(f_405_2,plain,
! [U_1100] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1100),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1100,
inference(variable_rename,[status(thm)],[f_405_1]) ).
cnf(f_405_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1100),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1100,
inference(clausify,[status(thm)],[f_405_2]) ).
fof(f_406_1,plain,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(f_406_2,plain,
! [U_1102,U_1101] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1101,c_Nat_OSuc(U_1102)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1101,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1102),
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1101,c_Nat_OSuc(U_1102)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1101,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1102),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_1,plain,
! [V_n,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n))
| ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__power__ineq]) ).
fof(f_407_2,plain,
! [U_1105,U_1104,U_1103] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1103,c_Power_Opower__class_Opower(U_1103,U_1104,U_1105)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1103,U_1104),U_1105))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1103) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
cnf(f_407_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1103,c_Power_Opower__class_Opower(U_1103,U_1104,U_1105)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1103,U_1104),U_1105))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1103) ),
inference(clausify,[status(thm)],[f_407_2]) ).
fof(f_408_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq]) ).
fof(f_408_2,plain,
! [U_1108,U_1107,U_1106] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1106,c_Groups_Oplus__class_Oplus(U_1106,U_1107,U_1108)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1106,U_1107),c_RealVector_Onorm__class_Onorm(U_1106,U_1108)))
| ~ class_RealVector_Oreal__normed__vector(U_1106) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
cnf(f_408_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1106,c_Groups_Oplus__class_Oplus(U_1106,U_1107,U_1108)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1106,U_1107),c_RealVector_Onorm__class_Onorm(U_1106,U_1108)))
| ~ class_RealVector_Oreal__normed__vector(U_1106) ),
inference(clausify,[status(thm)],[f_408_2]) ).
fof(f_409_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__mono]) ).
fof(f_409_2,plain,
! [U_1110,U_1109] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1109),c_NthRoot_Osqrt(U_1110))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1109,U_1110) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1109),c_NthRoot_Osqrt(U_1110))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1109,U_1110) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_NthRoot_Osqrt(V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_NthRoot_Osqrt(V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__iff]) ).
fof(f_410_2,plain,
! [U_1112,U_1111] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1111),c_NthRoot_Osqrt(U_1112))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1111,U_1112) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1111,U_1112)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1111),c_NthRoot_Osqrt(U_1112)) ) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
( ! [U_1116,U_1114] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1114),c_NthRoot_Osqrt(U_1116))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1114,U_1116) )
& ! [U_1115,U_1113] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1113,U_1115)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1113),c_NthRoot_Osqrt(U_1115)) ) ),
inference(miniscope,[status(thm)],[f_410_2]) ).
cnf(f_410_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1113,U_1115)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1113),c_NthRoot_Osqrt(U_1115)) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1114),c_NthRoot_Osqrt(U_1116))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1114,U_1116) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_x_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(T_a,V_y_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
& V_x_2 != V_y_2 ) )
& ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 = V_y_2
| c_Power_Opower__class_Opower(T_a,V_x_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Power_Opower__class_Opower(T_a,V_y_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__disj]) ).
fof(f_411_2,plain,
! [U_1119,U_1118,U_1117] :
( ( ( c_Power_Opower__class_Opower(U_1117,U_1118,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(U_1117,U_1119,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( U_1118 != c_Groups_Ouminus__class_Ouminus(U_1117,U_1119)
& U_1118 != U_1119 ) )
& ( U_1118 = c_Groups_Ouminus__class_Ouminus(U_1117,U_1119)
| U_1118 = U_1119
| c_Power_Opower__class_Opower(U_1117,U_1118,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Power_Opower__class_Opower(U_1117,U_1119,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(U_1117) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( U_1118 = c_Groups_Ouminus__class_Ouminus(U_1117,U_1119)
| U_1118 = U_1119
| c_Power_Opower__class_Opower(U_1117,U_1118,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Power_Opower__class_Opower(U_1117,U_1119,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(U_1117) ),
inference(clausify,[status(thm)],[f_411_2]) ).
cnf(f_411_4,plain,
( U_1118 != U_1119
| c_Power_Opower__class_Opower(U_1117,U_1118,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(U_1117,U_1119,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(U_1117) ),
inference(clausify,[status(thm)],[f_411_2]) ).
cnf(f_411_5,plain,
( U_1118 != c_Groups_Ouminus__class_Ouminus(U_1117,U_1119)
| c_Power_Opower__class_Opower(U_1117,U_1118,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(U_1117,U_1119,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(U_1117) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_1,plain,
! [V_c,V_w,V_v,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1]) ).
fof(f_412_2,plain,
! [U_1123,U_1122,U_1121,U_1120] :
( c_Groups_Oplus__class_Oplus(U_1120,c_Int_Onumber__class_Onumber__of(U_1120,U_1121),c_Groups_Ominus__class_Ominus(U_1120,c_Int_Onumber__class_Onumber__of(U_1120,U_1122),U_1123)) = c_Groups_Ominus__class_Ominus(U_1120,c_Int_Onumber__class_Onumber__of(U_1120,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1121,U_1122)),U_1123)
| ~ class_Int_Onumber__ring(U_1120) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
cnf(f_412_3,plain,
( c_Groups_Oplus__class_Oplus(U_1120,c_Int_Onumber__class_Onumber__of(U_1120,U_1121),c_Groups_Ominus__class_Ominus(U_1120,c_Int_Onumber__class_Onumber__of(U_1120,U_1122),U_1123)) = c_Groups_Ominus__class_Ominus(U_1120,c_Int_Onumber__class_Onumber__of(U_1120,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1121,U_1122)),U_1123)
| ~ class_Int_Onumber__ring(U_1120) ),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_1,plain,
! [V_x_2] :
( ( c_NthRoot_Osqrt(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(V_x_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__0__iff]) ).
fof(f_413_2,plain,
! [U_1124] :
( ( c_NthRoot_Osqrt(U_1124) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1124 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_1124 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_1124) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
( ! [U_1126] :
( c_NthRoot_Osqrt(U_1126) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1126 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1125] :
( U_1125 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_1125) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_413_2]) ).
cnf(f_413_4,plain,
( U_1125 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_1125) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_413_3]) ).
cnf(f_413_5,plain,
( c_NthRoot_Osqrt(U_1126) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1126 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_413_3]) ).
fof(f_414_1,plain,
c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__zero]) ).
cnf(f_414_2,plain,
c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_414_1]) ).
fof(f_415_1,plain,
! [V_n] : V_n != c_Nat_OSuc(V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_415_2,plain,
! [U_1127] : U_1127 != c_Nat_OSuc(U_1127),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
U_1127 != c_Nat_OSuc(U_1127),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_1,plain,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_416_2,plain,
! [U_1128] : c_Nat_OSuc(U_1128) != U_1128,
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
c_Nat_OSuc(U_1128) != U_1128,
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_1,plain,
! [V_nat_H_2,V_nat_2] :
( ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
| V_nat_2 != V_nat_H_2 )
& ( V_nat_2 = V_nat_H_2
| c_Nat_OSuc(V_nat_2) != c_Nat_OSuc(V_nat_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat_Oinject]) ).
fof(f_417_2,plain,
! [U_1130,U_1129] :
( ( c_Nat_OSuc(U_1129) = c_Nat_OSuc(U_1130)
| U_1129 != U_1130 )
& ( U_1129 = U_1130
| c_Nat_OSuc(U_1129) != c_Nat_OSuc(U_1130) ) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
( ! [U_1134,U_1132] :
( c_Nat_OSuc(U_1132) = c_Nat_OSuc(U_1134)
| U_1132 != U_1134 )
& ! [U_1133,U_1131] :
( U_1131 = U_1133
| c_Nat_OSuc(U_1131) != c_Nat_OSuc(U_1133) ) ),
inference(miniscope,[status(thm)],[f_417_2]) ).
cnf(f_417_4,plain,
( U_1131 = U_1133
| c_Nat_OSuc(U_1131) != c_Nat_OSuc(U_1133) ),
inference(clausify,[status(thm)],[f_417_3]) ).
cnf(f_417_5,plain,
( c_Nat_OSuc(U_1132) = c_Nat_OSuc(U_1134)
| U_1132 != U_1134 ),
inference(clausify,[status(thm)],[f_417_3]) ).
fof(f_418_1,plain,
! [V_x,V_n,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),V_p,V_n)),V_x) = c_Power_Opower__class_Opower(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),V_n)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__power]) ).
fof(f_418_2,plain,
! [U_1138,U_1137,U_1136,U_1135] :
( hAPP(c_Polynomial_Opoly(U_1135,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1135),U_1136,U_1137)),U_1138) = c_Power_Opower__class_Opower(U_1135,hAPP(c_Polynomial_Opoly(U_1135,U_1136),U_1138),U_1137)
| ~ class_Rings_Ocomm__semiring__1(U_1135) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
cnf(f_418_3,plain,
( hAPP(c_Polynomial_Opoly(U_1135,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1135),U_1136,U_1137)),U_1138) = c_Power_Opower__class_Opower(U_1135,hAPP(c_Polynomial_Opoly(U_1135,U_1136),U_1138),U_1137)
| ~ class_Rings_Ocomm__semiring__1(U_1135) ),
inference(clausify,[status(thm)],[f_418_2]) ).
fof(f_419_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__add]) ).
fof(f_419_2,plain,
! [U_1142,U_1141,U_1140,U_1139] :
( hAPP(c_Polynomial_Opoly(U_1139,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1139),U_1140,U_1141)),U_1142) = c_Groups_Oplus__class_Oplus(U_1139,hAPP(c_Polynomial_Opoly(U_1139,U_1140),U_1142),hAPP(c_Polynomial_Opoly(U_1139,U_1141),U_1142))
| ~ class_Rings_Ocomm__semiring__0(U_1139) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
( hAPP(c_Polynomial_Opoly(U_1139,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1139),U_1140,U_1141)),U_1142) = c_Groups_Oplus__class_Oplus(U_1139,hAPP(c_Polynomial_Opoly(U_1139,U_1140),U_1142),hAPP(c_Polynomial_Opoly(U_1139,U_1141),U_1142))
| ~ class_Rings_Ocomm__semiring__0(U_1139) ),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_1,plain,
! [V_y,V_x] :
( V_x = V_y
| c_Nat_OSuc(V_x) != c_Nat_OSuc(V_y) ),
inference(fof_nnf,[status(thm)],[fact_Suc__inject]) ).
fof(f_420_2,plain,
! [U_1144,U_1143] :
( U_1143 = U_1144
| c_Nat_OSuc(U_1143) != c_Nat_OSuc(U_1144) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
cnf(f_420_3,plain,
( U_1143 = U_1144
| c_Nat_OSuc(U_1143) != c_Nat_OSuc(U_1144) ),
inference(clausify,[status(thm)],[f_420_2]) ).
fof(f_421_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_m,V_n)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),V_n),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__power]) ).
fof(f_421_2,plain,
! [U_1146,U_1145] : c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,U_1145,U_1146)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1145),U_1146),
inference(variable_rename,[status(thm)],[f_421_1]) ).
cnf(f_421_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,U_1145,U_1146)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1145),U_1146),
inference(clausify,[status(thm)],[f_421_2]) ).
fof(f_422_1,plain,
! [V_n,V_m] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),V_n) = c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_power__real__of__nat]) ).
fof(f_422_2,plain,
! [U_1148,U_1147] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1147),U_1148) = c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,U_1147,U_1148)),
inference(variable_rename,[status(thm)],[f_422_1]) ).
cnf(f_422_3,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1147),U_1148) = c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,U_1147,U_1148)),
inference(clausify,[status(thm)],[f_422_2]) ).
fof(f_423_1,plain,
! [V_m_2,V_n_2] :
( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
| V_n_2 != V_m_2 )
& ( V_n_2 = V_m_2
| c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_RealDef_Oreal(tc_Nat_Onat,V_m_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject]) ).
fof(f_423_2,plain,
! [U_1150,U_1149] :
( ( c_RealDef_Oreal(tc_Nat_Onat,U_1149) = c_RealDef_Oreal(tc_Nat_Onat,U_1150)
| U_1149 != U_1150 )
& ( U_1149 = U_1150
| c_RealDef_Oreal(tc_Nat_Onat,U_1149) != c_RealDef_Oreal(tc_Nat_Onat,U_1150) ) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
( ! [U_1154,U_1152] :
( c_RealDef_Oreal(tc_Nat_Onat,U_1152) = c_RealDef_Oreal(tc_Nat_Onat,U_1154)
| U_1152 != U_1154 )
& ! [U_1153,U_1151] :
( U_1151 = U_1153
| c_RealDef_Oreal(tc_Nat_Onat,U_1151) != c_RealDef_Oreal(tc_Nat_Onat,U_1153) ) ),
inference(miniscope,[status(thm)],[f_423_2]) ).
cnf(f_423_4,plain,
( U_1151 = U_1153
| c_RealDef_Oreal(tc_Nat_Onat,U_1151) != c_RealDef_Oreal(tc_Nat_Onat,U_1153) ),
inference(clausify,[status(thm)],[f_423_3]) ).
cnf(f_423_5,plain,
( c_RealDef_Oreal(tc_Nat_Onat,U_1152) = c_RealDef_Oreal(tc_Nat_Onat,U_1154)
| U_1152 != U_1154 ),
inference(clausify,[status(thm)],[f_423_3]) ).
fof(f_424_1,plain,
! [V_n,V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n)
| ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__power]) ).
fof(f_424_2,plain,
! [U_1157,U_1156,U_1155] :
( c_RealVector_Onorm__class_Onorm(U_1155,c_Power_Opower__class_Opower(U_1155,U_1156,U_1157)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1155,U_1156),U_1157)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1155) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
cnf(f_424_3,plain,
( c_RealVector_Onorm__class_Onorm(U_1155,c_Power_Opower__class_Opower(U_1155,U_1156,U_1157)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1155,U_1156),U_1157)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1155) ),
inference(clausify,[status(thm)],[f_424_2]) ).
fof(f_425_1,plain,
! [V_w,V_v,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__add]) ).
fof(f_425_2,plain,
! [U_1160,U_1159,U_1158] :
( c_Int_Onumber__class_Onumber__of(U_1158,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1159,U_1160)) = c_Groups_Oplus__class_Oplus(U_1158,c_Int_Onumber__class_Onumber__of(U_1158,U_1159),c_Int_Onumber__class_Onumber__of(U_1158,U_1160))
| ~ class_Int_Onumber__ring(U_1158) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
cnf(f_425_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1158,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1159,U_1160)) = c_Groups_Oplus__class_Oplus(U_1158,c_Int_Onumber__class_Onumber__of(U_1158,U_1159),c_Int_Onumber__class_Onumber__of(U_1158,U_1160))
| ~ class_Int_Onumber__ring(U_1158) ),
inference(clausify,[status(thm)],[f_425_2]) ).
fof(f_426_1,plain,
! [V_w,V_v,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__eq]) ).
fof(f_426_2,plain,
! [U_1163,U_1162,U_1161] :
( c_Groups_Oplus__class_Oplus(U_1161,c_Int_Onumber__class_Onumber__of(U_1161,U_1162),c_Int_Onumber__class_Onumber__of(U_1161,U_1163)) = c_Int_Onumber__class_Onumber__of(U_1161,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1162,U_1163))
| ~ class_Int_Onumber__ring(U_1161) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_3,plain,
( c_Groups_Oplus__class_Oplus(U_1161,c_Int_Onumber__class_Onumber__of(U_1161,U_1162),c_Int_Onumber__class_Onumber__of(U_1161,U_1163)) = c_Int_Onumber__class_Onumber__of(U_1161,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1162,U_1163))
| ~ class_Int_Onumber__ring(U_1161) ),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_1,plain,
! [V_z,V_w,V_v,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__left]) ).
fof(f_427_2,plain,
! [U_1167,U_1166,U_1165,U_1164] :
( c_Groups_Oplus__class_Oplus(U_1164,c_Int_Onumber__class_Onumber__of(U_1164,U_1165),c_Groups_Oplus__class_Oplus(U_1164,c_Int_Onumber__class_Onumber__of(U_1164,U_1166),U_1167)) = c_Groups_Oplus__class_Oplus(U_1164,c_Int_Onumber__class_Onumber__of(U_1164,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1165,U_1166)),U_1167)
| ~ class_Int_Onumber__ring(U_1164) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
cnf(f_427_3,plain,
( c_Groups_Oplus__class_Oplus(U_1164,c_Int_Onumber__class_Onumber__of(U_1164,U_1165),c_Groups_Oplus__class_Oplus(U_1164,c_Int_Onumber__class_Onumber__of(U_1164,U_1166),U_1167)) = c_Groups_Oplus__class_Oplus(U_1164,c_Int_Onumber__class_Onumber__of(U_1164,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1165,U_1166)),U_1167)
| ~ class_Int_Onumber__ring(U_1164) ),
inference(clausify,[status(thm)],[f_427_2]) ).
fof(f_428_1,plain,
! [V_k,V_x] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),V_k),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__power]) ).
fof(f_428_2,plain,
! [U_1169,U_1168] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1168,U_1169)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1168),U_1169),
inference(variable_rename,[status(thm)],[f_428_1]) ).
cnf(f_428_3,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1168,U_1169)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1168),U_1169),
inference(clausify,[status(thm)],[f_428_2]) ).
fof(f_429_1,plain,
! [V_y_2,V_x_2] :
( ( c_NthRoot_Osqrt(V_x_2) = c_NthRoot_Osqrt(V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_NthRoot_Osqrt(V_x_2) != c_NthRoot_Osqrt(V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__iff]) ).
fof(f_429_2,plain,
! [U_1171,U_1170] :
( ( c_NthRoot_Osqrt(U_1170) = c_NthRoot_Osqrt(U_1171)
| U_1170 != U_1171 )
& ( U_1170 = U_1171
| c_NthRoot_Osqrt(U_1170) != c_NthRoot_Osqrt(U_1171) ) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
( ! [U_1175,U_1173] :
( c_NthRoot_Osqrt(U_1173) = c_NthRoot_Osqrt(U_1175)
| U_1173 != U_1175 )
& ! [U_1174,U_1172] :
( U_1172 = U_1174
| c_NthRoot_Osqrt(U_1172) != c_NthRoot_Osqrt(U_1174) ) ),
inference(miniscope,[status(thm)],[f_429_2]) ).
cnf(f_429_4,plain,
( U_1172 = U_1174
| c_NthRoot_Osqrt(U_1172) != c_NthRoot_Osqrt(U_1174) ),
inference(clausify,[status(thm)],[f_429_3]) ).
cnf(f_429_5,plain,
( c_NthRoot_Osqrt(U_1173) = c_NthRoot_Osqrt(U_1175)
| U_1173 != U_1175 ),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ class_Groups_Oab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J]) ).
fof(f_430_2,plain,
! [U_1179,U_1178,U_1177,U_1176] :
( c_Groups_Oplus__class_Oplus(U_1176,c_Groups_Oplus__class_Oplus(U_1176,U_1177,U_1178),U_1179) = c_Groups_Oplus__class_Oplus(U_1176,U_1177,c_Groups_Oplus__class_Oplus(U_1176,U_1178,U_1179))
| ~ class_Groups_Oab__semigroup__add(U_1176) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
( c_Groups_Oplus__class_Oplus(U_1176,c_Groups_Oplus__class_Oplus(U_1176,U_1177,U_1178),U_1179) = c_Groups_Oplus__class_Oplus(U_1176,U_1177,c_Groups_Oplus__class_Oplus(U_1176,U_1178,U_1179))
| ~ class_Groups_Oab__semigroup__add(U_1176) ),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_1,plain,
! [V_c_2,V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) != c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_431_2,plain,
! [U_1183,U_1182,U_1181,U_1180] :
( ( ( c_Groups_Oplus__class_Oplus(U_1180,U_1181,U_1182) = c_Groups_Oplus__class_Oplus(U_1180,U_1181,U_1183)
| U_1182 != U_1183 )
& ( U_1182 = U_1183
| c_Groups_Oplus__class_Oplus(U_1180,U_1181,U_1182) != c_Groups_Oplus__class_Oplus(U_1180,U_1181,U_1183) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_1180) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
cnf(f_431_3,plain,
( U_1182 = U_1183
| c_Groups_Oplus__class_Oplus(U_1180,U_1181,U_1182) != c_Groups_Oplus__class_Oplus(U_1180,U_1181,U_1183)
| ~ class_Groups_Ocancel__semigroup__add(U_1180) ),
inference(clausify,[status(thm)],[f_431_2]) ).
cnf(f_431_4,plain,
( c_Groups_Oplus__class_Oplus(U_1180,U_1181,U_1182) = c_Groups_Oplus__class_Oplus(U_1180,U_1181,U_1183)
| U_1182 != U_1183
| ~ class_Groups_Ocancel__semigroup__add(U_1180) ),
inference(clausify,[status(thm)],[f_431_2]) ).
fof(f_432_1,plain,
! [V_c_2,V_a_2,V_b_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) != c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_432_2,plain,
! [U_1187,U_1186,U_1185,U_1184] :
( ( ( c_Groups_Oplus__class_Oplus(U_1184,U_1185,U_1186) = c_Groups_Oplus__class_Oplus(U_1184,U_1187,U_1186)
| U_1185 != U_1187 )
& ( U_1185 = U_1187
| c_Groups_Oplus__class_Oplus(U_1184,U_1185,U_1186) != c_Groups_Oplus__class_Oplus(U_1184,U_1187,U_1186) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_1184) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
cnf(f_432_3,plain,
( U_1185 = U_1187
| c_Groups_Oplus__class_Oplus(U_1184,U_1185,U_1186) != c_Groups_Oplus__class_Oplus(U_1184,U_1187,U_1186)
| ~ class_Groups_Ocancel__semigroup__add(U_1184) ),
inference(clausify,[status(thm)],[f_432_2]) ).
cnf(f_432_4,plain,
( c_Groups_Oplus__class_Oplus(U_1184,U_1185,U_1186) = c_Groups_Oplus__class_Oplus(U_1184,U_1187,U_1186)
| U_1185 != U_1187
| ~ class_Groups_Ocancel__semigroup__add(U_1184) ),
inference(clausify,[status(thm)],[f_432_2]) ).
fof(f_433_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq]) ).
fof(f_433_2,plain,
! [U_1191,U_1190,U_1189,U_1188] :
( U_1190 = U_1191
| c_Groups_Oplus__class_Oplus(U_1188,U_1189,U_1190) != c_Groups_Oplus__class_Oplus(U_1188,U_1189,U_1191)
| ~ class_Groups_Ocancel__semigroup__add(U_1188) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
( U_1190 = U_1191
| c_Groups_Oplus__class_Oplus(U_1188,U_1189,U_1190) != c_Groups_Oplus__class_Oplus(U_1188,U_1189,U_1191)
| ~ class_Groups_Ocancel__semigroup__add(U_1188) ),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
| ~ class_Groups_Ocancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__imp__eq]) ).
fof(f_434_2,plain,
! [U_1195,U_1194,U_1193,U_1192] :
( U_1194 = U_1195
| c_Groups_Oplus__class_Oplus(U_1192,U_1193,U_1194) != c_Groups_Oplus__class_Oplus(U_1192,U_1193,U_1195)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1192) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
cnf(f_434_3,plain,
( U_1194 = U_1195
| c_Groups_Oplus__class_Oplus(U_1192,U_1193,U_1194) != c_Groups_Oplus__class_Oplus(U_1192,U_1193,U_1195)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1192) ),
inference(clausify,[status(thm)],[f_434_2]) ).
fof(f_435_1,plain,
! [V_c,V_a,V_b,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) != c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq]) ).
fof(f_435_2,plain,
! [U_1199,U_1198,U_1197,U_1196] :
( U_1197 = U_1199
| c_Groups_Oplus__class_Oplus(U_1196,U_1197,U_1198) != c_Groups_Oplus__class_Oplus(U_1196,U_1199,U_1198)
| ~ class_Groups_Ocancel__semigroup__add(U_1196) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
cnf(f_435_3,plain,
( U_1197 = U_1199
| c_Groups_Oplus__class_Oplus(U_1196,U_1197,U_1198) != c_Groups_Oplus__class_Oplus(U_1196,U_1199,U_1198)
| ~ class_Groups_Ocancel__semigroup__add(U_1196) ),
inference(clausify,[status(thm)],[f_435_2]) ).
fof(f_436_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left]) ).
fof(f_436_2,plain,
! [U_1203,U_1202,U_1201,U_1200] :
( c_Orderings_Oord__class_Oless(U_1200,U_1202,U_1203)
| ~ c_Orderings_Oord__class_Oless(U_1200,c_Groups_Oplus__class_Oplus(U_1200,U_1201,U_1202),c_Groups_Oplus__class_Oplus(U_1200,U_1201,U_1203))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1200) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
cnf(f_436_3,plain,
( c_Orderings_Oord__class_Oless(U_1200,U_1202,U_1203)
| ~ c_Orderings_Oord__class_Oless(U_1200,c_Groups_Oplus__class_Oplus(U_1200,U_1201,U_1202),c_Groups_Oplus__class_Oplus(U_1200,U_1201,U_1203))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1200) ),
inference(clausify,[status(thm)],[f_436_2]) ).
fof(f_437_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right]) ).
fof(f_437_2,plain,
! [U_1207,U_1206,U_1205,U_1204] :
( c_Orderings_Oord__class_Oless(U_1204,U_1205,U_1207)
| ~ c_Orderings_Oord__class_Oless(U_1204,c_Groups_Oplus__class_Oplus(U_1204,U_1205,U_1206),c_Groups_Oplus__class_Oplus(U_1204,U_1207,U_1206))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1204) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
cnf(f_437_3,plain,
( c_Orderings_Oord__class_Oless(U_1204,U_1205,U_1207)
| ~ c_Orderings_Oord__class_Oless(U_1204,c_Groups_Oplus__class_Oplus(U_1204,U_1205,U_1206),c_Groups_Oplus__class_Oplus(U_1204,U_1207,U_1206))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1204) ),
inference(clausify,[status(thm)],[f_437_2]) ).
fof(f_438_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__mono]) ).
fof(f_438_2,plain,
! [U_1212,U_1211,U_1210,U_1209,U_1208] :
( c_Orderings_Oord__class_Oless(U_1208,c_Groups_Oplus__class_Oplus(U_1208,U_1209,U_1211),c_Groups_Oplus__class_Oplus(U_1208,U_1210,U_1212))
| ~ c_Orderings_Oord__class_Oless(U_1208,U_1211,U_1212)
| ~ c_Orderings_Oord__class_Oless(U_1208,U_1209,U_1210)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1208) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
( c_Orderings_Oord__class_Oless(U_1208,c_Groups_Oplus__class_Oplus(U_1208,U_1209,U_1211),c_Groups_Oplus__class_Oplus(U_1208,U_1210,U_1212))
| ~ c_Orderings_Oord__class_Oless(U_1208,U_1211,U_1212)
| ~ c_Orderings_Oord__class_Oless(U_1208,U_1209,U_1210)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1208) ),
inference(clausify,[status(thm)],[f_438_2]) ).
fof(f_439_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono]) ).
fof(f_439_2,plain,
! [U_1216,U_1215,U_1214,U_1213] :
( c_Orderings_Oord__class_Oless(U_1213,c_Groups_Oplus__class_Oplus(U_1213,U_1216,U_1214),c_Groups_Oplus__class_Oplus(U_1213,U_1216,U_1215))
| ~ c_Orderings_Oord__class_Oless(U_1213,U_1214,U_1215)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1213) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
( c_Orderings_Oord__class_Oless(U_1213,c_Groups_Oplus__class_Oplus(U_1213,U_1216,U_1214),c_Groups_Oplus__class_Oplus(U_1213,U_1216,U_1215))
| ~ c_Orderings_Oord__class_Oless(U_1213,U_1214,U_1215)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1213) ),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono]) ).
fof(f_440_2,plain,
! [U_1220,U_1219,U_1218,U_1217] :
( c_Orderings_Oord__class_Oless(U_1217,c_Groups_Oplus__class_Oplus(U_1217,U_1218,U_1220),c_Groups_Oplus__class_Oplus(U_1217,U_1219,U_1220))
| ~ c_Orderings_Oord__class_Oless(U_1217,U_1218,U_1219)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1217) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
cnf(f_440_3,plain,
( c_Orderings_Oord__class_Oless(U_1217,c_Groups_Oplus__class_Oplus(U_1217,U_1218,U_1220),c_Groups_Oplus__class_Oplus(U_1217,U_1219,U_1220))
| ~ c_Orderings_Oord__class_Oless(U_1217,U_1218,U_1219)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1217) ),
inference(clausify,[status(thm)],[f_440_2]) ).
fof(f_441_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).
fof(f_441_2,plain,
! [U_1224,U_1223,U_1222,U_1221] :
( ( ( c_Orderings_Oord__class_Oless(U_1221,c_Groups_Oplus__class_Oplus(U_1221,U_1222,U_1223),c_Groups_Oplus__class_Oplus(U_1221,U_1222,U_1224))
| ~ c_Orderings_Oord__class_Oless(U_1221,U_1223,U_1224) )
& ( c_Orderings_Oord__class_Oless(U_1221,U_1223,U_1224)
| ~ c_Orderings_Oord__class_Oless(U_1221,c_Groups_Oplus__class_Oplus(U_1221,U_1222,U_1223),c_Groups_Oplus__class_Oplus(U_1221,U_1222,U_1224)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1221) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
cnf(f_441_3,plain,
( c_Orderings_Oord__class_Oless(U_1221,U_1223,U_1224)
| ~ c_Orderings_Oord__class_Oless(U_1221,c_Groups_Oplus__class_Oplus(U_1221,U_1222,U_1223),c_Groups_Oplus__class_Oplus(U_1221,U_1222,U_1224))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1221) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_4,plain,
( c_Orderings_Oord__class_Oless(U_1221,c_Groups_Oplus__class_Oplus(U_1221,U_1222,U_1223),c_Groups_Oplus__class_Oplus(U_1221,U_1222,U_1224))
| ~ c_Orderings_Oord__class_Oless(U_1221,U_1223,U_1224)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1221) ),
inference(clausify,[status(thm)],[f_441_2]) ).
fof(f_442_1,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).
fof(f_442_2,plain,
! [U_1228,U_1227,U_1226,U_1225] :
( ( ( c_Orderings_Oord__class_Oless(U_1225,c_Groups_Oplus__class_Oplus(U_1225,U_1226,U_1227),c_Groups_Oplus__class_Oplus(U_1225,U_1228,U_1227))
| ~ c_Orderings_Oord__class_Oless(U_1225,U_1226,U_1228) )
& ( c_Orderings_Oord__class_Oless(U_1225,U_1226,U_1228)
| ~ c_Orderings_Oord__class_Oless(U_1225,c_Groups_Oplus__class_Oplus(U_1225,U_1226,U_1227),c_Groups_Oplus__class_Oplus(U_1225,U_1228,U_1227)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1225) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
cnf(f_442_3,plain,
( c_Orderings_Oord__class_Oless(U_1225,U_1226,U_1228)
| ~ c_Orderings_Oord__class_Oless(U_1225,c_Groups_Oplus__class_Oplus(U_1225,U_1226,U_1227),c_Groups_Oplus__class_Oplus(U_1225,U_1228,U_1227))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1225) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_4,plain,
( c_Orderings_Oord__class_Oless(U_1225,c_Groups_Oplus__class_Oplus(U_1225,U_1226,U_1227),c_Groups_Oplus__class_Oplus(U_1225,U_1228,U_1227))
| ~ c_Orderings_Oord__class_Oless(U_1225,U_1226,U_1228)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1225) ),
inference(clausify,[status(thm)],[f_442_2]) ).
fof(f_443_1,plain,
! [V_x] : c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__minus]) ).
fof(f_443_2,plain,
! [U_1229] : c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1229)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1229)),
inference(variable_rename,[status(thm)],[f_443_1]) ).
cnf(f_443_3,plain,
c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1229)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1229)),
inference(clausify,[status(thm)],[f_443_2]) ).
fof(f_444_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left]) ).
fof(f_444_2,plain,
! [U_1233,U_1232,U_1231,U_1230] :
( c_Orderings_Oord__class_Oless__eq(U_1230,U_1232,U_1233)
| ~ c_Orderings_Oord__class_Oless__eq(U_1230,c_Groups_Oplus__class_Oplus(U_1230,U_1231,U_1232),c_Groups_Oplus__class_Oplus(U_1230,U_1231,U_1233))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1230) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1230,U_1232,U_1233)
| ~ c_Orderings_Oord__class_Oless__eq(U_1230,c_Groups_Oplus__class_Oplus(U_1230,U_1231,U_1232),c_Groups_Oplus__class_Oplus(U_1230,U_1231,U_1233))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1230) ),
inference(clausify,[status(thm)],[f_444_2]) ).
fof(f_445_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right]) ).
fof(f_445_2,plain,
! [U_1237,U_1236,U_1235,U_1234] :
( c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1237)
| ~ c_Orderings_Oord__class_Oless__eq(U_1234,c_Groups_Oplus__class_Oplus(U_1234,U_1235,U_1236),c_Groups_Oplus__class_Oplus(U_1234,U_1237,U_1236))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1234) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1237)
| ~ c_Orderings_Oord__class_Oless__eq(U_1234,c_Groups_Oplus__class_Oplus(U_1234,U_1235,U_1236),c_Groups_Oplus__class_Oplus(U_1234,U_1237,U_1236))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1234) ),
inference(clausify,[status(thm)],[f_445_2]) ).
fof(f_446_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__mono]) ).
fof(f_446_2,plain,
! [U_1242,U_1241,U_1240,U_1239,U_1238] :
( c_Orderings_Oord__class_Oless__eq(U_1238,c_Groups_Oplus__class_Oplus(U_1238,U_1239,U_1241),c_Groups_Oplus__class_Oplus(U_1238,U_1240,U_1242))
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1241,U_1242)
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1239,U_1240)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1238) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1238,c_Groups_Oplus__class_Oplus(U_1238,U_1239,U_1241),c_Groups_Oplus__class_Oplus(U_1238,U_1240,U_1242))
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1241,U_1242)
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1239,U_1240)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1238) ),
inference(clausify,[status(thm)],[f_446_2]) ).
fof(f_447_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__mono]) ).
fof(f_447_2,plain,
! [U_1246,U_1245,U_1244,U_1243] :
( c_Orderings_Oord__class_Oless__eq(U_1243,c_Groups_Oplus__class_Oplus(U_1243,U_1246,U_1244),c_Groups_Oplus__class_Oplus(U_1243,U_1246,U_1245))
| ~ c_Orderings_Oord__class_Oless__eq(U_1243,U_1244,U_1245)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1243) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1243,c_Groups_Oplus__class_Oplus(U_1243,U_1246,U_1244),c_Groups_Oplus__class_Oplus(U_1243,U_1246,U_1245))
| ~ c_Orderings_Oord__class_Oless__eq(U_1243,U_1244,U_1245)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1243) ),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__mono]) ).
fof(f_448_2,plain,
! [U_1250,U_1249,U_1248,U_1247] :
( c_Orderings_Oord__class_Oless__eq(U_1247,c_Groups_Oplus__class_Oplus(U_1247,U_1248,U_1250),c_Groups_Oplus__class_Oplus(U_1247,U_1249,U_1250))
| ~ c_Orderings_Oord__class_Oless__eq(U_1247,U_1248,U_1249)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1247) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
cnf(f_448_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1247,c_Groups_Oplus__class_Oplus(U_1247,U_1248,U_1250),c_Groups_Oplus__class_Oplus(U_1247,U_1249,U_1250))
| ~ c_Orderings_Oord__class_Oless__eq(U_1247,U_1248,U_1249)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1247) ),
inference(clausify,[status(thm)],[f_448_2]) ).
fof(f_449_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).
fof(f_449_2,plain,
! [U_1254,U_1253,U_1252,U_1251] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1251,c_Groups_Oplus__class_Oplus(U_1251,U_1252,U_1253),c_Groups_Oplus__class_Oplus(U_1251,U_1252,U_1254))
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,U_1253,U_1254) )
& ( c_Orderings_Oord__class_Oless__eq(U_1251,U_1253,U_1254)
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,c_Groups_Oplus__class_Oplus(U_1251,U_1252,U_1253),c_Groups_Oplus__class_Oplus(U_1251,U_1252,U_1254)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1251) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
cnf(f_449_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1251,U_1253,U_1254)
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,c_Groups_Oplus__class_Oplus(U_1251,U_1252,U_1253),c_Groups_Oplus__class_Oplus(U_1251,U_1252,U_1254))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1251) ),
inference(clausify,[status(thm)],[f_449_2]) ).
cnf(f_449_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1251,c_Groups_Oplus__class_Oplus(U_1251,U_1252,U_1253),c_Groups_Oplus__class_Oplus(U_1251,U_1252,U_1254))
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,U_1253,U_1254)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1251) ),
inference(clausify,[status(thm)],[f_449_2]) ).
fof(f_450_1,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).
fof(f_450_2,plain,
! [U_1258,U_1257,U_1256,U_1255] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,U_1256,U_1257),c_Groups_Oplus__class_Oplus(U_1255,U_1258,U_1257))
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,U_1256,U_1258) )
& ( c_Orderings_Oord__class_Oless__eq(U_1255,U_1256,U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,U_1256,U_1257),c_Groups_Oplus__class_Oplus(U_1255,U_1258,U_1257)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1255) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
cnf(f_450_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1255,U_1256,U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,U_1256,U_1257),c_Groups_Oplus__class_Oplus(U_1255,U_1258,U_1257))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1255) ),
inference(clausify,[status(thm)],[f_450_2]) ).
cnf(f_450_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,U_1256,U_1257),c_Groups_Oplus__class_Oplus(U_1255,U_1258,U_1257))
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,U_1256,U_1258)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1255) ),
inference(clausify,[status(thm)],[f_450_2]) ).
fof(f_451_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).
fof(f_451_2,plain,
! [U_1260,U_1259] :
( ( ( c_Groups_Oplus__class_Oplus(U_1259,U_1260,U_1260) = c_Groups_Ozero__class_Ozero(U_1259)
| U_1260 != c_Groups_Ozero__class_Ozero(U_1259) )
& ( U_1260 = c_Groups_Ozero__class_Ozero(U_1259)
| c_Groups_Oplus__class_Oplus(U_1259,U_1260,U_1260) != c_Groups_Ozero__class_Ozero(U_1259) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1259) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,plain,
( U_1260 = c_Groups_Ozero__class_Ozero(U_1259)
| c_Groups_Oplus__class_Oplus(U_1259,U_1260,U_1260) != c_Groups_Ozero__class_Ozero(U_1259)
| ~ class_Groups_Olinordered__ab__group__add(U_1259) ),
inference(clausify,[status(thm)],[f_451_2]) ).
cnf(f_451_4,plain,
( c_Groups_Oplus__class_Oplus(U_1259,U_1260,U_1260) = c_Groups_Ozero__class_Ozero(U_1259)
| U_1260 != c_Groups_Ozero__class_Ozero(U_1259)
| ~ class_Groups_Olinordered__ab__group__add(U_1259) ),
inference(clausify,[status(thm)],[f_451_2]) ).
fof(f_452_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral]) ).
fof(f_452_2,plain,
! [U_1262,U_1261] :
( c_Groups_Oplus__class_Oplus(U_1261,U_1262,c_Groups_Ozero__class_Ozero(U_1261)) = U_1262
| ~ class_Groups_Ocomm__monoid__add(U_1261) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
cnf(f_452_3,plain,
( c_Groups_Oplus__class_Oplus(U_1261,U_1262,c_Groups_Ozero__class_Ozero(U_1261)) = U_1262
| ~ class_Groups_Ocomm__monoid__add(U_1261) ),
inference(clausify,[status(thm)],[f_452_2]) ).
fof(f_453_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Omonoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__right]) ).
fof(f_453_2,plain,
! [U_1264,U_1263] :
( c_Groups_Oplus__class_Oplus(U_1263,U_1264,c_Groups_Ozero__class_Ozero(U_1263)) = U_1264
| ~ class_Groups_Omonoid__add(U_1263) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,plain,
( c_Groups_Oplus__class_Oplus(U_1263,U_1264,c_Groups_Ozero__class_Ozero(U_1263)) = U_1264
| ~ class_Groups_Omonoid__add(U_1263) ),
inference(clausify,[status(thm)],[f_453_2]) ).
fof(f_454_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).
fof(f_454_2,plain,
! [U_1266,U_1265] :
( ( ( c_Groups_Ozero__class_Ozero(U_1265) = c_Groups_Oplus__class_Oplus(U_1265,U_1266,U_1266)
| U_1266 != c_Groups_Ozero__class_Ozero(U_1265) )
& ( U_1266 = c_Groups_Ozero__class_Ozero(U_1265)
| c_Groups_Ozero__class_Ozero(U_1265) != c_Groups_Oplus__class_Oplus(U_1265,U_1266,U_1266) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1265) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
cnf(f_454_3,plain,
( U_1266 = c_Groups_Ozero__class_Ozero(U_1265)
| c_Groups_Ozero__class_Ozero(U_1265) != c_Groups_Oplus__class_Oplus(U_1265,U_1266,U_1266)
| ~ class_Groups_Olinordered__ab__group__add(U_1265) ),
inference(clausify,[status(thm)],[f_454_2]) ).
cnf(f_454_4,plain,
( c_Groups_Ozero__class_Ozero(U_1265) = c_Groups_Oplus__class_Oplus(U_1265,U_1266,U_1266)
| U_1266 != c_Groups_Ozero__class_Ozero(U_1265)
| ~ class_Groups_Olinordered__ab__group__add(U_1265) ),
inference(clausify,[status(thm)],[f_454_2]) ).
fof(f_455_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0]) ).
fof(f_455_2,plain,
! [U_1268,U_1267] :
( c_Groups_Oplus__class_Oplus(U_1267,c_Groups_Ozero__class_Ozero(U_1267),U_1268) = U_1268
| ~ class_Groups_Ocomm__monoid__add(U_1267) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
cnf(f_455_3,plain,
( c_Groups_Oplus__class_Oplus(U_1267,c_Groups_Ozero__class_Ozero(U_1267),U_1268) = U_1268
| ~ class_Groups_Ocomm__monoid__add(U_1267) ),
inference(clausify,[status(thm)],[f_455_2]) ).
fof(f_456_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
| ~ class_Groups_Omonoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__left]) ).
fof(f_456_2,plain,
! [U_1270,U_1269] :
( c_Groups_Oplus__class_Oplus(U_1269,c_Groups_Ozero__class_Ozero(U_1269),U_1270) = U_1270
| ~ class_Groups_Omonoid__add(U_1269) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
cnf(f_456_3,plain,
( c_Groups_Oplus__class_Oplus(U_1269,c_Groups_Ozero__class_Ozero(U_1269),U_1270) = U_1270
| ~ class_Groups_Omonoid__add(U_1269) ),
inference(clausify,[status(thm)],[f_456_2]) ).
fof(f_457_1,plain,
! [V_y,V_x] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__divide]) ).
fof(f_457_2,plain,
! [U_1272,U_1271] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1271,U_1272)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1271),c_NthRoot_Osqrt(U_1272)),
inference(variable_rename,[status(thm)],[f_457_1]) ).
cnf(f_457_3,plain,
c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1271,U_1272)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1271),c_NthRoot_Osqrt(U_1272)),
inference(clausify,[status(thm)],[f_457_2]) ).
fof(f_458_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_NthRoot_Osqrt(V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_NthRoot_Osqrt(V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__iff]) ).
fof(f_458_2,plain,
! [U_1274,U_1273] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1273),c_NthRoot_Osqrt(U_1274))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1273,U_1274) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1273,U_1274)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1273),c_NthRoot_Osqrt(U_1274)) ) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
( ! [U_1278,U_1276] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1276),c_NthRoot_Osqrt(U_1278))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1276,U_1278) )
& ! [U_1277,U_1275] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1275,U_1277)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1275),c_NthRoot_Osqrt(U_1277)) ) ),
inference(miniscope,[status(thm)],[f_458_2]) ).
cnf(f_458_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1275,U_1277)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1275),c_NthRoot_Osqrt(U_1277)) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1276),c_NthRoot_Osqrt(U_1278))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1276,U_1278) ),
inference(clausify,[status(thm)],[f_458_3]) ).
fof(f_459_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__mono]) ).
fof(f_459_2,plain,
! [U_1280,U_1279] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1279),c_NthRoot_Osqrt(U_1280))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1279,U_1280) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
cnf(f_459_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1279),c_NthRoot_Osqrt(U_1280))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1279,U_1280) ),
inference(clausify,[status(thm)],[f_459_2]) ).
fof(f_460_1,plain,
! [V_s,V_y,V_r,V_x,T_a] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__add__less]) ).
fof(f_460_2,plain,
! [U_1285,U_1284,U_1283,U_1282,U_1281] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1281,c_Groups_Oplus__class_Oplus(U_1281,U_1282,U_1284)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1283,U_1285))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1281,U_1284),U_1285)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1281,U_1282),U_1283)
| ~ class_RealVector_Oreal__normed__vector(U_1281) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
cnf(f_460_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1281,c_Groups_Oplus__class_Oplus(U_1281,U_1282,U_1284)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1283,U_1285))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1281,U_1284),U_1285)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1281,U_1282),U_1283)
| ~ class_RealVector_Oreal__normed__vector(U_1281) ),
inference(clausify,[status(thm)],[f_460_2]) ).
fof(f_461_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__Suc__gt__zero]) ).
fof(f_461_2,plain,
! [U_1286] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1286))),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1286))),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__cancel]) ).
fof(f_462_2,plain,
! [U_1289,U_1288,U_1287] :
( c_Groups_Oplus__class_Oplus(U_1287,c_Groups_Ominus__class_Ominus(U_1287,U_1288,U_1289),U_1289) = U_1288
| ~ class_Groups_Ogroup__add(U_1287) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
cnf(f_462_3,plain,
( c_Groups_Oplus__class_Oplus(U_1287,c_Groups_Ominus__class_Ominus(U_1287,U_1288,U_1289),U_1289) = U_1288
| ~ class_Groups_Ogroup__add(U_1287) ),
inference(clausify,[status(thm)],[f_462_2]) ).
fof(f_463_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__cancel]) ).
fof(f_463_2,plain,
! [U_1292,U_1291,U_1290] :
( c_Groups_Ominus__class_Ominus(U_1290,c_Groups_Oplus__class_Oplus(U_1290,U_1291,U_1292),U_1292) = U_1291
| ~ class_Groups_Ogroup__add(U_1290) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
( c_Groups_Ominus__class_Ominus(U_1290,c_Groups_Oplus__class_Oplus(U_1290,U_1291,U_1292),U_1292) = U_1291
| ~ class_Groups_Ogroup__add(U_1290) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add__distrib]) ).
fof(f_464_2,plain,
! [U_1295,U_1294,U_1293] :
( c_Groups_Ouminus__class_Ouminus(U_1293,c_Groups_Oplus__class_Oplus(U_1293,U_1294,U_1295)) = c_Groups_Oplus__class_Oplus(U_1293,c_Groups_Ouminus__class_Ouminus(U_1293,U_1294),c_Groups_Ouminus__class_Ouminus(U_1293,U_1295))
| ~ class_Groups_Oab__group__add(U_1293) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
cnf(f_464_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1293,c_Groups_Oplus__class_Oplus(U_1293,U_1294,U_1295)) = c_Groups_Oplus__class_Oplus(U_1293,c_Groups_Ouminus__class_Ouminus(U_1293,U_1294),c_Groups_Ouminus__class_Ouminus(U_1293,U_1295))
| ~ class_Groups_Oab__group__add(U_1293) ),
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add]) ).
fof(f_465_2,plain,
! [U_1298,U_1297,U_1296] :
( c_Groups_Ouminus__class_Ouminus(U_1296,c_Groups_Oplus__class_Oplus(U_1296,U_1297,U_1298)) = c_Groups_Oplus__class_Oplus(U_1296,c_Groups_Ouminus__class_Ouminus(U_1296,U_1298),c_Groups_Ouminus__class_Ouminus(U_1296,U_1297))
| ~ class_Groups_Ogroup__add(U_1296) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
cnf(f_465_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1296,c_Groups_Oplus__class_Oplus(U_1296,U_1297,U_1298)) = c_Groups_Oplus__class_Oplus(U_1296,c_Groups_Ouminus__class_Ouminus(U_1296,U_1298),c_Groups_Ouminus__class_Ouminus(U_1296,U_1297))
| ~ class_Groups_Ogroup__add(U_1296) ),
inference(clausify,[status(thm)],[f_465_2]) ).
fof(f_466_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__minus__cancel]) ).
fof(f_466_2,plain,
! [U_1301,U_1300,U_1299] :
( c_Groups_Oplus__class_Oplus(U_1299,U_1300,c_Groups_Oplus__class_Oplus(U_1299,c_Groups_Ouminus__class_Ouminus(U_1299,U_1300),U_1301)) = U_1301
| ~ class_Groups_Ogroup__add(U_1299) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
cnf(f_466_3,plain,
( c_Groups_Oplus__class_Oplus(U_1299,U_1300,c_Groups_Oplus__class_Oplus(U_1299,c_Groups_Ouminus__class_Ouminus(U_1299,U_1300),U_1301)) = U_1301
| ~ class_Groups_Ogroup__add(U_1299) ),
inference(clausify,[status(thm)],[f_466_2]) ).
fof(f_467_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add__cancel]) ).
fof(f_467_2,plain,
! [U_1304,U_1303,U_1302] :
( c_Groups_Oplus__class_Oplus(U_1302,c_Groups_Ouminus__class_Ouminus(U_1302,U_1303),c_Groups_Oplus__class_Oplus(U_1302,U_1303,U_1304)) = U_1304
| ~ class_Groups_Ogroup__add(U_1302) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
cnf(f_467_3,plain,
( c_Groups_Oplus__class_Oplus(U_1302,c_Groups_Ouminus__class_Ouminus(U_1302,U_1303),c_Groups_Oplus__class_Oplus(U_1302,U_1303,U_1304)) = U_1304
| ~ class_Groups_Ogroup__add(U_1302) ),
inference(clausify,[status(thm)],[f_467_2]) ).
fof(f_468_1,plain,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
inference(fof_nnf,[status(thm)],[fact_Zero__not__Suc]) ).
fof(f_468_2,plain,
! [U_1305] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1305),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1305),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_1,plain,
! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H),
inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(f_469_2,plain,
! [U_1306] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1306),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1306),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_1,plain,
! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_Suc__not__Zero]) ).
fof(f_470_2,plain,
! [U_1307] : c_Nat_OSuc(U_1307) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_470_1]) ).
cnf(f_470_3,plain,
c_Nat_OSuc(U_1307) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_470_2]) ).
fof(f_471_1,plain,
! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(f_471_2,plain,
! [U_1308] : c_Nat_OSuc(U_1308) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
c_Nat_OSuc(U_1308) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_1,plain,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
inference(fof_nnf,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(f_472_2,plain,
! [U_1309] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1309),
inference(variable_rename,[status(thm)],[f_472_1]) ).
cnf(f_472_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1309),
inference(clausify,[status(thm)],[f_472_2]) ).
fof(f_473_1,plain,
! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(f_473_2,plain,
! [U_1310] : c_Nat_OSuc(U_1310) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_473_1]) ).
cnf(f_473_3,plain,
c_Nat_OSuc(U_1310) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_473_2]) ).
fof(f_474_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__divide__distrib]) ).
fof(f_474_2,plain,
! [U_1314,U_1313,U_1312,U_1311] :
( c_Rings_Oinverse__class_Odivide(U_1311,c_Groups_Oplus__class_Oplus(U_1311,U_1312,U_1313),U_1314) = c_Groups_Oplus__class_Oplus(U_1311,c_Rings_Oinverse__class_Odivide(U_1311,U_1312,U_1314),c_Rings_Oinverse__class_Odivide(U_1311,U_1313,U_1314))
| ~ class_Rings_Odivision__ring(U_1311) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1311,c_Groups_Oplus__class_Oplus(U_1311,U_1312,U_1313),U_1314) = c_Groups_Oplus__class_Oplus(U_1311,c_Rings_Oinverse__class_Odivide(U_1311,U_1312,U_1314),c_Rings_Oinverse__class_Odivide(U_1311,U_1313,U_1314))
| ~ class_Rings_Odivision__ring(U_1311) ),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_1,plain,
! [V_ya,V_y,V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya))
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Oadd]) ).
fof(f_475_2,plain,
! [U_1318,U_1317,U_1316,U_1315] :
( c_Rings_Oinverse__class_Odivide(U_1315,c_Groups_Oplus__class_Oplus(U_1315,U_1316,U_1317),U_1318) = c_Groups_Oplus__class_Oplus(U_1315,c_Rings_Oinverse__class_Odivide(U_1315,U_1316,U_1318),c_Rings_Oinverse__class_Odivide(U_1315,U_1317,U_1318))
| ~ class_RealVector_Oreal__normed__field(U_1315) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
cnf(f_475_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1315,c_Groups_Oplus__class_Oplus(U_1315,U_1316,U_1317),U_1318) = c_Groups_Oplus__class_Oplus(U_1315,c_Rings_Oinverse__class_Odivide(U_1315,U_1316,U_1318),c_Rings_Oinverse__class_Odivide(U_1315,U_1317,U_1318))
| ~ class_RealVector_Oreal__normed__field(U_1315) ),
inference(clausify,[status(thm)],[f_475_2]) ).
fof(f_476_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__add__left__mono]) ).
fof(f_476_2,plain,
! [U_1321,U_1320,U_1319] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1321,U_1319),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1321,U_1320))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1319,U_1320) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
cnf(f_476_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1321,U_1319),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1321,U_1320))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1319,U_1320) ),
inference(clausify,[status(thm)],[f_476_2]) ).
fof(f_477_1,plain,
! [V_n_2,V_m_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).
fof(f_477_2,plain,
! [U_1323,U_1322] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1322,U_1323)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1323,c_Nat_OSuc(U_1322)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1323,c_Nat_OSuc(U_1322))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1322,U_1323) ) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
( ! [U_1327,U_1325] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1325,U_1327)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1327,c_Nat_OSuc(U_1325)) )
& ! [U_1326,U_1324] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1326,c_Nat_OSuc(U_1324))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1324,U_1326) ) ),
inference(miniscope,[status(thm)],[f_477_2]) ).
cnf(f_477_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1326,c_Nat_OSuc(U_1324))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1324,U_1326) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1325,U_1327)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1327,c_Nat_OSuc(U_1325)) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
| ( V_m_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) )
& ( V_m_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).
fof(f_478_2,plain,
! [U_1329,U_1328] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1328,c_Nat_OSuc(U_1329))
| ( U_1328 != U_1329
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1328,U_1329) ) )
& ( U_1328 = U_1329
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1328,U_1329)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1328,c_Nat_OSuc(U_1329)) ) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
( ! [U_1333,U_1331] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1331,c_Nat_OSuc(U_1333))
| ( U_1331 != U_1333
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1331,U_1333) ) )
& ! [U_1332,U_1330] :
( U_1330 = U_1332
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1330,U_1332)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1330,c_Nat_OSuc(U_1332)) ) ),
inference(miniscope,[status(thm)],[f_478_2]) ).
cnf(f_478_4,plain,
( U_1330 = U_1332
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1330,U_1332)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1330,c_Nat_OSuc(U_1332)) ),
inference(clausify,[status(thm)],[f_478_3]) ).
cnf(f_478_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1331,U_1333)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1331,c_Nat_OSuc(U_1333)) ),
inference(clausify,[status(thm)],[f_478_3]) ).
cnf(f_478_6,plain,
( U_1331 != U_1333
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1331,c_Nat_OSuc(U_1333)) ),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).
fof(f_479_2,plain,
! [U_1335,U_1334] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1334),c_Nat_OSuc(U_1335))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1334,U_1335) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1334,U_1335)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1334),c_Nat_OSuc(U_1335)) ) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
( ! [U_1339,U_1337] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1337),c_Nat_OSuc(U_1339))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1337,U_1339) )
& ! [U_1338,U_1336] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1336,U_1338)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1336),c_Nat_OSuc(U_1338)) ) ),
inference(miniscope,[status(thm)],[f_479_2]) ).
cnf(f_479_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1336,U_1338)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1336),c_Nat_OSuc(U_1338)) ),
inference(clausify,[status(thm)],[f_479_3]) ).
cnf(f_479_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1337),c_Nat_OSuc(U_1339))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1337,U_1339) ),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_1,plain,
! [V_m_2,V_n_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
| V_n_2 != V_m_2 )
& ( V_n_2 = V_m_2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(f_480_2,plain,
! [U_1341,U_1340] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1340,c_Nat_OSuc(U_1341))
| U_1340 != U_1341 )
& ( U_1340 = U_1341
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1340,c_Nat_OSuc(U_1341)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1340,U_1341) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
cnf(f_480_3,plain,
( U_1340 = U_1341
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1340,c_Nat_OSuc(U_1341))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1340,U_1341) ),
inference(clausify,[status(thm)],[f_480_2]) ).
cnf(f_480_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1340,c_Nat_OSuc(U_1341))
| U_1340 != U_1341
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1340,U_1341) ),
inference(clausify,[status(thm)],[f_480_2]) ).
fof(f_481_1,plain,
! [V_m,V_n] :
( V_m = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_less__antisym]) ).
fof(f_481_2,plain,
! [U_1343,U_1342] :
( U_1343 = U_1342
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1342,c_Nat_OSuc(U_1343))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1342,U_1343) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
cnf(f_481_3,plain,
( U_1343 = U_1342
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1342,c_Nat_OSuc(U_1343))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1342,U_1343) ),
inference(clausify,[status(thm)],[f_481_2]) ).
fof(f_482_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_less__SucI]) ).
fof(f_482_2,plain,
! [U_1345,U_1344] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344,c_Nat_OSuc(U_1345))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344,U_1345) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
cnf(f_482_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344,c_Nat_OSuc(U_1345))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344,U_1345) ),
inference(clausify,[status(thm)],[f_482_2]) ).
fof(f_483_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
| c_Nat_OSuc(V_m) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessI]) ).
fof(f_483_2,plain,
! [U_1347,U_1346] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1346),U_1347)
| c_Nat_OSuc(U_1346) = U_1347
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1346,U_1347) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
cnf(f_483_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1346),U_1347)
| c_Nat_OSuc(U_1346) = U_1347
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1346,U_1347) ),
inference(clausify,[status(thm)],[f_483_2]) ).
fof(f_484_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_less__trans__Suc]) ).
fof(f_484_2,plain,
! [U_1350,U_1349,U_1348] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1348),U_1350)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1349,U_1350)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1348,U_1349) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
cnf(f_484_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1348),U_1350)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1349,U_1350)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1348,U_1349) ),
inference(clausify,[status(thm)],[f_484_2]) ).
fof(f_485_1,plain,
! [V_n,V_m] :
( V_m = V_n
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_less__SucE]) ).
fof(f_485_2,plain,
! [U_1352,U_1351] :
( U_1351 = U_1352
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1351,U_1352)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1351,c_Nat_OSuc(U_1352)) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
cnf(f_485_3,plain,
( U_1351 = U_1352
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1351,U_1352)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1351,c_Nat_OSuc(U_1352)) ),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessD]) ).
fof(f_486_2,plain,
! [U_1354,U_1353] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1353,U_1354)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1353),U_1354) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1353,U_1354)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1353),U_1354) ),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD]) ).
fof(f_487_2,plain,
! [U_1356,U_1355] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1355,U_1356)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1355),c_Nat_OSuc(U_1356)) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1355,U_1356)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1355),c_Nat_OSuc(U_1356)) ),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__add__abs]) ).
fof(f_488_2,plain,
! [U_1359,U_1358,U_1357] :
( c_Groups_Oabs__class_Oabs(U_1357,c_Groups_Oplus__class_Oplus(U_1357,c_Groups_Oabs__class_Oabs(U_1357,U_1358),c_Groups_Oabs__class_Oabs(U_1357,U_1359))) = c_Groups_Oplus__class_Oplus(U_1357,c_Groups_Oabs__class_Oabs(U_1357,U_1358),c_Groups_Oabs__class_Oabs(U_1357,U_1359))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1357) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
cnf(f_488_3,plain,
( c_Groups_Oabs__class_Oabs(U_1357,c_Groups_Oplus__class_Oplus(U_1357,c_Groups_Oabs__class_Oabs(U_1357,U_1358),c_Groups_Oabs__class_Oabs(U_1357,U_1359))) = c_Groups_Oplus__class_Oplus(U_1357,c_Groups_Oabs__class_Oabs(U_1357,U_1358),c_Groups_Oabs__class_Oabs(U_1357,U_1359))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1357) ),
inference(clausify,[status(thm)],[f_488_2]) ).
fof(f_489_1,plain,
! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
inference(fof_nnf,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
fof(f_489_2,plain,
! [U_1360] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1360)) = c_RealDef_Oreal(tc_Nat_Onat,U_1360),
inference(variable_rename,[status(thm)],[f_489_1]) ).
cnf(f_489_3,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1360)) = c_RealDef_Oreal(tc_Nat_Onat,U_1360),
inference(clausify,[status(thm)],[f_489_2]) ).
fof(f_490_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leD]) ).
fof(f_490_2,plain,
! [U_1362,U_1361] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1361,U_1362)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1361),U_1362) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1361,U_1362)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1361),U_1362) ),
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_1,plain,
! [V_n,V_m] :
( V_m = c_Nat_OSuc(V_n)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__SucE]) ).
fof(f_491_2,plain,
! [U_1364,U_1363] :
( U_1363 = c_Nat_OSuc(U_1364)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1363,U_1364)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1363,c_Nat_OSuc(U_1364)) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
( U_1363 = c_Nat_OSuc(U_1364)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1363,U_1364)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1363,c_Nat_OSuc(U_1364)) ),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__SucI]) ).
fof(f_492_2,plain,
! [U_1366,U_1365] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1365,c_Nat_OSuc(U_1366))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1365,U_1366) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
cnf(f_492_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1365,c_Nat_OSuc(U_1366))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1365,U_1366) ),
inference(clausify,[status(thm)],[f_492_2]) ).
fof(f_493_1,plain,
! [V_m_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).
fof(f_493_2,plain,
! [U_1368,U_1367] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1367),c_Nat_OSuc(U_1368))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1367,U_1368) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1367,U_1368)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1367),c_Nat_OSuc(U_1368)) ) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
( ! [U_1372,U_1370] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1370),c_Nat_OSuc(U_1372))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1370,U_1372) )
& ! [U_1371,U_1369] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1369,U_1371)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1369),c_Nat_OSuc(U_1371)) ) ),
inference(miniscope,[status(thm)],[f_493_2]) ).
cnf(f_493_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1369,U_1371)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1369),c_Nat_OSuc(U_1371)) ),
inference(clausify,[status(thm)],[f_493_3]) ).
cnf(f_493_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1370),c_Nat_OSuc(U_1372))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1370,U_1372) ),
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
| ( V_m_2 != c_Nat_OSuc(V_n_2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) )
& ( V_m_2 = c_Nat_OSuc(V_n_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).
fof(f_494_2,plain,
! [U_1374,U_1373] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1373,c_Nat_OSuc(U_1374))
| ( U_1373 != c_Nat_OSuc(U_1374)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1373,U_1374) ) )
& ( U_1373 = c_Nat_OSuc(U_1374)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1373,U_1374)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1373,c_Nat_OSuc(U_1374)) ) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
( ! [U_1378,U_1376] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1376,c_Nat_OSuc(U_1378))
| ( U_1376 != c_Nat_OSuc(U_1378)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1376,U_1378) ) )
& ! [U_1377,U_1375] :
( U_1375 = c_Nat_OSuc(U_1377)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1375,U_1377)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1375,c_Nat_OSuc(U_1377)) ) ),
inference(miniscope,[status(thm)],[f_494_2]) ).
cnf(f_494_4,plain,
( U_1375 = c_Nat_OSuc(U_1377)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1375,U_1377)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1375,c_Nat_OSuc(U_1377)) ),
inference(clausify,[status(thm)],[f_494_3]) ).
cnf(f_494_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1376,U_1378)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1376,c_Nat_OSuc(U_1378)) ),
inference(clausify,[status(thm)],[f_494_3]) ).
cnf(f_494_6,plain,
( U_1376 != c_Nat_OSuc(U_1378)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1376,c_Nat_OSuc(U_1378)) ),
inference(clausify,[status(thm)],[f_494_3]) ).
fof(f_495_1,plain,
! [V_n_2,V_m_2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).
fof(f_495_2,plain,
! [U_1380,U_1379] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1379,U_1380)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1380),U_1379) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1380),U_1379)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1379,U_1380) ) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
( ! [U_1384,U_1382] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1382,U_1384)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1384),U_1382) )
& ! [U_1383,U_1381] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1383),U_1381)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1381,U_1383) ) ),
inference(miniscope,[status(thm)],[f_495_2]) ).
cnf(f_495_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1383),U_1381)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1381,U_1383) ),
inference(clausify,[status(thm)],[f_495_3]) ).
cnf(f_495_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1382,U_1384)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1384),U_1382) ),
inference(clausify,[status(thm)],[f_495_3]) ).
fof(f_496_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n),
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(f_496_2,plain,
! [U_1385] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1385),U_1385),
inference(variable_rename,[status(thm)],[f_496_1]) ).
cnf(f_496_3,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1385),U_1385),
inference(clausify,[status(thm)],[f_496_2]) ).
fof(f_497_1,plain,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(f_497_2,plain,
! [U_1387,U_1386] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1386),c_Nat_OSuc(U_1387)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1386,U_1387),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1386),c_Nat_OSuc(U_1387)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1386,U_1387),
inference(clausify,[status(thm)],[f_497_2]) ).
fof(f_498_1,plain,
! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__diff]) ).
fof(f_498_2,plain,
! [U_1390,U_1389,U_1388] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1388),U_1389),c_Nat_OSuc(U_1390)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1388,U_1389),U_1390),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1388),U_1389),c_Nat_OSuc(U_1390)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1388,U_1389),U_1390),
inference(clausify,[status(thm)],[f_498_2]) ).
fof(f_499_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_int__0__neq__1]) ).
cnf(f_499_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_499_1]) ).
fof(f_500_1,plain,
! [V_n,V_r,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_r,c_Nat_OSuc(V_n)),V_r)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self]) ).
fof(f_500_2,plain,
! [U_1393,U_1392,U_1391] :
( c_Orderings_Oord__class_Oless__eq(U_1391,c_Power_Opower__class_Opower(U_1391,U_1392,c_Nat_OSuc(U_1393)),U_1392)
| ~ c_Orderings_Oord__class_Oless__eq(U_1391,U_1392,c_Groups_Oone__class_Oone(U_1391))
| ~ c_Orderings_Oord__class_Oless__eq(U_1391,c_Groups_Ozero__class_Ozero(U_1391),U_1392)
| ~ class_Rings_Olinordered__semidom(U_1391) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
cnf(f_500_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1391,c_Power_Opower__class_Opower(U_1391,U_1392,c_Nat_OSuc(U_1393)),U_1392)
| ~ c_Orderings_Oord__class_Oless__eq(U_1391,U_1392,c_Groups_Oone__class_Oone(U_1391))
| ~ c_Orderings_Oord__class_Oless__eq(U_1391,c_Groups_Ozero__class_Ozero(U_1391),U_1392)
| ~ class_Rings_Olinordered__semidom(U_1391) ),
inference(clausify,[status(thm)],[f_500_2]) ).
fof(f_501_1,plain,
! [V_m_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__real__le]) ).
fof(f_501_2,plain,
! [U_1395,U_1394] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1394,U_1395)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1394),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1395)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1394),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1395))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1394,U_1395) ) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
( ! [U_1399,U_1397] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1397,U_1399)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1397),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1399)) )
& ! [U_1398,U_1396] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1396),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1398))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1396,U_1398) ) ),
inference(miniscope,[status(thm)],[f_501_2]) ).
cnf(f_501_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1396),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1398))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1396,U_1398) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1397,U_1399)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1397),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1399)) ),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_1,plain,
! [V_m_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__real__less]) ).
fof(f_502_2,plain,
! [U_1401,U_1400] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1400,U_1401)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1400),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1401),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1400),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1401),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1400,U_1401) ) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
( ! [U_1405,U_1403] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1403,U_1405)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1403),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1405),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ! [U_1404,U_1402] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1402),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1404),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1402,U_1404) ) ),
inference(miniscope,[status(thm)],[f_502_2]) ).
cnf(f_502_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1402),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1404),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1402,U_1404) ),
inference(clausify,[status(thm)],[f_502_3]) ).
cnf(f_502_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1403,U_1405)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1403),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1405),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq]) ).
fof(f_503_2,plain,
! [U_1410,U_1409,U_1408,U_1407,U_1406] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1406,c_Groups_Ominus__class_Ominus(U_1406,c_Groups_Oplus__class_Oplus(U_1406,U_1407,U_1408),c_Groups_Oplus__class_Oplus(U_1406,U_1409,U_1410))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1406,c_Groups_Ominus__class_Ominus(U_1406,U_1407,U_1409)),c_RealVector_Onorm__class_Onorm(U_1406,c_Groups_Ominus__class_Ominus(U_1406,U_1408,U_1410))))
| ~ class_RealVector_Oreal__normed__vector(U_1406) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
cnf(f_503_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1406,c_Groups_Ominus__class_Ominus(U_1406,c_Groups_Oplus__class_Oplus(U_1406,U_1407,U_1408),c_Groups_Oplus__class_Oplus(U_1406,U_1409,U_1410))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1406,c_Groups_Ominus__class_Ominus(U_1406,U_1407,U_1409)),c_RealVector_Onorm__class_Onorm(U_1406,c_Groups_Ominus__class_Ominus(U_1406,U_1408,U_1410))))
| ~ class_RealVector_Oreal__normed__vector(U_1406) ),
inference(clausify,[status(thm)],[f_503_2]) ).
fof(f_504_1,plain,
! [V_w,V_c,V_v,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,V_c,c_Int_Onumber__class_Onumber__of(T_a,V_w))) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_c)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2]) ).
fof(f_504_2,plain,
! [U_1414,U_1413,U_1412,U_1411] :
( c_Groups_Oplus__class_Oplus(U_1411,c_Int_Onumber__class_Onumber__of(U_1411,U_1412),c_Groups_Ominus__class_Ominus(U_1411,U_1413,c_Int_Onumber__class_Onumber__of(U_1411,U_1414))) = c_Groups_Oplus__class_Oplus(U_1411,c_Int_Onumber__class_Onumber__of(U_1411,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1412,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1414))),U_1413)
| ~ class_Int_Onumber__ring(U_1411) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
cnf(f_504_3,plain,
( c_Groups_Oplus__class_Oplus(U_1411,c_Int_Onumber__class_Onumber__of(U_1411,U_1412),c_Groups_Ominus__class_Ominus(U_1411,U_1413,c_Int_Onumber__class_Onumber__of(U_1411,U_1414))) = c_Groups_Oplus__class_Oplus(U_1411,c_Int_Onumber__class_Onumber__of(U_1411,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1412,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1414))),U_1413)
| ~ class_Int_Onumber__ring(U_1411) ),
inference(clausify,[status(thm)],[f_504_2]) ).
fof(f_505_1,plain,
! [V_n] :
( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred_H]) ).
fof(f_505_2,plain,
! [U_1415] :
( U_1415 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1415,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1415) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
cnf(f_505_3,plain,
( U_1415 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1415,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1415) ),
inference(clausify,[status(thm)],[f_505_2]) ).
fof(f_506_1,plain,
! [V_n] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__1]) ).
fof(f_506_2,plain,
! [U_1416] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1416,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_1416
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1416) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
cnf(f_506_3,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1416,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_1416
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1416) ),
inference(clausify,[status(thm)],[f_506_2]) ).
fof(f_507_1,plain,
! [V_d,V_b,V_c,V_a] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__triangle__ineq]) ).
fof(f_507_2,plain,
! [U_1420,U_1419,U_1418,U_1417] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1417,U_1418),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1419,U_1420),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1417,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1419,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1418,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1420,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(variable_rename,[status(thm)],[f_507_1]) ).
cnf(f_507_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1417,U_1418),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1419,U_1420),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1417,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1419,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1418,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1420,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(clausify,[status(thm)],[f_507_2]) ).
fof(f_508_1,plain,
! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__ge2]) ).
fof(f_508_2,plain,
! [U_1422,U_1421] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1421,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1422,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1421,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_508_1]) ).
cnf(f_508_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1421,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1422,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1421,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__ge1]) ).
fof(f_509_2,plain,
! [U_1424,U_1423] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1423,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1423,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1424,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_509_1]) ).
cnf(f_509_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1423,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1423,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1424,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_509_2]) ).
fof(f_510_1,plain,
! [V_y,V_x] :
( V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != V_x ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__eq__cancel]) ).
fof(f_510_2,plain,
! [U_1426,U_1425] :
( U_1426 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1425,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1426,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_1425 ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
! [U_1426] :
( ! [U_1425] : c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1425,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1426,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_1425
| U_1426 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(miniscope,[status(thm)],[f_510_2]) ).
cnf(f_510_4,plain,
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1425,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1426,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_1425
| U_1426 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_510_3]) ).
fof(f_511_1,plain,
! [V_y,V_x] :
( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != V_y ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__eq__cancel2]) ).
fof(f_511_2,plain,
! [U_1428,U_1427] :
( U_1427 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1427,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1428,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_1428 ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
cnf(f_511_3,plain,
( U_1427 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1427,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1428,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_1428 ),
inference(clausify,[status(thm)],[f_511_2]) ).
fof(f_512_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__ge__zero]) ).
fof(f_512_2,plain,
! [U_1430,U_1429] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1429,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1430,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_512_1]) ).
cnf(f_512_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1429,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1430,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_512_2]) ).
fof(f_513_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__abs1]) ).
fof(f_513_2,plain,
! [U_1432,U_1431] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1431),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1431,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1432,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_513_1]) ).
cnf(f_513_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1431),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1431,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1432,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_513_2]) ).
fof(f_514_1,plain,
! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__abs2]) ).
fof(f_514_2,plain,
! [U_1434,U_1433] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1433),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1434,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1433,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_514_1]) ).
cnf(f_514_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1433),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1434,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1433,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_514_2]) ).
fof(f_515_1,plain,
! [V_X_2,T_b] :
( ( ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ! [B_K] :
( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) )
| ~ class_RealVector_Oreal__normed__vector(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def2]) ).
fof(f_515_2,plain,
! [U_1444,U_1443] :
( ( ( ? [U_1442] :
( ! [U_1441] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1441)),U_1442)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1442) )
| ! [U_1440] :
? [U_1439] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1439)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1440))) )
& ( ? [U_1438] :
! [U_1437] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1437)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1438)))
| ! [U_1436] :
( ? [U_1435] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1435)),U_1436)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1436) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1443) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_1444,U_1443] :
( ( ( ? [U_1442] :
( ! [U_1441] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1441)),U_1442)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1442) )
| ! [U_1440] :
? [U_1439] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1439)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1440))) )
& ( ? [U_1438] :
! [U_1437] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1437)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1438)))
| ! [U_1436] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK23(U_1444,U_1443,U_1436))),U_1436)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1436) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1443) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1435,sK23(U_1444,U_1443,U_1436))],[f_515_2]) ).
fof(f_515_4,plain,
! [U_1444,U_1443] :
( ( ( ? [U_1442] :
( ! [U_1441] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1441)),U_1442)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1442) )
| ! [U_1440] :
? [U_1439] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1439)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1440))) )
& ( ! [U_1437] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1437)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK24(U_1444,U_1443))))
| ! [U_1436] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK23(U_1444,U_1443,U_1436))),U_1436)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1436) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1443) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1438,sK24(U_1444,U_1443))],[f_515_3]) ).
fof(f_515_5,plain,
! [U_1444,U_1443] :
( ( ( ? [U_1442] :
( ! [U_1441] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1441)),U_1442)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1442) )
| ! [U_1440] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK25(U_1444,U_1443,U_1440))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1440))) )
& ( ! [U_1437] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1437)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK24(U_1444,U_1443))))
| ! [U_1436] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK23(U_1444,U_1443,U_1436))),U_1436)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1436) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1443) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1439,sK25(U_1444,U_1443,U_1440))],[f_515_4]) ).
fof(f_515_6,plain,
! [U_1444,U_1443] :
( ( ( ( ! [U_1441] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1441)),sK26(U_1444,U_1443))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(U_1444,U_1443)) )
| ! [U_1440] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK25(U_1444,U_1443,U_1440))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1440))) )
& ( ! [U_1437] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1437)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK24(U_1444,U_1443))))
| ! [U_1436] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK23(U_1444,U_1443,U_1436))),U_1436)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1436) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1443) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1442,sK26(U_1444,U_1443))],[f_515_5]) ).
cnf(f_515_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1437)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK24(U_1444,U_1443))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK23(U_1444,U_1443,U_1436))),U_1436)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1436)
| ~ class_RealVector_Oreal__normed__vector(U_1443) ),
inference(clausify,[status(thm)],[f_515_6]) ).
cnf(f_515_8,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(U_1444,U_1443))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK25(U_1444,U_1443,U_1440))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1440)))
| ~ class_RealVector_Oreal__normed__vector(U_1443) ),
inference(clausify,[status(thm)],[f_515_6]) ).
cnf(f_515_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,U_1441)),sK26(U_1444,U_1443))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1443,hAPP(U_1444,sK25(U_1444,U_1443,U_1440))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1440)))
| ~ class_RealVector_Oreal__normed__vector(U_1443) ),
inference(clausify,[status(thm)],[f_515_6]) ).
fof(f_516_1,plain,
! [V_X_2,T_b] :
( ( ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ! [B_K] :
( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) )
| ~ class_RealVector_Oreal__normed__vector(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def]) ).
fof(f_516_2,plain,
! [U_1454,U_1453] :
( ( ( ? [U_1452] :
( ! [U_1451] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1451)),U_1452)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1452) )
| ! [U_1450] :
? [U_1449] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1449)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1450))) )
& ( ? [U_1448] :
! [U_1447] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1447)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1448)))
| ! [U_1446] :
( ? [U_1445] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1445)),U_1446)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1446) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1453) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
! [U_1454,U_1453] :
( ( ( ? [U_1452] :
( ! [U_1451] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1451)),U_1452)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1452) )
| ! [U_1450] :
? [U_1449] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1449)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1450))) )
& ( ? [U_1448] :
! [U_1447] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1447)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1448)))
| ! [U_1446] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK27(U_1454,U_1453,U_1446))),U_1446)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1446) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1445,sK27(U_1454,U_1453,U_1446))],[f_516_2]) ).
fof(f_516_4,plain,
! [U_1454,U_1453] :
( ( ( ? [U_1452] :
( ! [U_1451] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1451)),U_1452)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1452) )
| ! [U_1450] :
? [U_1449] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1449)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1450))) )
& ( ! [U_1447] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1447)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK28(U_1454,U_1453))))
| ! [U_1446] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK27(U_1454,U_1453,U_1446))),U_1446)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1446) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1448,sK28(U_1454,U_1453))],[f_516_3]) ).
fof(f_516_5,plain,
! [U_1454,U_1453] :
( ( ( ? [U_1452] :
( ! [U_1451] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1451)),U_1452)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1452) )
| ! [U_1450] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK29(U_1454,U_1453,U_1450))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1450))) )
& ( ! [U_1447] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1447)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK28(U_1454,U_1453))))
| ! [U_1446] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK27(U_1454,U_1453,U_1446))),U_1446)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1446) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1449,sK29(U_1454,U_1453,U_1450))],[f_516_4]) ).
fof(f_516_6,plain,
! [U_1454,U_1453] :
( ( ( ( ! [U_1451] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1451)),sK30(U_1454,U_1453))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK30(U_1454,U_1453)) )
| ! [U_1450] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK29(U_1454,U_1453,U_1450))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1450))) )
& ( ! [U_1447] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1447)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK28(U_1454,U_1453))))
| ! [U_1446] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK27(U_1454,U_1453,U_1446))),U_1446)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1446) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1452,sK30(U_1454,U_1453))],[f_516_5]) ).
cnf(f_516_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1447)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK28(U_1454,U_1453))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK27(U_1454,U_1453,U_1446))),U_1446)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1446)
| ~ class_RealVector_Oreal__normed__vector(U_1453) ),
inference(clausify,[status(thm)],[f_516_6]) ).
cnf(f_516_8,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK30(U_1454,U_1453))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK29(U_1454,U_1453,U_1450))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1450)))
| ~ class_RealVector_Oreal__normed__vector(U_1453) ),
inference(clausify,[status(thm)],[f_516_6]) ).
cnf(f_516_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,U_1451)),sK30(U_1454,U_1453))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1453,hAPP(U_1454,sK29(U_1454,U_1453,U_1450))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1450)))
| ~ class_RealVector_Oreal__normed__vector(U_1453) ),
inference(clausify,[status(thm)],[f_516_6]) ).
fof(f_517_1,plain,
! [V_v,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__special_I3_J]) ).
fof(f_517_2,plain,
! [U_1456,U_1455] :
( c_Groups_Oplus__class_Oplus(U_1455,c_Int_Onumber__class_Onumber__of(U_1455,U_1456),c_Groups_Oone__class_Oone(U_1455)) = c_Int_Onumber__class_Onumber__of(U_1455,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1456,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_1455) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
( c_Groups_Oplus__class_Oplus(U_1455,c_Int_Onumber__class_Onumber__of(U_1455,U_1456),c_Groups_Oone__class_Oone(U_1455)) = c_Int_Onumber__class_Onumber__of(U_1455,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1456,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_1455) ),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_1,plain,
! [V_w,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__special_I2_J]) ).
fof(f_518_2,plain,
! [U_1458,U_1457] :
( c_Groups_Oplus__class_Oplus(U_1457,c_Groups_Oone__class_Oone(U_1457),c_Int_Onumber__class_Onumber__of(U_1457,U_1458)) = c_Int_Onumber__class_Onumber__of(U_1457,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1458))
| ~ class_Int_Onumber__ring(U_1457) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
cnf(f_518_3,plain,
( c_Groups_Oplus__class_Oplus(U_1457,c_Groups_Oone__class_Oone(U_1457),c_Int_Onumber__class_Onumber__of(U_1457,U_1458)) = c_Int_Onumber__class_Onumber__of(U_1457,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1458))
| ~ class_Int_Onumber__ring(U_1457) ),
inference(clausify,[status(thm)],[f_518_2]) ).
fof(f_519_1,plain,
! [V_y_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__0__iff]) ).
fof(f_519_2,plain,
! [U_1459] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1459))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1459) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1459)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1459)) ) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
fof(f_519_3,plain,
( ! [U_1461] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1461))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1461) )
& ! [U_1460] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1460)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1460)) ) ),
inference(miniscope,[status(thm)],[f_519_2]) ).
cnf(f_519_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1460)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1460)) ),
inference(clausify,[status(thm)],[f_519_3]) ).
cnf(f_519_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1461))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1461) ),
inference(clausify,[status(thm)],[f_519_3]) ).
fof(f_520_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__0__iff]) ).
fof(f_520_2,plain,
! [U_1462] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1462),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1462,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1462,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1462),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
( ! [U_1464] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1464),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1464,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1463] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1463,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1463),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_520_2]) ).
cnf(f_520_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1463,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1463),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_520_3]) ).
cnf(f_520_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1464),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1464,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__zero]) ).
fof(f_521_2,plain,
! [U_1465] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1465))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1465) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
cnf(f_521_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1465))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1465) ),
inference(clausify,[status(thm)],[f_521_2]) ).
fof(f_522_1,plain,
! [V_x] :
( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__zero__cancel]) ).
fof(f_522_2,plain,
! [U_1466] :
( U_1466 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_1466) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1466) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
cnf(f_522_3,plain,
( U_1466 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_1466) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1466) ),
inference(clausify,[status(thm)],[f_522_2]) ).
fof(f_523_1,plain,
! [V_y_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__0__iff]) ).
fof(f_523_2,plain,
! [U_1467] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1467))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1467) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1467)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1467)) ) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
( ! [U_1469] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1469))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1469) )
& ! [U_1468] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1468)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1468)) ) ),
inference(miniscope,[status(thm)],[f_523_2]) ).
cnf(f_523_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1468)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1468)) ),
inference(clausify,[status(thm)],[f_523_3]) ).
cnf(f_523_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1469))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1469) ),
inference(clausify,[status(thm)],[f_523_3]) ).
fof(f_524_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__lt__0__iff]) ).
fof(f_524_2,plain,
! [U_1470] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1470),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1470,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1470,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1470),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
( ! [U_1472] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1472),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1472,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1471] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1471,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1471),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_524_2]) ).
cnf(f_524_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1471,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1471),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_524_3]) ).
cnf(f_524_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1472),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1472,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_524_3]) ).
fof(f_525_1,plain,
! [V_x] :
( c_NthRoot_Osqrt(V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__not__eq__zero]) ).
fof(f_525_2,plain,
! [U_1473] :
( c_NthRoot_Osqrt(U_1473) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1473) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
cnf(f_525_3,plain,
( c_NthRoot_Osqrt(U_1473) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1473) ),
inference(clausify,[status(thm)],[f_525_2]) ).
fof(f_526_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__zero]) ).
fof(f_526_2,plain,
! [U_1474] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1474))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1474) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
cnf(f_526_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1474))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1474) ),
inference(clausify,[status(thm)],[f_526_2]) ).
fof(f_527_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__one]) ).
fof(f_527_2,plain,
! [U_1475] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1475))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1475) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
cnf(f_527_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1475))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1475) ),
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__1__iff]) ).
fof(f_528_2,plain,
! [U_1476] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1476),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1476,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1476,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1476),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
( ! [U_1478] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1478),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1478,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_1477] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1477,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1477),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_528_2]) ).
cnf(f_528_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1477,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1477),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_528_3]) ).
cnf(f_528_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1478),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1478,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_528_3]) ).
fof(f_529_1,plain,
! [V_y_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__1__iff]) ).
fof(f_529_2,plain,
! [U_1479] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1479))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1479) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1479)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1479)) ) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
( ! [U_1481] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1481))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1481) )
& ! [U_1480] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1480)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1480)) ) ),
inference(miniscope,[status(thm)],[f_529_2]) ).
cnf(f_529_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1480)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1480)) ),
inference(clausify,[status(thm)],[f_529_3]) ).
cnf(f_529_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1481))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1481) ),
inference(clausify,[status(thm)],[f_529_3]) ).
fof(f_530_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__lt__1__iff]) ).
fof(f_530_2,plain,
! [U_1482] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1482),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1482,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1482,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1482),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
( ! [U_1484] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1484),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1484,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_1483] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1483,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1483),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_530_2]) ).
cnf(f_530_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1483,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1483),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_530_3]) ).
cnf(f_530_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1484),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1484,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_1,plain,
! [V_y_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__1__iff]) ).
fof(f_531_2,plain,
! [U_1485] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1485))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1485) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1485)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1485)) ) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
( ! [U_1487] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1487))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1487) )
& ! [U_1486] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1486)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1486)) ) ),
inference(miniscope,[status(thm)],[f_531_2]) ).
cnf(f_531_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1486)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1486)) ),
inference(clausify,[status(thm)],[f_531_3]) ).
cnf(f_531_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_1487))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1487) ),
inference(clausify,[status(thm)],[f_531_3]) ).
fof(f_532_1,plain,
! [V_n_2] :
( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero__iff]) ).
fof(f_532_2,plain,
! [U_1488] :
( ( c_RealDef_Oreal(tc_Nat_Onat,U_1488) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1488 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_1488) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
( ! [U_1490] :
( c_RealDef_Oreal(tc_Nat_Onat,U_1490) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1490 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1489] :
( U_1489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_1489) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_532_2]) ).
cnf(f_532_4,plain,
( U_1489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_1489) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_532_3]) ).
cnf(f_532_5,plain,
( c_RealDef_Oreal(tc_Nat_Onat,U_1490) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1490 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_532_3]) ).
fof(f_533_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero]) ).
cnf(f_533_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_533_1]) ).
fof(f_534_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_not__real__of__nat__less__zero]) ).
fof(f_534_2,plain,
! [U_1491] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1491),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_534_1]) ).
cnf(f_534_3,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1491),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_534_2]) ).
fof(f_535_1,plain,
! [V_v] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) ),
inference(fof_nnf,[status(thm)],[fact_expand__Suc]) ).
fof(f_535_2,plain,
! [U_1492] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1492) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1492),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1492)) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
cnf(f_535_3,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1492) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1492),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1492)) ),
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_1,plain,
! [V_m_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff]) ).
fof(f_536_2,plain,
! [U_1494,U_1493] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1493),c_RealDef_Oreal(tc_Nat_Onat,U_1494))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1493,U_1494) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1493,U_1494)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1493),c_RealDef_Oreal(tc_Nat_Onat,U_1494)) ) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
fof(f_536_3,plain,
( ! [U_1498,U_1496] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1496),c_RealDef_Oreal(tc_Nat_Onat,U_1498))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1496,U_1498) )
& ! [U_1497,U_1495] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1495,U_1497)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1495),c_RealDef_Oreal(tc_Nat_Onat,U_1497)) ) ),
inference(miniscope,[status(thm)],[f_536_2]) ).
cnf(f_536_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1495,U_1497)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1495),c_RealDef_Oreal(tc_Nat_Onat,U_1497)) ),
inference(clausify,[status(thm)],[f_536_3]) ).
cnf(f_536_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1496),c_RealDef_Oreal(tc_Nat_Onat,U_1498))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1496,U_1498) ),
inference(clausify,[status(thm)],[f_536_3]) ).
fof(f_537_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos]) ).
fof(f_537_2,plain,
! [U_1501,U_1500,U_1499] :
( c_Orderings_Oord__class_Oless__eq(U_1499,c_Groups_Oplus__class_Oplus(U_1499,U_1500,U_1501),c_Groups_Ozero__class_Ozero(U_1499))
| ~ c_Orderings_Oord__class_Oless__eq(U_1499,U_1501,c_Groups_Ozero__class_Ozero(U_1499))
| ~ c_Orderings_Oord__class_Oless__eq(U_1499,U_1500,c_Groups_Ozero__class_Ozero(U_1499))
| ~ class_Groups_Oordered__comm__monoid__add(U_1499) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
cnf(f_537_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1499,c_Groups_Oplus__class_Oplus(U_1499,U_1500,U_1501),c_Groups_Ozero__class_Ozero(U_1499))
| ~ c_Orderings_Oord__class_Oless__eq(U_1499,U_1501,c_Groups_Ozero__class_Ozero(U_1499))
| ~ c_Orderings_Oord__class_Oless__eq(U_1499,U_1500,c_Groups_Ozero__class_Ozero(U_1499))
| ~ class_Groups_Oordered__comm__monoid__add(U_1499) ),
inference(clausify,[status(thm)],[f_537_2]) ).
fof(f_538_1,plain,
! [V_a,V_b,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__increasing2]) ).
fof(f_538_2,plain,
! [U_1505,U_1504,U_1503,U_1502] :
( c_Orderings_Oord__class_Oless__eq(U_1502,U_1504,c_Groups_Oplus__class_Oplus(U_1502,U_1505,U_1503))
| ~ c_Orderings_Oord__class_Oless__eq(U_1502,U_1504,U_1505)
| ~ c_Orderings_Oord__class_Oless__eq(U_1502,c_Groups_Ozero__class_Ozero(U_1502),U_1503)
| ~ class_Groups_Oordered__comm__monoid__add(U_1502) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
cnf(f_538_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1502,U_1504,c_Groups_Oplus__class_Oplus(U_1502,U_1505,U_1503))
| ~ c_Orderings_Oord__class_Oless__eq(U_1502,U_1504,U_1505)
| ~ c_Orderings_Oord__class_Oless__eq(U_1502,c_Groups_Ozero__class_Ozero(U_1502),U_1503)
| ~ class_Groups_Oordered__comm__monoid__add(U_1502) ),
inference(clausify,[status(thm)],[f_538_2]) ).
fof(f_539_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__increasing]) ).
fof(f_539_2,plain,
! [U_1509,U_1508,U_1507,U_1506] :
( c_Orderings_Oord__class_Oless__eq(U_1506,U_1508,c_Groups_Oplus__class_Oplus(U_1506,U_1507,U_1509))
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,U_1508,U_1509)
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ozero__class_Ozero(U_1506),U_1507)
| ~ class_Groups_Oordered__comm__monoid__add(U_1506) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
cnf(f_539_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1506,U_1508,c_Groups_Oplus__class_Oplus(U_1506,U_1507,U_1509))
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,U_1508,U_1509)
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ozero__class_Ozero(U_1506),U_1507)
| ~ class_Groups_Oordered__comm__monoid__add(U_1506) ),
inference(clausify,[status(thm)],[f_539_2]) ).
fof(f_540_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).
fof(f_540_2,plain,
! [U_1512,U_1511,U_1510] :
( ( ( c_Groups_Oplus__class_Oplus(U_1510,U_1511,U_1512) = c_Groups_Ozero__class_Ozero(U_1510)
| U_1512 != c_Groups_Ozero__class_Ozero(U_1510)
| U_1511 != c_Groups_Ozero__class_Ozero(U_1510) )
& ( ( U_1512 = c_Groups_Ozero__class_Ozero(U_1510)
& U_1511 = c_Groups_Ozero__class_Ozero(U_1510) )
| c_Groups_Oplus__class_Oplus(U_1510,U_1511,U_1512) != c_Groups_Ozero__class_Ozero(U_1510) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),U_1512)
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),U_1511)
| ~ class_Groups_Oordered__comm__monoid__add(U_1510) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
cnf(f_540_3,plain,
( U_1511 = c_Groups_Ozero__class_Ozero(U_1510)
| c_Groups_Oplus__class_Oplus(U_1510,U_1511,U_1512) != c_Groups_Ozero__class_Ozero(U_1510)
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),U_1512)
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),U_1511)
| ~ class_Groups_Oordered__comm__monoid__add(U_1510) ),
inference(clausify,[status(thm)],[f_540_2]) ).
cnf(f_540_4,plain,
( U_1512 = c_Groups_Ozero__class_Ozero(U_1510)
| c_Groups_Oplus__class_Oplus(U_1510,U_1511,U_1512) != c_Groups_Ozero__class_Ozero(U_1510)
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),U_1512)
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),U_1511)
| ~ class_Groups_Oordered__comm__monoid__add(U_1510) ),
inference(clausify,[status(thm)],[f_540_2]) ).
cnf(f_540_5,plain,
( c_Groups_Oplus__class_Oplus(U_1510,U_1511,U_1512) = c_Groups_Ozero__class_Ozero(U_1510)
| U_1512 != c_Groups_Ozero__class_Ozero(U_1510)
| U_1511 != c_Groups_Ozero__class_Ozero(U_1510)
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),U_1512)
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),U_1511)
| ~ class_Groups_Oordered__comm__monoid__add(U_1510) ),
inference(clausify,[status(thm)],[f_540_2]) ).
fof(f_541_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg]) ).
fof(f_541_2,plain,
! [U_1515,U_1514,U_1513] :
( c_Orderings_Oord__class_Oless__eq(U_1513,c_Groups_Ozero__class_Ozero(U_1513),c_Groups_Oplus__class_Oplus(U_1513,U_1514,U_1515))
| ~ c_Orderings_Oord__class_Oless__eq(U_1513,c_Groups_Ozero__class_Ozero(U_1513),U_1515)
| ~ c_Orderings_Oord__class_Oless__eq(U_1513,c_Groups_Ozero__class_Ozero(U_1513),U_1514)
| ~ class_Groups_Oordered__comm__monoid__add(U_1513) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
cnf(f_541_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1513,c_Groups_Ozero__class_Ozero(U_1513),c_Groups_Oplus__class_Oplus(U_1513,U_1514,U_1515))
| ~ c_Orderings_Oord__class_Oless__eq(U_1513,c_Groups_Ozero__class_Ozero(U_1513),U_1515)
| ~ c_Orderings_Oord__class_Oless__eq(U_1513,c_Groups_Ozero__class_Ozero(U_1513),U_1514)
| ~ class_Groups_Oordered__comm__monoid__add(U_1513) ),
inference(clausify,[status(thm)],[f_541_2]) ).
fof(f_542_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).
fof(f_542_2,plain,
! [U_1517,U_1516] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1516,c_Groups_Oplus__class_Oplus(U_1516,U_1517,U_1517),c_Groups_Ozero__class_Ozero(U_1516))
| ~ c_Orderings_Oord__class_Oless__eq(U_1516,U_1517,c_Groups_Ozero__class_Ozero(U_1516)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1516,U_1517,c_Groups_Ozero__class_Ozero(U_1516))
| ~ c_Orderings_Oord__class_Oless__eq(U_1516,c_Groups_Oplus__class_Oplus(U_1516,U_1517,U_1517),c_Groups_Ozero__class_Ozero(U_1516)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1516) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
cnf(f_542_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1516,U_1517,c_Groups_Ozero__class_Ozero(U_1516))
| ~ c_Orderings_Oord__class_Oless__eq(U_1516,c_Groups_Oplus__class_Oplus(U_1516,U_1517,U_1517),c_Groups_Ozero__class_Ozero(U_1516))
| ~ class_Groups_Olinordered__ab__group__add(U_1516) ),
inference(clausify,[status(thm)],[f_542_2]) ).
cnf(f_542_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1516,c_Groups_Oplus__class_Oplus(U_1516,U_1517,U_1517),c_Groups_Ozero__class_Ozero(U_1516))
| ~ c_Orderings_Oord__class_Oless__eq(U_1516,U_1517,c_Groups_Ozero__class_Ozero(U_1516))
| ~ class_Groups_Olinordered__ab__group__add(U_1516) ),
inference(clausify,[status(thm)],[f_542_2]) ).
fof(f_543_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).
fof(f_543_2,plain,
! [U_1519,U_1518] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1518,c_Groups_Ozero__class_Ozero(U_1518),c_Groups_Oplus__class_Oplus(U_1518,U_1519,U_1519))
| ~ c_Orderings_Oord__class_Oless__eq(U_1518,c_Groups_Ozero__class_Ozero(U_1518),U_1519) )
& ( c_Orderings_Oord__class_Oless__eq(U_1518,c_Groups_Ozero__class_Ozero(U_1518),U_1519)
| ~ c_Orderings_Oord__class_Oless__eq(U_1518,c_Groups_Ozero__class_Ozero(U_1518),c_Groups_Oplus__class_Oplus(U_1518,U_1519,U_1519)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1518) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
cnf(f_543_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1518,c_Groups_Ozero__class_Ozero(U_1518),U_1519)
| ~ c_Orderings_Oord__class_Oless__eq(U_1518,c_Groups_Ozero__class_Ozero(U_1518),c_Groups_Oplus__class_Oplus(U_1518,U_1519,U_1519))
| ~ class_Groups_Olinordered__ab__group__add(U_1518) ),
inference(clausify,[status(thm)],[f_543_2]) ).
cnf(f_543_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1518,c_Groups_Ozero__class_Ozero(U_1518),c_Groups_Oplus__class_Oplus(U_1518,U_1519,U_1519))
| ~ c_Orderings_Oord__class_Oless__eq(U_1518,c_Groups_Ozero__class_Ozero(U_1518),U_1519)
| ~ class_Groups_Olinordered__ab__group__add(U_1518) ),
inference(clausify,[status(thm)],[f_543_2]) ).
fof(f_544_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).
fof(f_544_2,plain,
! [U_1521,U_1520] :
( ( ( c_Orderings_Oord__class_Oless(U_1520,c_Groups_Ozero__class_Ozero(U_1520),c_Groups_Oplus__class_Oplus(U_1520,U_1521,U_1521))
| ~ c_Orderings_Oord__class_Oless(U_1520,c_Groups_Ozero__class_Ozero(U_1520),U_1521) )
& ( c_Orderings_Oord__class_Oless(U_1520,c_Groups_Ozero__class_Ozero(U_1520),U_1521)
| ~ c_Orderings_Oord__class_Oless(U_1520,c_Groups_Ozero__class_Ozero(U_1520),c_Groups_Oplus__class_Oplus(U_1520,U_1521,U_1521)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1520) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
cnf(f_544_3,plain,
( c_Orderings_Oord__class_Oless(U_1520,c_Groups_Ozero__class_Ozero(U_1520),U_1521)
| ~ c_Orderings_Oord__class_Oless(U_1520,c_Groups_Ozero__class_Ozero(U_1520),c_Groups_Oplus__class_Oplus(U_1520,U_1521,U_1521))
| ~ class_Groups_Olinordered__ab__group__add(U_1520) ),
inference(clausify,[status(thm)],[f_544_2]) ).
cnf(f_544_4,plain,
( c_Orderings_Oord__class_Oless(U_1520,c_Groups_Ozero__class_Ozero(U_1520),c_Groups_Oplus__class_Oplus(U_1520,U_1521,U_1521))
| ~ c_Orderings_Oord__class_Oless(U_1520,c_Groups_Ozero__class_Ozero(U_1520),U_1521)
| ~ class_Groups_Olinordered__ab__group__add(U_1520) ),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).
fof(f_545_2,plain,
! [U_1523,U_1522] :
( ( ( c_Orderings_Oord__class_Oless(U_1522,c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1523),c_Groups_Ozero__class_Ozero(U_1522))
| ~ c_Orderings_Oord__class_Oless(U_1522,U_1523,c_Groups_Ozero__class_Ozero(U_1522)) )
& ( c_Orderings_Oord__class_Oless(U_1522,U_1523,c_Groups_Ozero__class_Ozero(U_1522))
| ~ c_Orderings_Oord__class_Oless(U_1522,c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1523),c_Groups_Ozero__class_Ozero(U_1522)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1522) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
cnf(f_545_3,plain,
( c_Orderings_Oord__class_Oless(U_1522,U_1523,c_Groups_Ozero__class_Ozero(U_1522))
| ~ c_Orderings_Oord__class_Oless(U_1522,c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1523),c_Groups_Ozero__class_Ozero(U_1522))
| ~ class_Groups_Olinordered__ab__group__add(U_1522) ),
inference(clausify,[status(thm)],[f_545_2]) ).
cnf(f_545_4,plain,
( c_Orderings_Oord__class_Oless(U_1522,c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1523),c_Groups_Ozero__class_Ozero(U_1522))
| ~ c_Orderings_Oord__class_Oless(U_1522,U_1523,c_Groups_Ozero__class_Ozero(U_1522))
| ~ class_Groups_Olinordered__ab__group__add(U_1522) ),
inference(clausify,[status(thm)],[f_545_2]) ).
fof(f_546_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pos__pos]) ).
fof(f_546_2,plain,
! [U_1526,U_1525,U_1524] :
( c_Orderings_Oord__class_Oless(U_1524,c_Groups_Ozero__class_Ozero(U_1524),c_Groups_Oplus__class_Oplus(U_1524,U_1525,U_1526))
| ~ c_Orderings_Oord__class_Oless(U_1524,c_Groups_Ozero__class_Ozero(U_1524),U_1526)
| ~ c_Orderings_Oord__class_Oless(U_1524,c_Groups_Ozero__class_Ozero(U_1524),U_1525)
| ~ class_Groups_Oordered__comm__monoid__add(U_1524) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
cnf(f_546_3,plain,
( c_Orderings_Oord__class_Oless(U_1524,c_Groups_Ozero__class_Ozero(U_1524),c_Groups_Oplus__class_Oplus(U_1524,U_1525,U_1526))
| ~ c_Orderings_Oord__class_Oless(U_1524,c_Groups_Ozero__class_Ozero(U_1524),U_1526)
| ~ c_Orderings_Oord__class_Oless(U_1524,c_Groups_Ozero__class_Ozero(U_1524),U_1525)
| ~ class_Groups_Oordered__comm__monoid__add(U_1524) ),
inference(clausify,[status(thm)],[f_546_2]) ).
fof(f_547_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__add__strict]) ).
fof(f_547_2,plain,
! [U_1530,U_1529,U_1528,U_1527] :
( c_Orderings_Oord__class_Oless(U_1527,U_1529,c_Groups_Oplus__class_Oplus(U_1527,U_1528,U_1530))
| ~ c_Orderings_Oord__class_Oless(U_1527,U_1529,U_1530)
| ~ c_Orderings_Oord__class_Oless(U_1527,c_Groups_Ozero__class_Ozero(U_1527),U_1528)
| ~ class_Rings_Olinordered__semidom(U_1527) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
cnf(f_547_3,plain,
( c_Orderings_Oord__class_Oless(U_1527,U_1529,c_Groups_Oplus__class_Oplus(U_1527,U_1528,U_1530))
| ~ c_Orderings_Oord__class_Oless(U_1527,U_1529,U_1530)
| ~ c_Orderings_Oord__class_Oless(U_1527,c_Groups_Ozero__class_Ozero(U_1527),U_1528)
| ~ class_Rings_Olinordered__semidom(U_1527) ),
inference(clausify,[status(thm)],[f_547_2]) ).
fof(f_548_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__neg__neg]) ).
fof(f_548_2,plain,
! [U_1533,U_1532,U_1531] :
( c_Orderings_Oord__class_Oless(U_1531,c_Groups_Oplus__class_Oplus(U_1531,U_1532,U_1533),c_Groups_Ozero__class_Ozero(U_1531))
| ~ c_Orderings_Oord__class_Oless(U_1531,U_1533,c_Groups_Ozero__class_Ozero(U_1531))
| ~ c_Orderings_Oord__class_Oless(U_1531,U_1532,c_Groups_Ozero__class_Ozero(U_1531))
| ~ class_Groups_Oordered__comm__monoid__add(U_1531) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
cnf(f_548_3,plain,
( c_Orderings_Oord__class_Oless(U_1531,c_Groups_Oplus__class_Oplus(U_1531,U_1532,U_1533),c_Groups_Ozero__class_Ozero(U_1531))
| ~ c_Orderings_Oord__class_Oless(U_1531,U_1533,c_Groups_Ozero__class_Ozero(U_1531))
| ~ c_Orderings_Oord__class_Oless(U_1531,U_1532,c_Groups_Ozero__class_Ozero(U_1531))
| ~ class_Groups_Oordered__comm__monoid__add(U_1531) ),
inference(clausify,[status(thm)],[f_548_2]) ).
fof(f_549_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).
fof(f_549_2,plain,
! [U_1535,U_1534] :
( ( ( c_Orderings_Oord__class_Oless(U_1534,c_Groups_Oplus__class_Oplus(U_1534,U_1535,U_1535),c_Groups_Ozero__class_Ozero(U_1534))
| ~ c_Orderings_Oord__class_Oless(U_1534,U_1535,c_Groups_Ozero__class_Ozero(U_1534)) )
& ( c_Orderings_Oord__class_Oless(U_1534,U_1535,c_Groups_Ozero__class_Ozero(U_1534))
| ~ c_Orderings_Oord__class_Oless(U_1534,c_Groups_Oplus__class_Oplus(U_1534,U_1535,U_1535),c_Groups_Ozero__class_Ozero(U_1534)) ) )
| ~ class_Rings_Olinordered__idom(U_1534) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
cnf(f_549_3,plain,
( c_Orderings_Oord__class_Oless(U_1534,U_1535,c_Groups_Ozero__class_Ozero(U_1534))
| ~ c_Orderings_Oord__class_Oless(U_1534,c_Groups_Oplus__class_Oplus(U_1534,U_1535,U_1535),c_Groups_Ozero__class_Ozero(U_1534))
| ~ class_Rings_Olinordered__idom(U_1534) ),
inference(clausify,[status(thm)],[f_549_2]) ).
cnf(f_549_4,plain,
( c_Orderings_Oord__class_Oless(U_1534,c_Groups_Oplus__class_Oplus(U_1534,U_1535,U_1535),c_Groups_Ozero__class_Ozero(U_1534))
| ~ c_Orderings_Oord__class_Oless(U_1534,U_1535,c_Groups_Ozero__class_Ozero(U_1534))
| ~ class_Rings_Olinordered__idom(U_1534) ),
inference(clausify,[status(thm)],[f_549_2]) ).
fof(f_550_1,plain,
! [V_m_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff]) ).
fof(f_550_2,plain,
! [U_1537,U_1536] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1536),c_RealDef_Oreal(tc_Nat_Onat,U_1537))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1536,U_1537) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1536,U_1537)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1536),c_RealDef_Oreal(tc_Nat_Onat,U_1537)) ) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
( ! [U_1541,U_1539] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1539),c_RealDef_Oreal(tc_Nat_Onat,U_1541))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1539,U_1541) )
& ! [U_1540,U_1538] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1538,U_1540)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1538),c_RealDef_Oreal(tc_Nat_Onat,U_1540)) ) ),
inference(miniscope,[status(thm)],[f_550_2]) ).
cnf(f_550_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1538,U_1540)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1538),c_RealDef_Oreal(tc_Nat_Onat,U_1540)) ),
inference(clausify,[status(thm)],[f_550_3]) ).
cnf(f_550_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1539),c_RealDef_Oreal(tc_Nat_Onat,U_1541))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1539,U_1541) ),
inference(clausify,[status(thm)],[f_550_3]) ).
fof(f_551_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__less__mono]) ).
fof(f_551_2,plain,
! [U_1546,U_1545,U_1544,U_1543,U_1542] :
( c_Orderings_Oord__class_Oless(U_1542,c_Groups_Oplus__class_Oplus(U_1542,U_1543,U_1545),c_Groups_Oplus__class_Oplus(U_1542,U_1544,U_1546))
| ~ c_Orderings_Oord__class_Oless(U_1542,U_1545,U_1546)
| ~ c_Orderings_Oord__class_Oless__eq(U_1542,U_1543,U_1544)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1542) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
cnf(f_551_3,plain,
( c_Orderings_Oord__class_Oless(U_1542,c_Groups_Oplus__class_Oplus(U_1542,U_1543,U_1545),c_Groups_Oplus__class_Oplus(U_1542,U_1544,U_1546))
| ~ c_Orderings_Oord__class_Oless(U_1542,U_1545,U_1546)
| ~ c_Orderings_Oord__class_Oless__eq(U_1542,U_1543,U_1544)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1542) ),
inference(clausify,[status(thm)],[f_551_2]) ).
fof(f_552_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__le__mono]) ).
fof(f_552_2,plain,
! [U_1551,U_1550,U_1549,U_1548,U_1547] :
( c_Orderings_Oord__class_Oless(U_1547,c_Groups_Oplus__class_Oplus(U_1547,U_1548,U_1550),c_Groups_Oplus__class_Oplus(U_1547,U_1549,U_1551))
| ~ c_Orderings_Oord__class_Oless__eq(U_1547,U_1550,U_1551)
| ~ c_Orderings_Oord__class_Oless(U_1547,U_1548,U_1549)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1547) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
cnf(f_552_3,plain,
( c_Orderings_Oord__class_Oless(U_1547,c_Groups_Oplus__class_Oplus(U_1547,U_1548,U_1550),c_Groups_Oplus__class_Oplus(U_1547,U_1549,U_1551))
| ~ c_Orderings_Oord__class_Oless__eq(U_1547,U_1550,U_1551)
| ~ c_Orderings_Oord__class_Oless(U_1547,U_1548,U_1549)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1547) ),
inference(clausify,[status(thm)],[f_552_2]) ).
fof(f_553_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__one]) ).
fof(f_553_2,plain,
! [U_1553,U_1552] :
( c_Orderings_Oord__class_Oless(U_1552,U_1553,c_Groups_Oplus__class_Oplus(U_1552,U_1553,c_Groups_Oone__class_Oone(U_1552)))
| ~ class_Rings_Olinordered__semidom(U_1552) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
cnf(f_553_3,plain,
( c_Orderings_Oord__class_Oless(U_1552,U_1553,c_Groups_Oplus__class_Oplus(U_1552,U_1553,c_Groups_Oone__class_Oone(U_1552)))
| ~ class_Rings_Olinordered__semidom(U_1552) ),
inference(clausify,[status(thm)],[f_553_2]) ).
fof(f_554_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__minus]) ).
fof(f_554_2,plain,
! [U_1555,U_1554] :
( c_Groups_Oplus__class_Oplus(U_1554,U_1555,c_Groups_Ouminus__class_Ouminus(U_1554,U_1555)) = c_Groups_Ozero__class_Ozero(U_1554)
| ~ class_Groups_Ogroup__add(U_1554) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
cnf(f_554_3,plain,
( c_Groups_Oplus__class_Oplus(U_1554,U_1555,c_Groups_Ouminus__class_Ouminus(U_1554,U_1555)) = c_Groups_Ozero__class_Ozero(U_1554)
| ~ class_Groups_Ogroup__add(U_1554) ),
inference(clausify,[status(thm)],[f_554_2]) ).
fof(f_555_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).
fof(f_555_2,plain,
! [U_1558,U_1557,U_1556] :
( ( ( U_1557 = c_Groups_Ouminus__class_Ouminus(U_1556,U_1558)
| c_Groups_Oplus__class_Oplus(U_1556,U_1557,U_1558) != c_Groups_Ozero__class_Ozero(U_1556) )
& ( c_Groups_Oplus__class_Oplus(U_1556,U_1557,U_1558) = c_Groups_Ozero__class_Ozero(U_1556)
| U_1557 != c_Groups_Ouminus__class_Ouminus(U_1556,U_1558) ) )
| ~ class_Groups_Ogroup__add(U_1556) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
cnf(f_555_3,plain,
( c_Groups_Oplus__class_Oplus(U_1556,U_1557,U_1558) = c_Groups_Ozero__class_Ozero(U_1556)
| U_1557 != c_Groups_Ouminus__class_Ouminus(U_1556,U_1558)
| ~ class_Groups_Ogroup__add(U_1556) ),
inference(clausify,[status(thm)],[f_555_2]) ).
cnf(f_555_4,plain,
( U_1557 = c_Groups_Ouminus__class_Ouminus(U_1556,U_1558)
| c_Groups_Oplus__class_Oplus(U_1556,U_1557,U_1558) != c_Groups_Ozero__class_Ozero(U_1556)
| ~ class_Groups_Ogroup__add(U_1556) ),
inference(clausify,[status(thm)],[f_555_2]) ).
fof(f_556_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_left__minus]) ).
fof(f_556_2,plain,
! [U_1560,U_1559] :
( c_Groups_Oplus__class_Oplus(U_1559,c_Groups_Ouminus__class_Ouminus(U_1559,U_1560),U_1560) = c_Groups_Ozero__class_Ozero(U_1559)
| ~ class_Groups_Ogroup__add(U_1559) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
cnf(f_556_3,plain,
( c_Groups_Oplus__class_Oplus(U_1559,c_Groups_Ouminus__class_Ouminus(U_1559,U_1560),U_1560) = c_Groups_Ozero__class_Ozero(U_1559)
| ~ class_Groups_Ogroup__add(U_1559) ),
inference(clausify,[status(thm)],[f_556_2]) ).
fof(f_557_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__left__minus]) ).
fof(f_557_2,plain,
! [U_1562,U_1561] :
( c_Groups_Oplus__class_Oplus(U_1561,c_Groups_Ouminus__class_Ouminus(U_1561,U_1562),U_1562) = c_Groups_Ozero__class_Ozero(U_1561)
| ~ class_Groups_Oab__group__add(U_1561) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
cnf(f_557_3,plain,
( c_Groups_Oplus__class_Oplus(U_1561,c_Groups_Ouminus__class_Ouminus(U_1561,U_1562),U_1562) = c_Groups_Ozero__class_Ozero(U_1561)
| ~ class_Groups_Oab__group__add(U_1561) ),
inference(clausify,[status(thm)],[f_557_2]) ).
fof(f_558_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__unique]) ).
fof(f_558_2,plain,
! [U_1565,U_1564,U_1563] :
( c_Groups_Ouminus__class_Ouminus(U_1563,U_1564) = U_1565
| c_Groups_Oplus__class_Oplus(U_1563,U_1564,U_1565) != c_Groups_Ozero__class_Ozero(U_1563)
| ~ class_Groups_Ogroup__add(U_1563) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
cnf(f_558_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1563,U_1564) = U_1565
| c_Groups_Oplus__class_Oplus(U_1563,U_1564,U_1565) != c_Groups_Ozero__class_Ozero(U_1563)
| ~ class_Groups_Ogroup__add(U_1563) ),
inference(clausify,[status(thm)],[f_558_2]) ).
fof(f_559_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) )
& ( V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)
| c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff]) ).
fof(f_559_2,plain,
! [U_1568,U_1567,U_1566] :
( ( ( c_Groups_Oplus__class_Oplus(U_1566,U_1567,U_1568) = c_Groups_Ozero__class_Ozero(U_1566)
| U_1568 != c_Groups_Ouminus__class_Ouminus(U_1566,U_1567) )
& ( U_1568 = c_Groups_Ouminus__class_Ouminus(U_1566,U_1567)
| c_Groups_Oplus__class_Oplus(U_1566,U_1567,U_1568) != c_Groups_Ozero__class_Ozero(U_1566) ) )
| ~ class_Groups_Ogroup__add(U_1566) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
cnf(f_559_3,plain,
( U_1568 = c_Groups_Ouminus__class_Ouminus(U_1566,U_1567)
| c_Groups_Oplus__class_Oplus(U_1566,U_1567,U_1568) != c_Groups_Ozero__class_Ozero(U_1566)
| ~ class_Groups_Ogroup__add(U_1566) ),
inference(clausify,[status(thm)],[f_559_2]) ).
cnf(f_559_4,plain,
( c_Groups_Oplus__class_Oplus(U_1566,U_1567,U_1568) = c_Groups_Ozero__class_Ozero(U_1566)
| U_1568 != c_Groups_Ouminus__class_Ouminus(U_1566,U_1567)
| ~ class_Groups_Ogroup__add(U_1566) ),
inference(clausify,[status(thm)],[f_559_2]) ).
fof(f_560_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__def]) ).
fof(f_560_2,plain,
! [U_1571,U_1570,U_1569] :
( c_Groups_Ominus__class_Ominus(U_1569,U_1570,U_1571) = c_Groups_Oplus__class_Oplus(U_1569,U_1570,c_Groups_Ouminus__class_Ouminus(U_1569,U_1571))
| ~ class_Groups_Ogroup__add(U_1569) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
cnf(f_560_3,plain,
( c_Groups_Ominus__class_Ominus(U_1569,U_1570,U_1571) = c_Groups_Oplus__class_Oplus(U_1569,U_1570,c_Groups_Ouminus__class_Ouminus(U_1569,U_1571))
| ~ class_Groups_Ogroup__add(U_1569) ),
inference(clausify,[status(thm)],[f_560_2]) ).
fof(f_561_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__diff__minus]) ).
fof(f_561_2,plain,
! [U_1574,U_1573,U_1572] :
( c_Groups_Ominus__class_Ominus(U_1572,U_1573,U_1574) = c_Groups_Oplus__class_Oplus(U_1572,U_1573,c_Groups_Ouminus__class_Ouminus(U_1572,U_1574))
| ~ class_Groups_Oab__group__add(U_1572) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
cnf(f_561_3,plain,
( c_Groups_Ominus__class_Ominus(U_1572,U_1573,U_1574) = c_Groups_Oplus__class_Oplus(U_1572,U_1573,c_Groups_Ouminus__class_Ouminus(U_1572,U_1574))
| ~ class_Groups_Oab__group__add(U_1572) ),
inference(clausify,[status(thm)],[f_561_2]) ).
fof(f_562_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add]) ).
fof(f_562_2,plain,
! [U_1577,U_1576,U_1575] :
( c_Groups_Ominus__class_Ominus(U_1575,U_1576,c_Groups_Ouminus__class_Ouminus(U_1575,U_1577)) = c_Groups_Oplus__class_Oplus(U_1575,U_1576,U_1577)
| ~ class_Groups_Ogroup__add(U_1575) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
cnf(f_562_3,plain,
( c_Groups_Ominus__class_Ominus(U_1575,U_1576,c_Groups_Ouminus__class_Ouminus(U_1575,U_1577)) = c_Groups_Oplus__class_Oplus(U_1575,U_1576,U_1577)
| ~ class_Groups_Ogroup__add(U_1575) ),
inference(clausify,[status(thm)],[f_562_2]) ).
fof(f_563_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right]) ).
fof(f_563_2,plain,
! [U_1579,U_1578] :
( c_Groups_Oplus__class_Oplus(U_1578,U_1579,c_Int_Onumber__class_Onumber__of(U_1578,c_Int_OPls)) = U_1579
| ~ class_Int_Onumber__ring(U_1578) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
cnf(f_563_3,plain,
( c_Groups_Oplus__class_Oplus(U_1578,U_1579,c_Int_Onumber__class_Onumber__of(U_1578,c_Int_OPls)) = U_1579
| ~ class_Int_Onumber__ring(U_1578) ),
inference(clausify,[status(thm)],[f_563_2]) ).
fof(f_564_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__numeral__0]) ).
fof(f_564_2,plain,
! [U_1581,U_1580] :
( c_Groups_Oplus__class_Oplus(U_1580,c_Int_Onumber__class_Onumber__of(U_1580,c_Int_OPls),U_1581) = U_1581
| ~ class_Int_Onumber__ring(U_1580) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
cnf(f_564_3,plain,
( c_Groups_Oplus__class_Oplus(U_1580,c_Int_Onumber__class_Onumber__of(U_1580,c_Int_OPls),U_1581) = U_1581
| ~ class_Int_Onumber__ring(U_1580) ),
inference(clausify,[status(thm)],[f_564_2]) ).
fof(f_565_1,plain,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).
fof(f_565_2,plain,
! [U_1583,U_1582] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,U_1582,U_1583))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1582) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
cnf(f_565_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,U_1582,U_1583))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1582) ),
inference(clausify,[status(thm)],[f_565_2]) ).
fof(f_566_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq]) ).
fof(f_566_2,plain,
! [U_1586,U_1585,U_1584] :
( c_Orderings_Oord__class_Oless__eq(U_1584,c_Groups_Oabs__class_Oabs(U_1584,c_Groups_Oplus__class_Oplus(U_1584,U_1585,U_1586)),c_Groups_Oplus__class_Oplus(U_1584,c_Groups_Oabs__class_Oabs(U_1584,U_1585),c_Groups_Oabs__class_Oabs(U_1584,U_1586)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1584) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
cnf(f_566_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1584,c_Groups_Oabs__class_Oabs(U_1584,c_Groups_Oplus__class_Oplus(U_1584,U_1585,U_1586)),c_Groups_Oplus__class_Oplus(U_1584,c_Groups_Oabs__class_Oabs(U_1584,U_1585),c_Groups_Oabs__class_Oabs(U_1584,U_1586)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1584) ),
inference(clausify,[status(thm)],[f_566_2]) ).
fof(f_567_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| ! [B_m] : V_n_2 != c_Nat_OSuc(B_m) )
& ( ? [B_m] : V_n_2 = c_Nat_OSuc(B_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).
fof(f_567_2,plain,
! [U_1589] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1589)
| ! [U_1588] : U_1589 != c_Nat_OSuc(U_1588) )
& ( ? [U_1587] : U_1589 = c_Nat_OSuc(U_1587)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1589) ) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
( ! [U_1591] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1591)
| ! [U_1588] : U_1591 != c_Nat_OSuc(U_1588) )
& ! [U_1590] :
( ? [U_1587] : U_1590 = c_Nat_OSuc(U_1587)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1590) ) ),
inference(miniscope,[status(thm)],[f_567_2]) ).
fof(f_567_4,plain,
( ! [U_1591] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1591)
| ! [U_1588] : U_1591 != c_Nat_OSuc(U_1588) )
& ! [U_1590] :
( U_1590 = c_Nat_OSuc(sK31(U_1590))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1590) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1587,sK31(U_1590))],[f_567_3]) ).
cnf(f_567_5,plain,
( U_1590 = c_Nat_OSuc(sK31(U_1590))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1590) ),
inference(clausify,[status(thm)],[f_567_4]) ).
cnf(f_567_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1591)
| U_1591 != c_Nat_OSuc(U_1588) ),
inference(clausify,[status(thm)],[f_567_4]) ).
fof(f_568_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc0]) ).
fof(f_568_2,plain,
! [U_1592] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1592,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1592 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1592,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
fof(f_568_3,plain,
( ! [U_1594] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1594,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1594 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1593] :
( U_1593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1593,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_568_2]) ).
cnf(f_568_4,plain,
( U_1593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1593,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_568_3]) ).
cnf(f_568_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1594,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1594 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_568_3]) ).
fof(f_569_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
| ( ! [B_j] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
| V_m_2 != c_Nat_OSuc(B_j) )
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
& V_m_2 = c_Nat_OSuc(B_j) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).
fof(f_569_2,plain,
! [U_1598,U_1597] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1597,c_Nat_OSuc(U_1598))
| ( ! [U_1596] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1596,U_1598)
| U_1597 != c_Nat_OSuc(U_1596) )
& U_1597 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_1595] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1595,U_1598)
& U_1597 = c_Nat_OSuc(U_1595) )
| U_1597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1597,c_Nat_OSuc(U_1598)) ) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
( ! [U_1602,U_1600] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1600,c_Nat_OSuc(U_1602))
| ( ! [U_1596] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1596,U_1602)
| U_1600 != c_Nat_OSuc(U_1596) )
& U_1600 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1601,U_1599] :
( ? [U_1595] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1595,U_1601)
& U_1599 = c_Nat_OSuc(U_1595) )
| U_1599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1599,c_Nat_OSuc(U_1601)) ) ),
inference(miniscope,[status(thm)],[f_569_2]) ).
fof(f_569_4,plain,
( ! [U_1602,U_1600] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1600,c_Nat_OSuc(U_1602))
| ( ! [U_1596] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1596,U_1602)
| U_1600 != c_Nat_OSuc(U_1596) )
& U_1600 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1601,U_1599] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(U_1601,U_1599),U_1601)
& U_1599 = c_Nat_OSuc(sK32(U_1601,U_1599)) )
| U_1599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1599,c_Nat_OSuc(U_1601)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1595,sK32(U_1601,U_1599))],[f_569_3]) ).
cnf(f_569_5,plain,
( U_1599 = c_Nat_OSuc(sK32(U_1601,U_1599))
| U_1599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1599,c_Nat_OSuc(U_1601)) ),
inference(clausify,[status(thm)],[f_569_4]) ).
cnf(f_569_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(U_1601,U_1599),U_1601)
| U_1599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1599,c_Nat_OSuc(U_1601)) ),
inference(clausify,[status(thm)],[f_569_4]) ).
cnf(f_569_7,plain,
( U_1600 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1600,c_Nat_OSuc(U_1602)) ),
inference(clausify,[status(thm)],[f_569_4]) ).
cnf(f_569_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1596,U_1602)
| U_1600 != c_Nat_OSuc(U_1596)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1600,c_Nat_OSuc(U_1602)) ),
inference(clausify,[status(thm)],[f_569_4]) ).
fof(f_570_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD]) ).
fof(f_570_2,plain,
! [U_1604,U_1603] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1603,U_1604)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1603),U_1604) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
cnf(f_570_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1603,U_1604)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1603),U_1604) ),
inference(clausify,[status(thm)],[f_570_2]) ).
fof(f_571_1,plain,
! [V_n_2,V_m_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
| V_n_2 != V_m_2 )
& ( V_n_2 = V_m_2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).
fof(f_571_2,plain,
! [U_1606,U_1605] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1606,c_Nat_OSuc(U_1605))
| U_1606 != U_1605 )
& ( U_1606 = U_1605
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1606,c_Nat_OSuc(U_1605)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1605,U_1606) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
cnf(f_571_3,plain,
( U_1606 = U_1605
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1606,c_Nat_OSuc(U_1605))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1605,U_1606) ),
inference(clausify,[status(thm)],[f_571_2]) ).
cnf(f_571_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1606,c_Nat_OSuc(U_1605))
| U_1606 != U_1605
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1605,U_1606) ),
inference(clausify,[status(thm)],[f_571_2]) ).
fof(f_572_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leI]) ).
fof(f_572_2,plain,
! [U_1608,U_1607] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1607),U_1608)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1607,U_1608) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
cnf(f_572_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1607),U_1608)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1607,U_1608) ),
inference(clausify,[status(thm)],[f_572_2]) ).
fof(f_573_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc]) ).
fof(f_573_2,plain,
! [U_1610,U_1609] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1609,c_Nat_OSuc(U_1610))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1609,U_1610) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
cnf(f_573_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1609,c_Nat_OSuc(U_1610))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1609,U_1610) ),
inference(clausify,[status(thm)],[f_573_2]) ).
fof(f_574_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).
fof(f_574_2,plain,
! [U_1612,U_1611] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1611),U_1612)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1611,U_1612) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1611,U_1612)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1611),U_1612) ) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
( ! [U_1616,U_1614] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1614),U_1616)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1614,U_1616) )
& ! [U_1615,U_1613] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1613,U_1615)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1613),U_1615) ) ),
inference(miniscope,[status(thm)],[f_574_2]) ).
cnf(f_574_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1613,U_1615)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1613),U_1615) ),
inference(clausify,[status(thm)],[f_574_3]) ).
cnf(f_574_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1614),U_1616)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1614,U_1616) ),
inference(clausify,[status(thm)],[f_574_3]) ).
fof(f_575_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).
fof(f_575_2,plain,
! [U_1618,U_1617] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1617,c_Nat_OSuc(U_1618))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1617,U_1618) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1617,U_1618)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1617,c_Nat_OSuc(U_1618)) ) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
( ! [U_1622,U_1620] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1620,c_Nat_OSuc(U_1622))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1620,U_1622) )
& ! [U_1621,U_1619] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1619,U_1621)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1619,c_Nat_OSuc(U_1621)) ) ),
inference(miniscope,[status(thm)],[f_575_2]) ).
cnf(f_575_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1619,U_1621)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1619,c_Nat_OSuc(U_1621)) ),
inference(clausify,[status(thm)],[f_575_3]) ).
cnf(f_575_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1620,c_Nat_OSuc(U_1622))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1620,U_1622) ),
inference(clausify,[status(thm)],[f_575_3]) ).
fof(f_576_1,plain,
! [V_m_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).
fof(f_576_2,plain,
! [U_1624,U_1623] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1623,U_1624)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1623),U_1624) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1623),U_1624)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1623,U_1624) ) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
( ! [U_1628,U_1626] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1626,U_1628)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1626),U_1628) )
& ! [U_1627,U_1625] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1625),U_1627)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1625,U_1627) ) ),
inference(miniscope,[status(thm)],[f_576_2]) ).
cnf(f_576_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1625),U_1627)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1625,U_1627) ),
inference(clausify,[status(thm)],[f_576_3]) ).
cnf(f_576_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1626,U_1628)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1626),U_1628) ),
inference(clausify,[status(thm)],[f_576_3]) ).
fof(f_577_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
inference(fof_nnf,[status(thm)],[fact_diff__less__Suc]) ).
fof(f_577_2,plain,
! [U_1630,U_1629] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1629,U_1630),c_Nat_OSuc(U_1629)),
inference(variable_rename,[status(thm)],[f_577_1]) ).
cnf(f_577_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1629,U_1630),c_Nat_OSuc(U_1629)),
inference(clausify,[status(thm)],[f_577_2]) ).
fof(f_578_1,plain,
! [V_m,V_n] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__le]) ).
fof(f_578_2,plain,
! [U_1632,U_1631] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1632),U_1631) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1632,U_1631))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1631,U_1632) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
cnf(f_578_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1632),U_1631) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1632,U_1631))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1631,U_1632) ),
inference(clausify,[status(thm)],[f_578_2]) ).
fof(f_579_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y_2 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) )
& ( V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__eq__0__iff]) ).
fof(f_579_2,plain,
! [U_1634,U_1633] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1633,U_1634) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1634 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1633) )
& ( U_1634 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1633)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1633,U_1634) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
fof(f_579_3,plain,
( ! [U_1638,U_1636] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1636,U_1638) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1638 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1636) )
& ! [U_1637,U_1635] :
( U_1637 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1635)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1635,U_1637) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_579_2]) ).
cnf(f_579_4,plain,
( U_1637 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1635)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1635,U_1637) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_579_3]) ).
cnf(f_579_5,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1636,U_1638) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1638 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1636) ),
inference(clausify,[status(thm)],[f_579_3]) ).
fof(f_580_1,plain,
! [V_a_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != V_a_2 )
& ( V_x_2 = V_a_2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff]) ).
fof(f_580_2,plain,
! [U_1640,U_1639] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1639,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1640)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1639 != U_1640 )
& ( U_1639 = U_1640
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1639,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1640)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
( ! [U_1644,U_1642] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1642,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1644)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1642 != U_1644 )
& ! [U_1643,U_1641] :
( U_1641 = U_1643
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1641,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1643)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_580_2]) ).
cnf(f_580_4,plain,
( U_1641 = U_1643
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1641,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1643)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_580_3]) ).
cnf(f_580_5,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1642,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1644)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1642 != U_1644 ),
inference(clausify,[status(thm)],[f_580_3]) ).
fof(f_581_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
cnf(f_581_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_581_1]) ).
fof(f_582_1,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).
cnf(f_582_2,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_582_1]) ).
fof(f_583_1,plain,
! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)),
inference(fof_nnf,[status(thm)],[fact_real__diff__def]) ).
fof(f_583_2,plain,
! [U_1646,U_1645] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1645,U_1646) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1645,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1646)),
inference(variable_rename,[status(thm)],[f_583_1]) ).
cnf(f_583_3,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1645,U_1646) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1645,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1646)),
inference(clausify,[status(thm)],[f_583_2]) ).
fof(f_584_1,plain,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)),
inference(fof_nnf,[status(thm)],[fact_minus__real__def]) ).
fof(f_584_2,plain,
! [U_1648,U_1647] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1647,U_1648) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1647,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1648)),
inference(variable_rename,[status(thm)],[f_584_1]) ).
cnf(f_584_3,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1647,U_1648) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1647,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1648)),
inference(clausify,[status(thm)],[f_584_2]) ).
fof(f_585_1,plain,
! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))),
inference(fof_nnf,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(f_585_2,plain,
! [U_1650,U_1649] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1649,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1650))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1650,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1649))),
inference(variable_rename,[status(thm)],[f_585_1]) ).
cnf(f_585_3,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1649,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1650))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1650,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1649))),
inference(clausify,[status(thm)],[f_585_2]) ).
fof(f_586_1,plain,
! [V_x] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__abs]) ).
fof(f_586_2,plain,
! [U_1651] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1651,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1651),
inference(variable_rename,[status(thm)],[f_586_1]) ).
cnf(f_586_3,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1651,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1651),
inference(clausify,[status(thm)],[f_586_2]) ).
fof(f_587_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff]) ).
fof(f_587_2,plain,
! [U_1654,U_1653,U_1652] :
( ( ( c_Groups_Oplus__class_Oplus(U_1652,c_Power_Opower__class_Opower(U_1652,U_1653,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1652,U_1654,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_1652)
| U_1654 != c_Groups_Ozero__class_Ozero(U_1652)
| U_1653 != c_Groups_Ozero__class_Ozero(U_1652) )
& ( ( U_1654 = c_Groups_Ozero__class_Ozero(U_1652)
& U_1653 = c_Groups_Ozero__class_Ozero(U_1652) )
| c_Groups_Oplus__class_Oplus(U_1652,c_Power_Opower__class_Opower(U_1652,U_1653,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1652,U_1654,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_1652) ) )
| ~ class_Rings_Olinordered__idom(U_1652) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
cnf(f_587_3,plain,
( U_1653 = c_Groups_Ozero__class_Ozero(U_1652)
| c_Groups_Oplus__class_Oplus(U_1652,c_Power_Opower__class_Opower(U_1652,U_1653,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1652,U_1654,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_1652)
| ~ class_Rings_Olinordered__idom(U_1652) ),
inference(clausify,[status(thm)],[f_587_2]) ).
cnf(f_587_4,plain,
( U_1654 = c_Groups_Ozero__class_Ozero(U_1652)
| c_Groups_Oplus__class_Oplus(U_1652,c_Power_Opower__class_Opower(U_1652,U_1653,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1652,U_1654,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_1652)
| ~ class_Rings_Olinordered__idom(U_1652) ),
inference(clausify,[status(thm)],[f_587_2]) ).
cnf(f_587_5,plain,
( c_Groups_Oplus__class_Oplus(U_1652,c_Power_Opower__class_Opower(U_1652,U_1653,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1652,U_1654,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_1652)
| U_1654 != c_Groups_Ozero__class_Ozero(U_1652)
| U_1653 != c_Groups_Ozero__class_Ozero(U_1652)
| ~ class_Rings_Olinordered__idom(U_1652) ),
inference(clausify,[status(thm)],[f_587_2]) ).
fof(f_588_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)),
inference(fof_nnf,[status(thm)],[fact_two__realpow__gt]) ).
fof(f_588_2,plain,
! [U_1655] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1655),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_1655)),
inference(variable_rename,[status(thm)],[f_588_1]) ).
cnf(f_588_3,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1655),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_1655)),
inference(clausify,[status(thm)],[f_588_2]) ).
fof(f_589_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__sum__zero__iff]) ).
fof(f_589_2,plain,
! [U_1657,U_1656] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1656,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1657,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1657 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1656 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_1657 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_1656 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1656,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1657,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
( ! [U_1661,U_1659] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1659,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1661,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1661 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1659 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1660,U_1658] :
( ( U_1660 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_1658 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1658,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1660,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_589_2]) ).
cnf(f_589_4,plain,
( U_1658 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1658,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1660,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_589_3]) ).
cnf(f_589_5,plain,
( U_1660 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1658,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1660,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_589_3]) ).
cnf(f_589_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1659,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1661,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1661 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1659 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_589_3]) ).
fof(f_590_1,plain,
! [V_y,V_u,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(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_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__less]) ).
fof(f_590_2,plain,
! [U_1664,U_1663,U_1662] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1662,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1664,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1664),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1663,c_NthRoot_Osqrt(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_Oabs__class_Oabs(tc_RealDef_Oreal,U_1662),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1663,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
cnf(f_590_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1662,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1664,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1664),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1663,c_NthRoot_Osqrt(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_Oabs__class_Oabs(tc_RealDef_Oreal,U_1662),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1663,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(clausify,[status(thm)],[f_590_2]) ).
fof(f_591_1,plain,
! [V_fa_2] :
( ( c_SEQ_Osubseq(V_fa_2)
| ? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))) )
& ( ! [B_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n)))
| ~ c_SEQ_Osubseq(V_fa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_subseq__Suc__iff]) ).
fof(f_591_2,plain,
! [U_1667] :
( ( c_SEQ_Osubseq(U_1667)
| ? [U_1666] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1667,U_1666),hAPP(U_1667,c_Nat_OSuc(U_1666))) )
& ( ! [U_1665] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1667,U_1665),hAPP(U_1667,c_Nat_OSuc(U_1665)))
| ~ c_SEQ_Osubseq(U_1667) ) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
fof(f_591_3,plain,
( ! [U_1669] :
( c_SEQ_Osubseq(U_1669)
| ? [U_1666] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1669,U_1666),hAPP(U_1669,c_Nat_OSuc(U_1666))) )
& ! [U_1668] :
( ! [U_1665] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1668,U_1665),hAPP(U_1668,c_Nat_OSuc(U_1665)))
| ~ c_SEQ_Osubseq(U_1668) ) ),
inference(miniscope,[status(thm)],[f_591_2]) ).
fof(f_591_4,plain,
( ! [U_1669] :
( c_SEQ_Osubseq(U_1669)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1669,sK33(U_1669)),hAPP(U_1669,c_Nat_OSuc(sK33(U_1669)))) )
& ! [U_1668] :
( ! [U_1665] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1668,U_1665),hAPP(U_1668,c_Nat_OSuc(U_1665)))
| ~ c_SEQ_Osubseq(U_1668) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1666,sK33(U_1669))],[f_591_3]) ).
cnf(f_591_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1668,U_1665),hAPP(U_1668,c_Nat_OSuc(U_1665)))
| ~ c_SEQ_Osubseq(U_1668) ),
inference(clausify,[status(thm)],[f_591_4]) ).
cnf(f_591_6,plain,
( c_SEQ_Osubseq(U_1669)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1669,sK33(U_1669)),hAPP(U_1669,c_Nat_OSuc(sK33(U_1669)))) ),
inference(clausify,[status(thm)],[f_591_4]) ).
fof(f_592_1,plain,
! [V_x_2] :
( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != V_x_2 ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2__iff]) ).
fof(f_592_2,plain,
! [U_1670] :
( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1670),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_1670
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1670) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1670)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1670),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_1670 ) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
( ! [U_1672] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1672),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_1672
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1672) )
& ! [U_1671] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1671)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1671),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_1671 ) ),
inference(miniscope,[status(thm)],[f_592_2]) ).
cnf(f_592_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1671)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1671),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_1671 ),
inference(clausify,[status(thm)],[f_592_3]) ).
cnf(f_592_5,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1672),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_1672
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1672) ),
inference(clausify,[status(thm)],[f_592_3]) ).
fof(f_593_1,plain,
! [V_x] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2]) ).
fof(f_593_2,plain,
! [U_1673] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1673),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_1673
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1673) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
cnf(f_593_3,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1673),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_1673
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1673) ),
inference(clausify,[status(thm)],[f_593_2]) ).
fof(f_594_1,plain,
! [V_x,V_y] :
( c_NthRoot_Osqrt(V_x) = V_y
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != V_x ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__unique]) ).
fof(f_594_2,plain,
! [U_1675,U_1674] :
( c_NthRoot_Osqrt(U_1675) = U_1674
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1674)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1674,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_1675 ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
cnf(f_594_3,plain,
( c_NthRoot_Osqrt(U_1675) = U_1674
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1674)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1674,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_1675 ),
inference(clausify,[status(thm)],[f_594_2]) ).
fof(f_595_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2__gt__zero]) ).
fof(f_595_2,plain,
! [U_1676] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1676),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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),U_1676) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
cnf(f_595_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1676),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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),U_1676) ),
inference(clausify,[status(thm)],[f_595_2]) ).
fof(f_596_1,plain,
! [V_y,V_x,V_u] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,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,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,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),V_u) ),
inference(fof_nnf,[status(thm)],[fact_lemma__sqrt__hcomplex__capprox]) ).
fof(f_596_2,plain,
! [U_1679,U_1678,U_1677] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1678,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1679,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1677)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1679)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1678)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1679,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1677,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,U_1678,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1677,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),U_1677) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
cnf(f_596_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1678,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1679,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1677)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1679)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1678)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1679,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1677,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,U_1678,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1677,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),U_1677) ),
inference(clausify,[status(thm)],[f_596_2]) ).
fof(f_597_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero]) ).
fof(f_597_2,plain,
! [U_1682,U_1681,U_1680] :
( c_Orderings_Oord__class_Oless__eq(U_1680,c_Groups_Ozero__class_Ozero(U_1680),c_Groups_Oplus__class_Oplus(U_1680,c_Power_Opower__class_Opower(U_1680,U_1681,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1680,U_1682,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_1680) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
cnf(f_597_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1680,c_Groups_Ozero__class_Ozero(U_1680),c_Groups_Oplus__class_Oplus(U_1680,c_Power_Opower__class_Opower(U_1680,U_1681,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1680,U_1682,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_1680) ),
inference(clausify,[status(thm)],[f_597_2]) ).
fof(f_598_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff]) ).
fof(f_598_2,plain,
! [U_1685,U_1684,U_1683] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1683,c_Groups_Oplus__class_Oplus(U_1683,c_Power_Opower__class_Opower(U_1683,U_1684,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1683,U_1685,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1683))
| U_1685 != c_Groups_Ozero__class_Ozero(U_1683)
| U_1684 != c_Groups_Ozero__class_Ozero(U_1683) )
& ( ( U_1685 = c_Groups_Ozero__class_Ozero(U_1683)
& U_1684 = c_Groups_Ozero__class_Ozero(U_1683) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1683,c_Groups_Oplus__class_Oplus(U_1683,c_Power_Opower__class_Opower(U_1683,U_1684,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1683,U_1685,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1683)) ) )
| ~ class_Rings_Olinordered__idom(U_1683) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
cnf(f_598_3,plain,
( U_1684 = c_Groups_Ozero__class_Ozero(U_1683)
| ~ c_Orderings_Oord__class_Oless__eq(U_1683,c_Groups_Oplus__class_Oplus(U_1683,c_Power_Opower__class_Opower(U_1683,U_1684,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1683,U_1685,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1683))
| ~ class_Rings_Olinordered__idom(U_1683) ),
inference(clausify,[status(thm)],[f_598_2]) ).
cnf(f_598_4,plain,
( U_1685 = c_Groups_Ozero__class_Ozero(U_1683)
| ~ c_Orderings_Oord__class_Oless__eq(U_1683,c_Groups_Oplus__class_Oplus(U_1683,c_Power_Opower__class_Opower(U_1683,U_1684,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1683,U_1685,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1683))
| ~ class_Rings_Olinordered__idom(U_1683) ),
inference(clausify,[status(thm)],[f_598_2]) ).
cnf(f_598_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1683,c_Groups_Oplus__class_Oplus(U_1683,c_Power_Opower__class_Opower(U_1683,U_1684,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1683,U_1685,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1683))
| U_1685 != c_Groups_Ozero__class_Ozero(U_1683)
| U_1684 != c_Groups_Ozero__class_Ozero(U_1683)
| ~ class_Rings_Olinordered__idom(U_1683) ),
inference(clausify,[status(thm)],[f_598_2]) ).
fof(f_599_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__sum__power2__lt__zero]) ).
fof(f_599_2,plain,
! [U_1688,U_1687,U_1686] :
( ~ c_Orderings_Oord__class_Oless(U_1686,c_Groups_Oplus__class_Oplus(U_1686,c_Power_Opower__class_Opower(U_1686,U_1687,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1686,U_1688,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1686))
| ~ class_Rings_Olinordered__idom(U_1686) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
cnf(f_599_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1686,c_Groups_Oplus__class_Oplus(U_1686,c_Power_Opower__class_Opower(U_1686,U_1687,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1686,U_1688,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1686))
| ~ class_Rings_Olinordered__idom(U_1686) ),
inference(clausify,[status(thm)],[f_599_2]) ).
fof(f_600_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff]) ).
fof(f_600_2,plain,
! [U_1691,U_1690,U_1689] :
( ( ( c_Orderings_Oord__class_Oless(U_1689,c_Groups_Ozero__class_Ozero(U_1689),c_Groups_Oplus__class_Oplus(U_1689,c_Power_Opower__class_Opower(U_1689,U_1690,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1689,U_1691,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ( U_1691 = c_Groups_Ozero__class_Ozero(U_1689)
& U_1690 = c_Groups_Ozero__class_Ozero(U_1689) ) )
& ( U_1691 != c_Groups_Ozero__class_Ozero(U_1689)
| U_1690 != c_Groups_Ozero__class_Ozero(U_1689)
| ~ c_Orderings_Oord__class_Oless(U_1689,c_Groups_Ozero__class_Ozero(U_1689),c_Groups_Oplus__class_Oplus(U_1689,c_Power_Opower__class_Opower(U_1689,U_1690,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1689,U_1691,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(U_1689) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
cnf(f_600_3,plain,
( U_1691 != c_Groups_Ozero__class_Ozero(U_1689)
| U_1690 != c_Groups_Ozero__class_Ozero(U_1689)
| ~ c_Orderings_Oord__class_Oless(U_1689,c_Groups_Ozero__class_Ozero(U_1689),c_Groups_Oplus__class_Oplus(U_1689,c_Power_Opower__class_Opower(U_1689,U_1690,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1689,U_1691,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_1689) ),
inference(clausify,[status(thm)],[f_600_2]) ).
cnf(f_600_4,plain,
( U_1690 = c_Groups_Ozero__class_Ozero(U_1689)
| c_Orderings_Oord__class_Oless(U_1689,c_Groups_Ozero__class_Ozero(U_1689),c_Groups_Oplus__class_Oplus(U_1689,c_Power_Opower__class_Opower(U_1689,U_1690,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1689,U_1691,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_1689) ),
inference(clausify,[status(thm)],[f_600_2]) ).
cnf(f_600_5,plain,
( U_1691 = c_Groups_Ozero__class_Ozero(U_1689)
| c_Orderings_Oord__class_Oless(U_1689,c_Groups_Ozero__class_Ozero(U_1689),c_Groups_Oplus__class_Oplus(U_1689,c_Power_Opower__class_Opower(U_1689,U_1690,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1689,U_1691,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_1689) ),
inference(clausify,[status(thm)],[f_600_2]) ).
fof(f_601_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__zero__cancel__iff]) ).
fof(f_601_2,plain,
! [U_1692] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1692),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_1692 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1692),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
fof(f_601_3,plain,
( ! [U_1694] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1694),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_1694 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1693] :
( U_1693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1693),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_601_2]) ).
cnf(f_601_4,plain,
( U_1693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1693),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_601_3]) ).
cnf(f_601_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1694),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_1694 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_601_3]) ).
fof(f_602_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg]) ).
fof(f_602_2,plain,
! [U_1697,U_1696,U_1695] :
( c_Orderings_Oord__class_Oless(U_1695,c_Groups_Ozero__class_Ozero(U_1695),c_Groups_Oplus__class_Oplus(U_1695,U_1696,U_1697))
| ~ c_Orderings_Oord__class_Oless__eq(U_1695,c_Groups_Ozero__class_Ozero(U_1695),U_1697)
| ~ c_Orderings_Oord__class_Oless(U_1695,c_Groups_Ozero__class_Ozero(U_1695),U_1696)
| ~ class_Groups_Oordered__comm__monoid__add(U_1695) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
cnf(f_602_3,plain,
( c_Orderings_Oord__class_Oless(U_1695,c_Groups_Ozero__class_Ozero(U_1695),c_Groups_Oplus__class_Oplus(U_1695,U_1696,U_1697))
| ~ c_Orderings_Oord__class_Oless__eq(U_1695,c_Groups_Ozero__class_Ozero(U_1695),U_1697)
| ~ c_Orderings_Oord__class_Oless(U_1695,c_Groups_Ozero__class_Ozero(U_1695),U_1696)
| ~ class_Groups_Oordered__comm__monoid__add(U_1695) ),
inference(clausify,[status(thm)],[f_602_2]) ).
fof(f_603_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos]) ).
fof(f_603_2,plain,
! [U_1700,U_1699,U_1698] :
( c_Orderings_Oord__class_Oless(U_1698,c_Groups_Ozero__class_Ozero(U_1698),c_Groups_Oplus__class_Oplus(U_1698,U_1699,U_1700))
| ~ c_Orderings_Oord__class_Oless(U_1698,c_Groups_Ozero__class_Ozero(U_1698),U_1700)
| ~ c_Orderings_Oord__class_Oless__eq(U_1698,c_Groups_Ozero__class_Ozero(U_1698),U_1699)
| ~ class_Groups_Oordered__comm__monoid__add(U_1698) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
cnf(f_603_3,plain,
( c_Orderings_Oord__class_Oless(U_1698,c_Groups_Ozero__class_Ozero(U_1698),c_Groups_Oplus__class_Oplus(U_1698,U_1699,U_1700))
| ~ c_Orderings_Oord__class_Oless(U_1698,c_Groups_Ozero__class_Ozero(U_1698),U_1700)
| ~ c_Orderings_Oord__class_Oless__eq(U_1698,c_Groups_Ozero__class_Ozero(U_1698),U_1699)
| ~ class_Groups_Oordered__comm__monoid__add(U_1698) ),
inference(clausify,[status(thm)],[f_603_2]) ).
fof(f_604_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__increasing]) ).
fof(f_604_2,plain,
! [U_1704,U_1703,U_1702,U_1701] :
( c_Orderings_Oord__class_Oless(U_1701,U_1703,c_Groups_Oplus__class_Oplus(U_1701,U_1702,U_1704))
| ~ c_Orderings_Oord__class_Oless__eq(U_1701,U_1703,U_1704)
| ~ c_Orderings_Oord__class_Oless(U_1701,c_Groups_Ozero__class_Ozero(U_1701),U_1702)
| ~ class_Groups_Oordered__comm__monoid__add(U_1701) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
cnf(f_604_3,plain,
( c_Orderings_Oord__class_Oless(U_1701,U_1703,c_Groups_Oplus__class_Oplus(U_1701,U_1702,U_1704))
| ~ c_Orderings_Oord__class_Oless__eq(U_1701,U_1703,U_1704)
| ~ c_Orderings_Oord__class_Oless(U_1701,c_Groups_Ozero__class_Ozero(U_1701),U_1702)
| ~ class_Groups_Oordered__comm__monoid__add(U_1701) ),
inference(clausify,[status(thm)],[f_604_2]) ).
fof(f_605_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2]) ).
fof(f_605_2,plain,
! [U_1708,U_1707,U_1706,U_1705] :
( c_Orderings_Oord__class_Oless(U_1705,U_1707,c_Groups_Oplus__class_Oplus(U_1705,U_1706,U_1708))
| ~ c_Orderings_Oord__class_Oless(U_1705,U_1707,U_1708)
| ~ c_Orderings_Oord__class_Oless__eq(U_1705,c_Groups_Ozero__class_Ozero(U_1705),U_1706)
| ~ class_Groups_Oordered__comm__monoid__add(U_1705) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
cnf(f_605_3,plain,
( c_Orderings_Oord__class_Oless(U_1705,U_1707,c_Groups_Oplus__class_Oplus(U_1705,U_1706,U_1708))
| ~ c_Orderings_Oord__class_Oless(U_1705,U_1707,U_1708)
| ~ c_Orderings_Oord__class_Oless__eq(U_1705,c_Groups_Ozero__class_Ozero(U_1705),U_1706)
| ~ class_Groups_Oordered__comm__monoid__add(U_1705) ),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos]) ).
fof(f_606_2,plain,
! [U_1711,U_1710,U_1709] :
( c_Orderings_Oord__class_Oless(U_1709,c_Groups_Oplus__class_Oplus(U_1709,U_1710,U_1711),c_Groups_Ozero__class_Ozero(U_1709))
| ~ c_Orderings_Oord__class_Oless__eq(U_1709,U_1711,c_Groups_Ozero__class_Ozero(U_1709))
| ~ c_Orderings_Oord__class_Oless(U_1709,U_1710,c_Groups_Ozero__class_Ozero(U_1709))
| ~ class_Groups_Oordered__comm__monoid__add(U_1709) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
cnf(f_606_3,plain,
( c_Orderings_Oord__class_Oless(U_1709,c_Groups_Oplus__class_Oplus(U_1709,U_1710,U_1711),c_Groups_Ozero__class_Ozero(U_1709))
| ~ c_Orderings_Oord__class_Oless__eq(U_1709,U_1711,c_Groups_Ozero__class_Ozero(U_1709))
| ~ c_Orderings_Oord__class_Oless(U_1709,U_1710,c_Groups_Ozero__class_Ozero(U_1709))
| ~ class_Groups_Oordered__comm__monoid__add(U_1709) ),
inference(clausify,[status(thm)],[f_606_2]) ).
fof(f_607_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg]) ).
fof(f_607_2,plain,
! [U_1714,U_1713,U_1712] :
( c_Orderings_Oord__class_Oless(U_1712,c_Groups_Oplus__class_Oplus(U_1712,U_1713,U_1714),c_Groups_Ozero__class_Ozero(U_1712))
| ~ c_Orderings_Oord__class_Oless(U_1712,U_1714,c_Groups_Ozero__class_Ozero(U_1712))
| ~ c_Orderings_Oord__class_Oless__eq(U_1712,U_1713,c_Groups_Ozero__class_Ozero(U_1712))
| ~ class_Groups_Oordered__comm__monoid__add(U_1712) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
cnf(f_607_3,plain,
( c_Orderings_Oord__class_Oless(U_1712,c_Groups_Oplus__class_Oplus(U_1712,U_1713,U_1714),c_Groups_Ozero__class_Ozero(U_1712))
| ~ c_Orderings_Oord__class_Oless(U_1712,U_1714,c_Groups_Ozero__class_Ozero(U_1712))
| ~ c_Orderings_Oord__class_Oless__eq(U_1712,U_1713,c_Groups_Ozero__class_Ozero(U_1712))
| ~ class_Groups_Oordered__comm__monoid__add(U_1712) ),
inference(clausify,[status(thm)],[f_607_2]) ).
fof(f_608_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__two]) ).
fof(f_608_2,plain,
! [U_1715] :
( c_Orderings_Oord__class_Oless(U_1715,c_Groups_Ozero__class_Ozero(U_1715),c_Groups_Oplus__class_Oplus(U_1715,c_Groups_Oone__class_Oone(U_1715),c_Groups_Oone__class_Oone(U_1715)))
| ~ class_Rings_Olinordered__semidom(U_1715) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
cnf(f_608_3,plain,
( c_Orderings_Oord__class_Oless(U_1715,c_Groups_Ozero__class_Ozero(U_1715),c_Groups_Oplus__class_Oplus(U_1715,c_Groups_Oone__class_Oone(U_1715),c_Groups_Oone__class_Oone(U_1715)))
| ~ class_Rings_Olinordered__semidom(U_1715) ),
inference(clausify,[status(thm)],[f_608_2]) ).
fof(f_609_1,plain,
! [V_w,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Bit0]) ).
fof(f_609_2,plain,
! [U_1717,U_1716] :
( c_Int_Onumber__class_Onumber__of(U_1716,c_Int_OBit0(U_1717)) = c_Groups_Oplus__class_Oplus(U_1716,c_Groups_Oplus__class_Oplus(U_1716,c_Groups_Ozero__class_Ozero(U_1716),c_Int_Onumber__class_Onumber__of(U_1716,U_1717)),c_Int_Onumber__class_Onumber__of(U_1716,U_1717))
| ~ class_Int_Onumber__ring(U_1716) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
cnf(f_609_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1716,c_Int_OBit0(U_1717)) = c_Groups_Oplus__class_Oplus(U_1716,c_Groups_Oplus__class_Oplus(U_1716,c_Groups_Ozero__class_Ozero(U_1716),c_Int_Onumber__class_Onumber__of(U_1716,U_1717)),c_Int_Onumber__class_Onumber__of(U_1716,U_1717))
| ~ class_Int_Onumber__ring(U_1716) ),
inference(clausify,[status(thm)],[f_609_2]) ).
fof(f_610_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__half__sum]) ).
fof(f_610_2,plain,
! [U_1720,U_1719,U_1718] :
( c_Orderings_Oord__class_Oless(U_1718,U_1719,c_Rings_Oinverse__class_Odivide(U_1718,c_Groups_Oplus__class_Oplus(U_1718,U_1719,U_1720),c_Groups_Oplus__class_Oplus(U_1718,c_Groups_Oone__class_Oone(U_1718),c_Groups_Oone__class_Oone(U_1718))))
| ~ c_Orderings_Oord__class_Oless(U_1718,U_1719,U_1720)
| ~ class_Fields_Olinordered__field(U_1718) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
cnf(f_610_3,plain,
( c_Orderings_Oord__class_Oless(U_1718,U_1719,c_Rings_Oinverse__class_Odivide(U_1718,c_Groups_Oplus__class_Oplus(U_1718,U_1719,U_1720),c_Groups_Oplus__class_Oplus(U_1718,c_Groups_Oone__class_Oone(U_1718),c_Groups_Oone__class_Oone(U_1718))))
| ~ c_Orderings_Oord__class_Oless(U_1718,U_1719,U_1720)
| ~ class_Fields_Olinordered__field(U_1718) ),
inference(clausify,[status(thm)],[f_610_2]) ).
fof(f_611_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_gt__half__sum]) ).
fof(f_611_2,plain,
! [U_1723,U_1722,U_1721] :
( c_Orderings_Oord__class_Oless(U_1721,c_Rings_Oinverse__class_Odivide(U_1721,c_Groups_Oplus__class_Oplus(U_1721,U_1722,U_1723),c_Groups_Oplus__class_Oplus(U_1721,c_Groups_Oone__class_Oone(U_1721),c_Groups_Oone__class_Oone(U_1721))),U_1723)
| ~ c_Orderings_Oord__class_Oless(U_1721,U_1722,U_1723)
| ~ class_Fields_Olinordered__field(U_1721) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
cnf(f_611_3,plain,
( c_Orderings_Oord__class_Oless(U_1721,c_Rings_Oinverse__class_Odivide(U_1721,c_Groups_Oplus__class_Oplus(U_1721,U_1722,U_1723),c_Groups_Oplus__class_Oplus(U_1721,c_Groups_Oone__class_Oone(U_1721),c_Groups_Oone__class_Oone(U_1721))),U_1723)
| ~ c_Orderings_Oord__class_Oless(U_1721,U_1722,U_1723)
| ~ class_Fields_Olinordered__field(U_1721) ),
inference(clausify,[status(thm)],[f_611_2]) ).
fof(f_612_1,plain,
! [V_w,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Bit1]) ).
fof(f_612_2,plain,
! [U_1725,U_1724] :
( c_Int_Onumber__class_Onumber__of(U_1724,c_Int_OBit1(U_1725)) = c_Groups_Oplus__class_Oplus(U_1724,c_Groups_Oplus__class_Oplus(U_1724,c_Groups_Oone__class_Oone(U_1724),c_Int_Onumber__class_Onumber__of(U_1724,U_1725)),c_Int_Onumber__class_Onumber__of(U_1724,U_1725))
| ~ class_Int_Onumber__ring(U_1724) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
cnf(f_612_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1724,c_Int_OBit1(U_1725)) = c_Groups_Oplus__class_Oplus(U_1724,c_Groups_Oplus__class_Oplus(U_1724,c_Groups_Oone__class_Oone(U_1724),c_Int_Onumber__class_Onumber__of(U_1724,U_1725)),c_Int_Onumber__class_Onumber__of(U_1724,U_1725))
| ~ class_Int_Onumber__ring(U_1724) ),
inference(clausify,[status(thm)],[f_612_2]) ).
fof(f_613_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4]) ).
fof(f_613_2,plain,
! [U_1728,U_1727,U_1726] :
( c_Orderings_Oord__class_Oless__eq(U_1726,c_Groups_Oabs__class_Oabs(U_1726,c_Groups_Ominus__class_Ominus(U_1726,U_1727,U_1728)),c_Groups_Oplus__class_Oplus(U_1726,c_Groups_Oabs__class_Oabs(U_1726,U_1727),c_Groups_Oabs__class_Oabs(U_1726,U_1728)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1726) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
cnf(f_613_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1726,c_Groups_Oabs__class_Oabs(U_1726,c_Groups_Ominus__class_Ominus(U_1726,U_1727,U_1728)),c_Groups_Oplus__class_Oplus(U_1726,c_Groups_Oabs__class_Oabs(U_1726,U_1727),c_Groups_Oabs__class_Oabs(U_1726,U_1728)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1726) ),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq]) ).
fof(f_614_2,plain,
! [U_1733,U_1732,U_1731,U_1730,U_1729] :
( c_Orderings_Oord__class_Oless__eq(U_1729,c_Groups_Oabs__class_Oabs(U_1729,c_Groups_Ominus__class_Ominus(U_1729,c_Groups_Oplus__class_Oplus(U_1729,U_1730,U_1731),c_Groups_Oplus__class_Oplus(U_1729,U_1732,U_1733))),c_Groups_Oplus__class_Oplus(U_1729,c_Groups_Oabs__class_Oabs(U_1729,c_Groups_Ominus__class_Ominus(U_1729,U_1730,U_1732)),c_Groups_Oabs__class_Oabs(U_1729,c_Groups_Ominus__class_Ominus(U_1729,U_1731,U_1733))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1729) ),
inference(variable_rename,[status(thm)],[f_614_1]) ).
cnf(f_614_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1729,c_Groups_Oabs__class_Oabs(U_1729,c_Groups_Ominus__class_Ominus(U_1729,c_Groups_Oplus__class_Oplus(U_1729,U_1730,U_1731),c_Groups_Oplus__class_Oplus(U_1729,U_1732,U_1733))),c_Groups_Oplus__class_Oplus(U_1729,c_Groups_Oabs__class_Oabs(U_1729,c_Groups_Ominus__class_Ominus(U_1729,U_1730,U_1732)),c_Groups_Oabs__class_Oabs(U_1729,c_Groups_Ominus__class_Ominus(U_1729,U_1731,U_1733))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1729) ),
inference(clausify,[status(thm)],[f_614_2]) ).
fof(f_615_1,plain,
! [V_m,V_n] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff]) ).
fof(f_615_2,plain,
! [U_1735,U_1734] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1735,U_1734)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1735),c_RealDef_Oreal(tc_Nat_Onat,U_1734))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1734,U_1735) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
cnf(f_615_3,plain,
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1735,U_1734)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1735),c_RealDef_Oreal(tc_Nat_Onat,U_1734))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1734,U_1735) ),
inference(clausify,[status(thm)],[f_615_2]) ).
fof(f_616_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4]) ).
fof(f_616_2,plain,
! [U_1738,U_1737,U_1736] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1736,c_Groups_Ominus__class_Ominus(U_1736,U_1737,U_1738)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1736,U_1737),c_RealVector_Onorm__class_Onorm(U_1736,U_1738)))
| ~ class_RealVector_Oreal__normed__vector(U_1736) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
cnf(f_616_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1736,c_Groups_Ominus__class_Ominus(U_1736,U_1737,U_1738)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1736,U_1737),c_RealVector_Onorm__class_Onorm(U_1736,U_1738)))
| ~ class_RealVector_Oreal__normed__vector(U_1736) ),
inference(clausify,[status(thm)],[f_616_2]) ).
fof(f_617_1,plain,
! [V_n] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred]) ).
fof(f_617_2,plain,
! [U_1739] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1739,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_1739
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1739) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
cnf(f_617_3,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1739,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_1739
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1739) ),
inference(clausify,[status(thm)],[f_617_2]) ).
fof(f_618_1,plain,
! [V_i,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__less]) ).
fof(f_618_2,plain,
! [U_1741,U_1740] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1740,c_Nat_OSuc(U_1741)),U_1740)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1740) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
cnf(f_618_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1740,c_Nat_OSuc(U_1741)),U_1740)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1740) ),
inference(clausify,[status(thm)],[f_618_2]) ).
fof(f_619_1,plain,
! [V_n,V_x] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x),V_n)),
inference(fof_nnf,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(f_619_2,plain,
! [U_1743,U_1742] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1742),U_1743)),
inference(variable_rename,[status(thm)],[f_619_1]) ).
cnf(f_619_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1742),U_1743)),
inference(clausify,[status(thm)],[f_619_2]) ).
fof(f_620_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq]) ).
fof(f_620_2,plain,
! [U_1746,U_1745,U_1744] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1744,U_1745),c_RealVector_Onorm__class_Onorm(U_1744,U_1746)),c_RealVector_Onorm__class_Onorm(U_1744,c_Groups_Oplus__class_Oplus(U_1744,U_1745,U_1746)))
| ~ class_RealVector_Oreal__normed__vector(U_1744) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
cnf(f_620_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1744,U_1745),c_RealVector_Onorm__class_Onorm(U_1744,U_1746)),c_RealVector_Onorm__class_Onorm(U_1744,c_Groups_Oplus__class_Oplus(U_1744,U_1745,U_1746)))
| ~ class_RealVector_Oreal__normed__vector(U_1744) ),
inference(clausify,[status(thm)],[f_620_2]) ).
fof(f_621_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff]) ).
fof(f_621_2,plain,
! [U_1748,U_1747] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1747,U_1748))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1747),U_1748) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1747),U_1748)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1747,U_1748)) ) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
( ! [U_1752,U_1750] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1750,U_1752))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1750),U_1752) )
& ! [U_1751,U_1749] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1749),U_1751)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1749,U_1751)) ) ),
inference(miniscope,[status(thm)],[f_621_2]) ).
cnf(f_621_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1749),U_1751)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1749,U_1751)) ),
inference(clausify,[status(thm)],[f_621_3]) ).
cnf(f_621_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1750,U_1752))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1750),U_1752) ),
inference(clausify,[status(thm)],[f_621_3]) ).
fof(f_622_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff]) ).
fof(f_622_2,plain,
! [U_1754,U_1753] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1753,U_1754),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1754,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1753)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1754,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1753))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1753,U_1754),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
( ! [U_1758,U_1756] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1756,U_1758),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1758,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1756)) )
& ! [U_1757,U_1755] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1757,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1755))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1755,U_1757),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_622_2]) ).
cnf(f_622_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1757,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1755))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1755,U_1757),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_622_3]) ).
cnf(f_622_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1756,U_1758),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1758,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1756)) ),
inference(clausify,[status(thm)],[f_622_3]) ).
fof(f_623_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff]) ).
fof(f_623_2,plain,
! [U_1760,U_1759] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1759,U_1760))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1759),U_1760) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1759),U_1760)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1759,U_1760)) ) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
( ! [U_1764,U_1762] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1762,U_1764))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1762),U_1764) )
& ! [U_1763,U_1761] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1761),U_1763)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1761,U_1763)) ) ),
inference(miniscope,[status(thm)],[f_623_2]) ).
cnf(f_623_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1761),U_1763)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1761,U_1763)) ),
inference(clausify,[status(thm)],[f_623_3]) ).
cnf(f_623_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1762,U_1764))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1762),U_1764) ),
inference(clausify,[status(thm)],[f_623_3]) ).
fof(f_624_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff]) ).
fof(f_624_2,plain,
! [U_1766,U_1765] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1765,U_1766),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1766,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1765)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1766,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1765))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1765,U_1766),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
fof(f_624_3,plain,
( ! [U_1770,U_1768] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1768,U_1770),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1770,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1768)) )
& ! [U_1769,U_1767] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1769,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1767))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1767,U_1769),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_624_2]) ).
cnf(f_624_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1769,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1767))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1767,U_1769),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_624_3]) ).
cnf(f_624_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1768,U_1770),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1770,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1768)) ),
inference(clausify,[status(thm)],[f_624_3]) ).
fof(f_625_1,plain,
! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
inference(fof_nnf,[status(thm)],[fact_abs__add__one__not__less__self]) ).
fof(f_625_2,plain,
! [U_1771] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1771),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1771),
inference(variable_rename,[status(thm)],[f_625_1]) ).
cnf(f_625_3,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1771),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1771),
inference(clausify,[status(thm)],[f_625_2]) ).
fof(f_626_1,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_Numeral1__eq1__nat]) ).
cnf(f_626_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
inference(clausify,[status(thm)],[f_626_1]) ).
fof(f_627_1,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat__numeral__1__eq__1]) ).
cnf(f_627_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_627_1]) ).
fof(f_628_1,plain,
! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))),
inference(fof_nnf,[status(thm)],[fact_abs__sum__triangle__ineq]) ).
fof(f_628_2,plain,
! [U_1775,U_1774,U_1773,U_1772] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1772,U_1773),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1774),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1775)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1772,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1774))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1773,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1775))))),
inference(variable_rename,[status(thm)],[f_628_1]) ).
cnf(f_628_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1772,U_1773),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1774),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1775)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1772,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1774))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1773,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1775))))),
inference(clausify,[status(thm)],[f_628_2]) ).
fof(f_629_1,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_one__is__num__one]) ).
cnf(f_629_2,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
inference(clausify,[status(thm)],[f_629_1]) ).
fof(f_630_1,plain,
! [V_za_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2) ) ),
inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).
fof(f_630_2,plain,
! [U_1776] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1776)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1776) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1776)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1776) ) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
( ! [U_1778] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1778)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1778) )
& ! [U_1777] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1777)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1777) ) ),
inference(miniscope,[status(thm)],[f_630_2]) ).
cnf(f_630_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1777)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1777) ),
inference(clausify,[status(thm)],[f_630_3]) ).
cnf(f_630_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1778)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1778) ),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_1,plain,
! [V_za_2,V_wa_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq]) ).
fof(f_631_2,plain,
! [U_1780,U_1779] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1779,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1780,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1779,U_1780) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1779,U_1780)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1779,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1780,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
fof(f_631_3,plain,
( ! [U_1784,U_1782] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1782,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1784,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1782,U_1784) )
& ! [U_1783,U_1781] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1781,U_1783)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1781,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1783,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_631_2]) ).
cnf(f_631_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1781,U_1783)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1781,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1783,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_631_3]) ).
cnf(f_631_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1782,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_1784,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1782,U_1784) ),
inference(clausify,[status(thm)],[f_631_3]) ).
fof(f_632_1,plain,
! [V_za_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
| V_za_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( V_za_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff]) ).
fof(f_632_2,plain,
! [U_1785] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1785),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_1785 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_1785 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1785),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
fof(f_632_3,plain,
( ! [U_1787] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1787),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_1787 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_1786] :
( U_1786 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1786),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_632_2]) ).
cnf(f_632_4,plain,
( U_1786 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1786),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_632_3]) ).
cnf(f_632_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1787),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_1787 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_632_3]) ).
fof(f_633_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff]) ).
fof(f_633_2,plain,
! [U_1788] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1788))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1788) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1788)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1788)) ) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
( ! [U_1790] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1790))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1790) )
& ! [U_1789] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1789)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1789)) ) ),
inference(miniscope,[status(thm)],[f_633_2]) ).
cnf(f_633_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1789)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1789)) ),
inference(clausify,[status(thm)],[f_633_3]) ).
cnf(f_633_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1790))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1790) ),
inference(clausify,[status(thm)],[f_633_3]) ).
fof(f_634_1,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__Suc__0]) ).
cnf(f_634_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_634_1]) ).
fof(f_635_1,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(fof_nnf,[status(thm)],[fact_numeral__3__eq__3]) ).
cnf(f_635_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(clausify,[status(thm)],[f_635_1]) ).
fof(f_636_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2),V_n_2))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff]) ).
fof(f_636_2,plain,
! [U_1792,U_1791] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1791),U_1792))
| ( U_1792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1791 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( U_1792 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1791 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1791),U_1792)) ) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
( ! [U_1796,U_1794] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1794),U_1796))
| ( U_1796 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1794 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_1795,U_1793] :
( U_1795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1793 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1793),U_1795)) ) ),
inference(miniscope,[status(thm)],[f_636_2]) ).
cnf(f_636_4,plain,
( U_1795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1793 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1793),U_1795)) ),
inference(clausify,[status(thm)],[f_636_3]) ).
cnf(f_636_5,plain,
( U_1794 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1794),U_1796)) ),
inference(clausify,[status(thm)],[f_636_3]) ).
cnf(f_636_6,plain,
( U_1796 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1794),U_1796)) ),
inference(clausify,[status(thm)],[f_636_3]) ).
fof(f_637_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))),
inference(fof_nnf,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(f_637_2,plain,
! [U_1797] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1797))),
inference(variable_rename,[status(thm)],[f_637_1]) ).
cnf(f_637_3,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1797))),
inference(clausify,[status(thm)],[f_637_2]) ).
fof(f_638_1,plain,
! [T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__power2]) ).
fof(f_638_2,plain,
! [U_1798] :
( c_Power_Opower__class_Opower(U_1798,c_Groups_Ozero__class_Ozero(U_1798),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_1798)
| ~ class_Rings_Osemiring__1(U_1798) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
cnf(f_638_3,plain,
( c_Power_Opower__class_Opower(U_1798,c_Groups_Ozero__class_Ozero(U_1798),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_1798)
| ~ class_Rings_Osemiring__1(U_1798) ),
inference(clausify,[status(thm)],[f_638_2]) ).
fof(f_639_1,plain,
! [V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__eq__power2]) ).
fof(f_639_2,plain,
! [U_1800,U_1799] :
( ( ( c_Power_Opower__class_Opower(U_1799,U_1800,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_1799)
| U_1800 != c_Groups_Ozero__class_Ozero(U_1799) )
& ( U_1800 = c_Groups_Ozero__class_Ozero(U_1799)
| c_Power_Opower__class_Opower(U_1799,U_1800,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_1799) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_1799) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
cnf(f_639_3,plain,
( U_1800 = c_Groups_Ozero__class_Ozero(U_1799)
| c_Power_Opower__class_Opower(U_1799,U_1800,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_1799)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1799) ),
inference(clausify,[status(thm)],[f_639_2]) ).
cnf(f_639_4,plain,
( c_Power_Opower__class_Opower(U_1799,U_1800,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_1799)
| U_1800 != c_Groups_Ozero__class_Ozero(U_1799)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1799) ),
inference(clausify,[status(thm)],[f_639_2]) ).
fof(f_640_1,plain,
! [T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__power2]) ).
fof(f_640_2,plain,
! [U_1801] :
( c_Power_Opower__class_Opower(U_1801,c_Groups_Oone__class_Oone(U_1801),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_1801)
| ~ class_Rings_Osemiring__1(U_1801) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
cnf(f_640_3,plain,
( c_Power_Opower__class_Opower(U_1801,c_Groups_Oone__class_Oone(U_1801),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_1801)
| ~ class_Rings_Osemiring__1(U_1801) ),
inference(clausify,[status(thm)],[f_640_2]) ).
fof(f_641_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__minus]) ).
fof(f_641_2,plain,
! [U_1803,U_1802] :
( c_Power_Opower__class_Opower(U_1802,c_Groups_Ouminus__class_Ouminus(U_1802,U_1803),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(U_1802,U_1803,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_1802) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
cnf(f_641_3,plain,
( c_Power_Opower__class_Opower(U_1802,c_Groups_Ouminus__class_Ouminus(U_1802,U_1803),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(U_1802,U_1803,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_1802) ),
inference(clausify,[status(thm)],[f_641_2]) ).
fof(f_642_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__power2]) ).
fof(f_642_2,plain,
! [U_1805,U_1804] :
( c_Groups_Oabs__class_Oabs(U_1804,c_Power_Opower__class_Opower(U_1804,U_1805,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(U_1804,U_1805,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_1804) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
cnf(f_642_3,plain,
( c_Groups_Oabs__class_Oabs(U_1804,c_Power_Opower__class_Opower(U_1804,U_1805,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(U_1804,U_1805,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_1804) ),
inference(clausify,[status(thm)],[f_642_2]) ).
fof(f_643_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__abs]) ).
fof(f_643_2,plain,
! [U_1807,U_1806] :
( c_Power_Opower__class_Opower(U_1806,c_Groups_Oabs__class_Oabs(U_1806,U_1807),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(U_1806,U_1807,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_1806) ),
inference(variable_rename,[status(thm)],[f_643_1]) ).
cnf(f_643_3,plain,
( c_Power_Opower__class_Opower(U_1806,c_Groups_Oabs__class_Oabs(U_1806,U_1807),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(U_1806,U_1807,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_1806) ),
inference(clausify,[status(thm)],[f_643_2]) ).
fof(f_644_1,plain,
! [T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two]) ).
fof(f_644_2,plain,
! [U_1808] :
( c_Groups_Oplus__class_Oplus(U_1808,c_Groups_Oone__class_Oone(U_1808),c_Groups_Oone__class_Oone(U_1808)) = c_Int_Onumber__class_Onumber__of(U_1808,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_1808) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
cnf(f_644_3,plain,
( c_Groups_Oplus__class_Oplus(U_1808,c_Groups_Oone__class_Oone(U_1808),c_Groups_Oone__class_Oone(U_1808)) = c_Int_Onumber__class_Onumber__of(U_1808,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_1808) ),
inference(clausify,[status(thm)],[f_644_2]) ).
fof(f_645_1,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I115_J]) ).
cnf(f_645_2,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(clausify,[status(thm)],[f_645_1]) ).
fof(f_646_1,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_numeral__2__eq__2]) ).
cnf(f_646_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_646_1]) ).
fof(f_647_1,plain,
! [V_m,V_n] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred]) ).
fof(f_647_2,plain,
! [U_1810,U_1809] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1810),U_1809) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1810,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1809,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),U_1809) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
cnf(f_647_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1810),U_1809) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1810,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1809,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),U_1809) ),
inference(clausify,[status(thm)],[f_647_2]) ).
fof(f_648_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__two__ge__zero]) ).
cnf(f_648_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_648_1]) ).
fof(f_649_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__two__gt__zero]) ).
cnf(f_649_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_649_1]) ).
fof(f_650_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__two__gt__one]) ).
cnf(f_650_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_650_1]) ).
fof(f_651_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power2]) ).
fof(f_651_2,plain,
! [U_1812,U_1811] :
( c_Orderings_Oord__class_Oless__eq(U_1811,c_Groups_Ozero__class_Ozero(U_1811),c_Power_Opower__class_Opower(U_1811,U_1812,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_1811) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
cnf(f_651_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1811,c_Groups_Ozero__class_Ozero(U_1811),c_Power_Opower__class_Opower(U_1811,U_1812,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_1811) ),
inference(clausify,[status(thm)],[f_651_2]) ).
fof(f_652_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le]) ).
fof(f_652_2,plain,
! [U_1815,U_1814,U_1813] :
( c_Orderings_Oord__class_Oless__eq(U_1813,U_1814,U_1815)
| ~ c_Orderings_Oord__class_Oless__eq(U_1813,c_Groups_Ozero__class_Ozero(U_1813),U_1815)
| ~ c_Orderings_Oord__class_Oless__eq(U_1813,c_Power_Opower__class_Opower(U_1813,U_1814,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1813,U_1815,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_1813) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
cnf(f_652_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1813,U_1814,U_1815)
| ~ c_Orderings_Oord__class_Oless__eq(U_1813,c_Groups_Ozero__class_Ozero(U_1813),U_1815)
| ~ c_Orderings_Oord__class_Oless__eq(U_1813,c_Power_Opower__class_Opower(U_1813,U_1814,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_1813,U_1815,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_1813) ),
inference(clausify,[status(thm)],[f_652_2]) ).
fof(f_653_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq]) ).
fof(f_653_2,plain,
! [U_1818,U_1817,U_1816] :
( U_1817 = U_1818
| ~ c_Orderings_Oord__class_Oless__eq(U_1816,c_Groups_Ozero__class_Ozero(U_1816),U_1818)
| ~ c_Orderings_Oord__class_Oless__eq(U_1816,c_Groups_Ozero__class_Ozero(U_1816),U_1817)
| c_Power_Opower__class_Opower(U_1816,U_1817,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(U_1816,U_1818,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_1816) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
cnf(f_653_3,plain,
( U_1817 = U_1818
| ~ c_Orderings_Oord__class_Oless__eq(U_1816,c_Groups_Ozero__class_Ozero(U_1816),U_1818)
| ~ c_Orderings_Oord__class_Oless__eq(U_1816,c_Groups_Ozero__class_Ozero(U_1816),U_1817)
| c_Power_Opower__class_Opower(U_1816,U_1817,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(U_1816,U_1818,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_1816) ),
inference(clausify,[status(thm)],[f_653_2]) ).
fof(f_654_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__less__0]) ).
fof(f_654_2,plain,
! [U_1820,U_1819] :
( ~ c_Orderings_Oord__class_Oless(U_1819,c_Power_Opower__class_Opower(U_1819,U_1820,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(U_1819))
| ~ class_Rings_Olinordered__idom(U_1819) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
cnf(f_654_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1819,c_Power_Opower__class_Opower(U_1819,U_1820,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(U_1819))
| ~ class_Rings_Olinordered__idom(U_1819) ),
inference(clausify,[status(thm)],[f_654_2]) ).
fof(f_655_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power2]) ).
fof(f_655_2,plain,
! [U_1822,U_1821] :
( ( ( c_Orderings_Oord__class_Oless(U_1821,c_Groups_Ozero__class_Ozero(U_1821),c_Power_Opower__class_Opower(U_1821,U_1822,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| U_1822 = c_Groups_Ozero__class_Ozero(U_1821) )
& ( U_1822 != c_Groups_Ozero__class_Ozero(U_1821)
| ~ c_Orderings_Oord__class_Oless(U_1821,c_Groups_Ozero__class_Ozero(U_1821),c_Power_Opower__class_Opower(U_1821,U_1822,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Rings_Olinordered__idom(U_1821) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
cnf(f_655_3,plain,
( U_1822 != c_Groups_Ozero__class_Ozero(U_1821)
| ~ c_Orderings_Oord__class_Oless(U_1821,c_Groups_Ozero__class_Ozero(U_1821),c_Power_Opower__class_Opower(U_1821,U_1822,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_1821) ),
inference(clausify,[status(thm)],[f_655_2]) ).
cnf(f_655_4,plain,
( c_Orderings_Oord__class_Oless(U_1821,c_Groups_Ozero__class_Ozero(U_1821),c_Power_Opower__class_Opower(U_1821,U_1822,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| U_1822 = c_Groups_Ozero__class_Ozero(U_1821)
| ~ class_Rings_Olinordered__idom(U_1821) ),
inference(clausify,[status(thm)],[f_655_2]) ).
fof(f_656_1,plain,
! [V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a)
| ( V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
& V_a_2 != c_Groups_Oone__class_Oone(T_a) ) )
& ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_a_2 = c_Groups_Oone__class_Oone(T_a)
| c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff]) ).
fof(f_656_2,plain,
! [U_1824,U_1823] :
( ( ( c_Power_Opower__class_Opower(U_1823,U_1824,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_1823)
| ( U_1824 != c_Groups_Ouminus__class_Ouminus(U_1823,c_Groups_Oone__class_Oone(U_1823))
& U_1824 != c_Groups_Oone__class_Oone(U_1823) ) )
& ( U_1824 = c_Groups_Ouminus__class_Ouminus(U_1823,c_Groups_Oone__class_Oone(U_1823))
| U_1824 = c_Groups_Oone__class_Oone(U_1823)
| c_Power_Opower__class_Opower(U_1823,U_1824,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_1823) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_1823) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
cnf(f_656_3,plain,
( U_1824 = c_Groups_Ouminus__class_Ouminus(U_1823,c_Groups_Oone__class_Oone(U_1823))
| U_1824 = c_Groups_Oone__class_Oone(U_1823)
| c_Power_Opower__class_Opower(U_1823,U_1824,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_1823)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1823) ),
inference(clausify,[status(thm)],[f_656_2]) ).
cnf(f_656_4,plain,
( U_1824 != c_Groups_Oone__class_Oone(U_1823)
| c_Power_Opower__class_Opower(U_1823,U_1824,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_1823)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1823) ),
inference(clausify,[status(thm)],[f_656_2]) ).
cnf(f_656_5,plain,
( U_1824 != c_Groups_Ouminus__class_Ouminus(U_1823,c_Groups_Oone__class_Oone(U_1823))
| c_Power_Opower__class_Opower(U_1823,U_1824,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_1823)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1823) ),
inference(clausify,[status(thm)],[f_656_2]) ).
fof(f_657_1,plain,
! [V_n] :
( V_n = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(fof_nnf,[status(thm)],[fact_less__2__cases]) ).
fof(f_657_2,plain,
! [U_1825] :
( U_1825 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1825 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1825,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
cnf(f_657_3,plain,
( U_1825 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1825 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1825,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(clausify,[status(thm)],[f_657_2]) ).
fof(f_658_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)),
inference(fof_nnf,[status(thm)],[fact_two__realpow__ge__one]) ).
fof(f_658_2,plain,
! [U_1826] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_1826)),
inference(variable_rename,[status(thm)],[f_658_1]) ).
cnf(f_658_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_1826)),
inference(clausify,[status(thm)],[f_658_2]) ).
fof(f_659_1,plain,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_realpow__square__minus__le]) ).
fof(f_659_2,plain,
! [U_1828,U_1827] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1827,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1828,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(variable_rename,[status(thm)],[f_659_1]) ).
cnf(f_659_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1827,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1828,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_659_2]) ).
fof(f_660_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),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,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__less__half__sum]) ).
fof(f_660_2,plain,
! [U_1830,U_1829] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1829,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1829,U_1830),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,U_1829,U_1830) ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
cnf(f_660_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1829,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1829,U_1830),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,U_1829,U_1830) ),
inference(clausify,[status(thm)],[f_660_2]) ).
fof(f_661_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__gt__half__sum]) ).
fof(f_661_2,plain,
! [U_1832,U_1831] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1831,U_1832),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1832)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1831,U_1832) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
cnf(f_661_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1831,U_1832),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1832)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1831,U_1832) ),
inference(clausify,[status(thm)],[f_661_2]) ).
fof(f_662_1,plain,
! [B_n] :
? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
inference(fof_nnf,[status(thm)],[fact_th]) ).
fof(f_662_2,plain,
! [U_1834] :
? [U_1833] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1833)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1834)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1833),v_r) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
! [U_1834] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK34(U_1834))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1834)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK34(U_1834)),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1833,sK34(U_1834))],[f_662_2]) ).
cnf(f_662_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK34(U_1834)),v_r),
inference(clausify,[status(thm)],[f_662_3]) ).
cnf(f_662_5,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK34(U_1834))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1834))))),
inference(clausify,[status(thm)],[f_662_3]) ).
fof(f_663_1,plain,
? [B_f] :
! [B_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(B_f,B_x))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_x)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B_f,B_x)),v_r) ),
inference(fof_nnf,[status(thm)],[fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096]) ).
fof(f_663_2,plain,
? [U_1836] :
! [U_1835] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(U_1836,U_1835))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1835)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(U_1836,U_1835)),v_r) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
? [U_1836] :
( ! [U_1838] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(U_1836,U_1838))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1838)))))
& ! [U_1837] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(U_1836,U_1837)),v_r) ),
inference(miniscope,[status(thm)],[f_663_2]) ).
fof(f_663_4,plain,
( ! [U_1838] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK35,U_1838))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1838)))))
& ! [U_1837] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(sK35,U_1837)),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1836,sK35)],[f_663_3]) ).
cnf(f_663_5,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(sK35,U_1837)),v_r),
inference(clausify,[status(thm)],[f_663_4]) ).
cnf(f_663_6,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK35,U_1838))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1838))))),
inference(clausify,[status(thm)],[f_663_4]) ).
fof(f_664_1,plain,
! [V_n_2] :
? [B_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n_2)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
inference(fof_nnf,[status(thm)],[fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096]) ).
fof(f_664_2,plain,
! [U_1840] :
? [U_1839] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_1839)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1840)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1839),v_r) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
! [U_1840] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK36(U_1840))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1840)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK36(U_1840)),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1839,sK36(U_1840))],[f_664_2]) ).
cnf(f_664_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK36(U_1840)),v_r),
inference(clausify,[status(thm)],[f_664_3]) ).
cnf(f_664_5,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK36(U_1840))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1840))))),
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_cos__x__y__le__one]) ).
fof(f_665_2,plain,
! [U_1842,U_1841] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1841,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1841,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1842,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_665_1]) ).
cnf(f_665_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1841,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1841,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_1842,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_665_2]) ).
fof(f_666_1,plain,
! [V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_real__average__minus__first]) ).
fof(f_666_2,plain,
! [U_1844,U_1843] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1843,U_1844),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1843) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1844,U_1843),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[f_666_1]) ).
cnf(f_666_3,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1843,U_1844),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1843) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1844,U_1843),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_666_2]) ).
fof(f_667_1,plain,
! [V_za_2,V_wa_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( V_wa_2 != V_za_2
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) )
& ( V_wa_2 = V_za_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).
fof(f_667_2,plain,
! [U_1846,U_1845] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1845,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1846,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_1845 != U_1846
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1845,U_1846) ) )
& ( U_1845 = U_1846
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1845,U_1846)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1845,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1846,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
( ! [U_1850,U_1848] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1848,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1850,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_1848 != U_1850
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1848,U_1850) ) )
& ! [U_1849,U_1847] :
( U_1847 = U_1849
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1847,U_1849)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1847,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1849,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_667_2]) ).
cnf(f_667_4,plain,
( U_1847 = U_1849
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1847,U_1849)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1847,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1849,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_667_3]) ).
cnf(f_667_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1848,U_1850)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1848,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1850,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_667_3]) ).
cnf(f_667_6,plain,
( U_1848 != U_1850
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1848,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1850,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_1,plain,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(f_668_2,plain,
! [U_1851] : c_Nat_OSuc(U_1851) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1851,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_668_1]) ).
cnf(f_668_3,plain,
c_Nat_OSuc(U_1851) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1851,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_668_2]) ).
fof(f_669_1,plain,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(f_669_2,plain,
! [U_1852] : c_Nat_OSuc(U_1852) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1852),
inference(variable_rename,[status(thm)],[f_669_1]) ).
cnf(f_669_3,plain,
c_Nat_OSuc(U_1852) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1852),
inference(clausify,[status(thm)],[f_669_2]) ).
fof(f_670_1,plain,
! [V_k] : c_Int_OBit1(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k),
inference(fof_nnf,[status(thm)],[fact_Bit1__def]) ).
fof(f_670_2,plain,
! [U_1853] : c_Int_OBit1(U_1853) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1853),U_1853),
inference(variable_rename,[status(thm)],[f_670_1]) ).
cnf(f_670_3,plain,
c_Int_OBit1(U_1853) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1853),U_1853),
inference(clausify,[status(thm)],[f_670_2]) ).
fof(f_671_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_odd__nonzero]) ).
fof(f_671_2,plain,
! [U_1854] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1854),U_1854) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_671_1]) ).
cnf(f_671_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1854),U_1854) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_671_2]) ).
fof(f_672_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
| ! [B_n] : V_l_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) )
& ( ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__ex__iff]) ).
fof(f_672_2,plain,
! [U_1858,U_1857] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1857,U_1858)
| ! [U_1856] : U_1858 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1857,U_1856) )
& ( ? [U_1855] : U_1858 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1857,U_1855)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1857,U_1858) ) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
( ! [U_1862,U_1860] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1860,U_1862)
| ! [U_1856] : U_1862 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1860,U_1856) )
& ! [U_1861,U_1859] :
( ? [U_1855] : U_1861 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1859,U_1855)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1859,U_1861) ) ),
inference(miniscope,[status(thm)],[f_672_2]) ).
fof(f_672_4,plain,
( ! [U_1862,U_1860] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1860,U_1862)
| ! [U_1856] : U_1862 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1860,U_1856) )
& ! [U_1861,U_1859] :
( U_1861 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1859,sK37(U_1861,U_1859))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1859,U_1861) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_1855,sK37(U_1861,U_1859))],[f_672_3]) ).
cnf(f_672_5,plain,
( U_1861 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1859,sK37(U_1861,U_1859))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1859,U_1861) ),
inference(clausify,[status(thm)],[f_672_4]) ).
cnf(f_672_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1860,U_1862)
| U_1862 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1860,U_1856) ),
inference(clausify,[status(thm)],[f_672_4]) ).
fof(f_673_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__right]) ).
fof(f_673_2,plain,
! [U_1864,U_1863] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1863,c_Nat_OSuc(U_1864)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1863,U_1864)),
inference(variable_rename,[status(thm)],[f_673_1]) ).
cnf(f_673_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1863,c_Nat_OSuc(U_1864)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1863,U_1864)),
inference(clausify,[status(thm)],[f_673_2]) ).
fof(f_674_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc]) ).
fof(f_674_2,plain,
! [U_1866,U_1865] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1865),U_1866) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1865,U_1866)),
inference(variable_rename,[status(thm)],[f_674_1]) ).
cnf(f_674_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1865),U_1866) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1865,U_1866)),
inference(clausify,[status(thm)],[f_674_2]) ).
fof(f_675_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__shift]) ).
fof(f_675_2,plain,
! [U_1868,U_1867] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1867),U_1868) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1867,c_Nat_OSuc(U_1868)),
inference(variable_rename,[status(thm)],[f_675_1]) ).
cnf(f_675_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1867),U_1868) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1867,c_Nat_OSuc(U_1868)),
inference(clausify,[status(thm)],[f_675_2]) ).
fof(f_676_1,plain,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
inference(fof_nnf,[status(thm)],[fact_zadd__commute]) ).
fof(f_676_2,plain,
! [U_1870,U_1869] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1869,U_1870) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1870,U_1869),
inference(variable_rename,[status(thm)],[f_676_1]) ).
cnf(f_676_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1869,U_1870) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1870,U_1869),
inference(clausify,[status(thm)],[f_676_2]) ).
fof(f_677_1,plain,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
inference(fof_nnf,[status(thm)],[fact_zadd__left__commute]) ).
fof(f_677_2,plain,
! [U_1873,U_1872,U_1871] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1871,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1872,U_1873)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1872,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1871,U_1873)),
inference(variable_rename,[status(thm)],[f_677_1]) ).
cnf(f_677_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1871,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1872,U_1873)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1872,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1871,U_1873)),
inference(clausify,[status(thm)],[f_677_2]) ).
fof(f_678_1,plain,
! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
inference(fof_nnf,[status(thm)],[fact_zadd__assoc]) ).
fof(f_678_2,plain,
! [U_1876,U_1875,U_1874] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1874,U_1875),U_1876) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1874,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1875,U_1876)),
inference(variable_rename,[status(thm)],[f_678_1]) ).
cnf(f_678_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1874,U_1875),U_1876) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1874,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1875,U_1876)),
inference(clausify,[status(thm)],[f_678_2]) ).
fof(f_679_1,plain,
! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(f_679_2,plain,
! [U_1877] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1877) = U_1877,
inference(variable_rename,[status(thm)],[f_679_1]) ).
cnf(f_679_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1877) = U_1877,
inference(clausify,[status(thm)],[f_679_2]) ).
fof(f_680_1,plain,
! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
inference(fof_nnf,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(f_680_2,plain,
! [U_1878] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1878,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1878,
inference(variable_rename,[status(thm)],[f_680_1]) ).
cnf(f_680_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1878,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1878,
inference(clausify,[status(thm)],[f_680_2]) ).
fof(f_681_1,plain,
! [V_n_2,V_m_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).
fof(f_681_2,plain,
! [U_1880,U_1879] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1879,U_1880) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1880 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1879 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_1880 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1879,U_1880) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
( ! [U_1884,U_1882] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1882,U_1884) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1884 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1882 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1883,U_1881] :
( ( U_1883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1881 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1881,U_1883) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_681_2]) ).
cnf(f_681_4,plain,
( U_1881 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1881,U_1883) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_681_3]) ).
cnf(f_681_5,plain,
( U_1883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1881,U_1883) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_681_3]) ).
cnf(f_681_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1882,U_1884) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1884 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1882 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_681_3]) ).
fof(f_682_1,plain,
! [V_n,V_m] :
( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) != V_m ),
inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero]) ).
fof(f_682_2,plain,
! [U_1886,U_1885] :
( U_1886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1885,U_1886) != U_1885 ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
fof(f_682_3,plain,
! [U_1886] :
( ! [U_1885] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1885,U_1886) != U_1885
| U_1886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_682_2]) ).
cnf(f_682_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1885,U_1886) != U_1885
| U_1886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_682_3]) ).
fof(f_683_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z,
inference(fof_nnf,[status(thm)],[fact_zadd__0]) ).
fof(f_683_2,plain,
! [U_1887] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1887) = U_1887,
inference(variable_rename,[status(thm)],[f_683_1]) ).
cnf(f_683_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1887) = U_1887,
inference(clausify,[status(thm)],[f_683_2]) ).
fof(f_684_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zadd__0__right]) ).
fof(f_684_2,plain,
! [U_1888] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1888,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1888,
inference(variable_rename,[status(thm)],[f_684_1]) ).
cnf(f_684_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1888,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1888,
inference(clausify,[status(thm)],[f_684_2]) ).
fof(f_685_1,plain,
! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k,
inference(fof_nnf,[status(thm)],[fact_add__Pls]) ).
fof(f_685_2,plain,
! [U_1889] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_1889) = U_1889,
inference(variable_rename,[status(thm)],[f_685_1]) ).
cnf(f_685_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_1889) = U_1889,
inference(clausify,[status(thm)],[f_685_2]) ).
fof(f_686_1,plain,
! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
inference(fof_nnf,[status(thm)],[fact_add__Pls__right]) ).
fof(f_686_2,plain,
! [U_1890] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1890,c_Int_OPls) = U_1890,
inference(variable_rename,[status(thm)],[f_686_1]) ).
cnf(f_686_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1890,c_Int_OPls) = U_1890,
inference(clausify,[status(thm)],[f_686_2]) ).
fof(f_687_1,plain,
! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k),
inference(fof_nnf,[status(thm)],[fact_Bit0__def]) ).
fof(f_687_2,plain,
! [U_1891] : c_Int_OBit0(U_1891) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1891,U_1891),
inference(variable_rename,[status(thm)],[f_687_1]) ).
cnf(f_687_3,plain,
c_Int_OBit0(U_1891) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1891,U_1891),
inference(clausify,[status(thm)],[f_687_2]) ).
fof(f_688_1,plain,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit0]) ).
fof(f_688_2,plain,
! [U_1893,U_1892] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_1892),c_Int_OBit0(U_1893)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1892,U_1893)),
inference(variable_rename,[status(thm)],[f_688_1]) ).
cnf(f_688_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_1892),c_Int_OBit0(U_1893)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1892,U_1893)),
inference(clausify,[status(thm)],[f_688_2]) ).
fof(f_689_1,plain,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J]) ).
fof(f_689_2,plain,
! [U_1896,U_1895,U_1894] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1894,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1896,U_1895))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1894,U_1895) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
cnf(f_689_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1894,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1896,U_1895))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1894,U_1895) ),
inference(clausify,[status(thm)],[f_689_2]) ).
fof(f_690_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J]) ).
fof(f_690_2,plain,
! [U_1899,U_1898,U_1897] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1897,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1898,U_1899))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1897,U_1898) ),
inference(variable_rename,[status(thm)],[f_690_1]) ).
cnf(f_690_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1897,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1898,U_1899))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1897,U_1898) ),
inference(clausify,[status(thm)],[f_690_2]) ).
fof(f_691_1,plain,
! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i),
inference(fof_nnf,[status(thm)],[fact_not__add__less1]) ).
fof(f_691_2,plain,
! [U_1901,U_1900] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1900,U_1901),U_1900),
inference(variable_rename,[status(thm)],[f_691_1]) ).
cnf(f_691_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1900,U_1901),U_1900),
inference(clausify,[status(thm)],[f_691_2]) ).
fof(f_692_1,plain,
! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i),
inference(fof_nnf,[status(thm)],[fact_not__add__less2]) ).
fof(f_692_2,plain,
! [U_1903,U_1902] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1902,U_1903),U_1903),
inference(variable_rename,[status(thm)],[f_692_1]) ).
cnf(f_692_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1902,U_1903),U_1903),
inference(clausify,[status(thm)],[f_692_2]) ).
fof(f_693_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).
fof(f_693_2,plain,
! [U_1906,U_1905,U_1904] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1904,U_1905),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1904,U_1906))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1905,U_1906) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1905,U_1906)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1904,U_1905),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1904,U_1906)) ) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
fof(f_693_3,plain,
( ! [U_1912,U_1910] :
( ! [U_1908] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1908,U_1910),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1908,U_1912))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1910,U_1912) )
& ! [U_1911,U_1909] :
( ! [U_1907] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1907,U_1909),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1907,U_1911))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1909,U_1911) ) ),
inference(miniscope,[status(thm)],[f_693_2]) ).
cnf(f_693_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1907,U_1909),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1907,U_1911))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1909,U_1911) ),
inference(clausify,[status(thm)],[f_693_3]) ).
cnf(f_693_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1908,U_1910),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1908,U_1912))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1910,U_1912) ),
inference(clausify,[status(thm)],[f_693_3]) ).
fof(f_694_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add1]) ).
fof(f_694_2,plain,
! [U_1915,U_1914,U_1913] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1913,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1914,U_1915))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1913,U_1914) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
cnf(f_694_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1913,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1914,U_1915))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1913,U_1914) ),
inference(clausify,[status(thm)],[f_694_2]) ).
fof(f_695_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add2]) ).
fof(f_695_2,plain,
! [U_1918,U_1917,U_1916] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1916,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1918,U_1917))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1916,U_1917) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
cnf(f_695_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1916,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1918,U_1917))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1916,U_1917) ),
inference(clausify,[status(thm)],[f_695_2]) ).
fof(f_696_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono1]) ).
fof(f_696_2,plain,
! [U_1921,U_1920,U_1919] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1919,U_1921),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1920,U_1921))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1919,U_1920) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
cnf(f_696_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1919,U_1921),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1920,U_1921))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1919,U_1920) ),
inference(clausify,[status(thm)],[f_696_2]) ).
fof(f_697_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono]) ).
fof(f_697_2,plain,
! [U_1925,U_1924,U_1923,U_1922] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1922,U_1924),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1923,U_1925))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1924,U_1925)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1922,U_1923) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
cnf(f_697_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1922,U_1924),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1923,U_1925))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1924,U_1925)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1922,U_1923) ),
inference(clausify,[status(thm)],[f_697_2]) ).
fof(f_698_1,plain,
! [V_n,V_m,V_l,V_k] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) ),
inference(fof_nnf,[status(thm)],[fact_less__add__eq__less]) ).
fof(f_698_2,plain,
! [U_1929,U_1928,U_1927,U_1926] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1928,U_1929)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1928,U_1927) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1926,U_1929)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1926,U_1927) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
cnf(f_698_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1928,U_1929)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1928,U_1927) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1926,U_1929)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1926,U_1927) ),
inference(clausify,[status(thm)],[f_698_2]) ).
fof(f_699_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ),
inference(fof_nnf,[status(thm)],[fact_add__lessD1]) ).
fof(f_699_2,plain,
! [U_1932,U_1931,U_1930] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1930,U_1932)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1930,U_1931),U_1932) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
cnf(f_699_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1930,U_1932)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1930,U_1931),U_1932) ),
inference(clausify,[status(thm)],[f_699_2]) ).
fof(f_700_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zadd__left__mono]) ).
fof(f_700_2,plain,
! [U_1935,U_1934,U_1933] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1935,U_1933),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1935,U_1934))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1933,U_1934) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
cnf(f_700_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1935,U_1933),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1935,U_1934))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1933,U_1934) ),
inference(clausify,[status(thm)],[f_700_2]) ).
fof(f_701_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono]) ).
fof(f_701_2,plain,
! [U_1938,U_1937,U_1936] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1936,U_1938),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1937,U_1938))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1936,U_1937) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
cnf(f_701_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1936,U_1938),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1937,U_1938))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1936,U_1937) ),
inference(clausify,[status(thm)],[f_701_2]) ).
fof(f_702_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J]) ).
fof(f_702_2,plain,
! [U_1941,U_1940,U_1939] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1939,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1940,U_1941))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1939,U_1940) ),
inference(variable_rename,[status(thm)],[f_702_1]) ).
cnf(f_702_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1939,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1940,U_1941))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1939,U_1940) ),
inference(clausify,[status(thm)],[f_702_2]) ).
fof(f_703_1,plain,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J]) ).
fof(f_703_2,plain,
! [U_1944,U_1943,U_1942] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1942,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1944,U_1943))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1942,U_1943) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
cnf(f_703_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1942,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1944,U_1943))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1942,U_1943) ),
inference(clausify,[status(thm)],[f_703_2]) ).
fof(f_704_1,plain,
! [V_n,V_k,V_m] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leE]) ).
fof(f_704_2,plain,
! [U_1947,U_1946,U_1945] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1946,U_1947)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1945,U_1947) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1945,U_1946),U_1947) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
cnf(f_704_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1945,U_1947)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1945,U_1946),U_1947) ),
inference(clausify,[status(thm)],[f_704_2]) ).
cnf(f_704_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1946,U_1947)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1945,U_1946),U_1947) ),
inference(clausify,[status(thm)],[f_704_2]) ).
fof(f_705_1,plain,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leD1]) ).
fof(f_705_2,plain,
! [U_1950,U_1949,U_1948] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1948,U_1950)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1948,U_1949),U_1950) ),
inference(variable_rename,[status(thm)],[f_705_1]) ).
cnf(f_705_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1948,U_1950)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1948,U_1949),U_1950) ),
inference(clausify,[status(thm)],[f_705_2]) ).
fof(f_706_1,plain,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leD2]) ).
fof(f_706_2,plain,
! [U_1953,U_1952,U_1951] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1952,U_1953)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1951,U_1952),U_1953) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
fof(f_706_3,plain,
! [U_1953,U_1952] :
( ! [U_1951] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1951,U_1952),U_1953)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1952,U_1953) ),
inference(miniscope,[status(thm)],[f_706_2]) ).
cnf(f_706_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1951,U_1952),U_1953)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1952,U_1953) ),
inference(clausify,[status(thm)],[f_706_3]) ).
fof(f_707_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono]) ).
fof(f_707_2,plain,
! [U_1957,U_1956,U_1955,U_1954] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1954,U_1956),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1955,U_1957))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1956,U_1957)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1954,U_1955) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
cnf(f_707_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1954,U_1956),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1955,U_1957))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1956,U_1957)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1954,U_1955) ),
inference(clausify,[status(thm)],[f_707_2]) ).
fof(f_708_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono1]) ).
fof(f_708_2,plain,
! [U_1960,U_1959,U_1958] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1958,U_1960),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1959,U_1960))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1958,U_1959) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
cnf(f_708_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1958,U_1960),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1959,U_1960))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1958,U_1959) ),
inference(clausify,[status(thm)],[f_708_2]) ).
fof(f_709_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add2]) ).
fof(f_709_2,plain,
! [U_1963,U_1962,U_1961] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1961,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1963,U_1962))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1961,U_1962) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
cnf(f_709_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1961,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1963,U_1962))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1961,U_1962) ),
inference(clausify,[status(thm)],[f_709_2]) ).
fof(f_710_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add1]) ).
fof(f_710_2,plain,
! [U_1966,U_1965,U_1964] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1964,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1965,U_1966))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1964,U_1965) ),
inference(variable_rename,[status(thm)],[f_710_1]) ).
cnf(f_710_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1964,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1965,U_1966))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1964,U_1965) ),
inference(clausify,[status(thm)],[f_710_2]) ).
fof(f_711_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).
fof(f_711_2,plain,
! [U_1969,U_1968,U_1967] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1967,U_1968),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1967,U_1969))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1968,U_1969) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1968,U_1969)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1967,U_1968),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1967,U_1969)) ) ),
inference(variable_rename,[status(thm)],[f_711_1]) ).
fof(f_711_3,plain,
( ! [U_1975,U_1973] :
( ! [U_1971] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1971,U_1973),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1971,U_1975))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1973,U_1975) )
& ! [U_1974,U_1972] :
( ! [U_1970] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1970,U_1972),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1970,U_1974))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1972,U_1974) ) ),
inference(miniscope,[status(thm)],[f_711_2]) ).
cnf(f_711_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1970,U_1972),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1970,U_1974))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1972,U_1974) ),
inference(clausify,[status(thm)],[f_711_3]) ).
cnf(f_711_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1971,U_1973),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1971,U_1975))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1973,U_1975) ),
inference(clausify,[status(thm)],[f_711_3]) ).
fof(f_712_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| ! [B_k] : V_n_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) )
& ( ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).
fof(f_712_2,plain,
! [U_1979,U_1978] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1978,U_1979)
| ! [U_1977] : U_1979 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1978,U_1977) )
& ( ? [U_1976] : U_1979 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1978,U_1976)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1978,U_1979) ) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
( ! [U_1983,U_1981] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1981,U_1983)
| ! [U_1977] : U_1983 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1981,U_1977) )
& ! [U_1982,U_1980] :
( ? [U_1976] : U_1982 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1980,U_1976)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1980,U_1982) ) ),
inference(miniscope,[status(thm)],[f_712_2]) ).
fof(f_712_4,plain,
( ! [U_1983,U_1981] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1981,U_1983)
| ! [U_1977] : U_1983 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1981,U_1977) )
& ! [U_1982,U_1980] :
( U_1982 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1980,sK38(U_1982,U_1980))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1980,U_1982) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_1976,sK38(U_1982,U_1980))],[f_712_3]) ).
cnf(f_712_5,plain,
( U_1982 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1980,sK38(U_1982,U_1980))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1980,U_1982) ),
inference(clausify,[status(thm)],[f_712_4]) ).
cnf(f_712_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1981,U_1983)
| U_1983 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1981,U_1977) ),
inference(clausify,[status(thm)],[f_712_4]) ).
fof(f_713_1,plain,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)),
inference(fof_nnf,[status(thm)],[fact_le__add1]) ).
fof(f_713_2,plain,
! [U_1985,U_1984] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1984,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1984,U_1985)),
inference(variable_rename,[status(thm)],[f_713_1]) ).
cnf(f_713_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1984,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1984,U_1985)),
inference(clausify,[status(thm)],[f_713_2]) ).
fof(f_714_1,plain,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_le__add2]) ).
fof(f_714_2,plain,
! [U_1987,U_1986] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1986,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1987,U_1986)),
inference(variable_rename,[status(thm)],[f_714_1]) ).
cnf(f_714_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1986,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1987,U_1986)),
inference(clausify,[status(thm)],[f_714_2]) ).
fof(f_715_1,plain,
! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),
inference(fof_nnf,[status(thm)],[fact_plus__numeral__code_I9_J]) ).
fof(f_715_2,plain,
! [U_1989,U_1988] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1988),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1989)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1988,U_1989)),
inference(variable_rename,[status(thm)],[f_715_1]) ).
cnf(f_715_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1988),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1989)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1988,U_1989)),
inference(clausify,[status(thm)],[f_715_2]) ).
fof(f_716_1,plain,
! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__cancel2]) ).
fof(f_716_2,plain,
! [U_1992,U_1991,U_1990] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1990,U_1991),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1992,U_1991)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1990,U_1992),
inference(variable_rename,[status(thm)],[f_716_1]) ).
cnf(f_716_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1990,U_1991),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1992,U_1991)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1990,U_1992),
inference(clausify,[status(thm)],[f_716_2]) ).
fof(f_717_1,plain,
! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__cancel]) ).
fof(f_717_2,plain,
! [U_1995,U_1994,U_1993] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1993,U_1994),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1993,U_1995)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1994,U_1995),
inference(variable_rename,[status(thm)],[f_717_1]) ).
cnf(f_717_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1993,U_1994),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1993,U_1995)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1994,U_1995),
inference(clausify,[status(thm)],[f_717_2]) ).
fof(f_718_1,plain,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)),
inference(fof_nnf,[status(thm)],[fact_diff__diff__left]) ).
fof(f_718_2,plain,
! [U_1998,U_1997,U_1996] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1996,U_1997),U_1998) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1996,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1997,U_1998)),
inference(variable_rename,[status(thm)],[f_718_1]) ).
cnf(f_718_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1996,U_1997),U_1998) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1996,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1997,U_1998)),
inference(clausify,[status(thm)],[f_718_2]) ).
fof(f_719_1,plain,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m,
inference(fof_nnf,[status(thm)],[fact_diff__add__inverse]) ).
fof(f_719_2,plain,
! [U_2000,U_1999] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1999,U_2000),U_1999) = U_2000,
inference(variable_rename,[status(thm)],[f_719_1]) ).
cnf(f_719_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1999,U_2000),U_1999) = U_2000,
inference(clausify,[status(thm)],[f_719_2]) ).
fof(f_720_1,plain,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m,
inference(fof_nnf,[status(thm)],[fact_diff__add__inverse2]) ).
fof(f_720_2,plain,
! [U_2002,U_2001] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2001,U_2002),U_2002) = U_2001,
inference(variable_rename,[status(thm)],[f_720_1]) ).
cnf(f_720_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2001,U_2002),U_2002) = U_2001,
inference(clausify,[status(thm)],[f_720_2]) ).
fof(f_721_1,plain,
! [V_q,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J]) ).
fof(f_721_2,plain,
! [U_2004,U_2003] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2003),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2003)),U_2004) = U_2004
| ~ class_Groups_Ocomm__monoid__add(U_2003) ),
inference(variable_rename,[status(thm)],[f_721_1]) ).
cnf(f_721_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2003),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2003)),U_2004) = U_2004
| ~ class_Groups_Ocomm__monoid__add(U_2003) ),
inference(clausify,[status(thm)],[f_721_2]) ).
fof(f_722_1,plain,
! [V_p,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J]) ).
fof(f_722_2,plain,
! [U_2006,U_2005] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2005),U_2006,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2005))) = U_2006
| ~ class_Groups_Ocomm__monoid__add(U_2005) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
cnf(f_722_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2005),U_2006,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2005))) = U_2006
| ~ class_Groups_Ocomm__monoid__add(U_2005) ),
inference(clausify,[status(thm)],[f_722_2]) ).
fof(f_723_1,plain,
! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(f_723_2,plain,
! [U_2008,U_2007] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2007,U_2008)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2007),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2008)),
inference(variable_rename,[status(thm)],[f_723_1]) ).
cnf(f_723_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2007,U_2008)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2007),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2008)),
inference(clausify,[status(thm)],[f_723_2]) ).
fof(f_724_1,plain,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
inference(fof_nnf,[status(thm)],[fact_complex__diff__def]) ).
fof(f_724_2,plain,
! [U_2010,U_2009] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2009,U_2010) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2009,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2010)),
inference(variable_rename,[status(thm)],[f_724_1]) ).
cnf(f_724_3,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2009,U_2010) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2009,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2010)),
inference(clausify,[status(thm)],[f_724_2]) ).
fof(f_725_1,plain,
! [V_v_H,V_v] :
( ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) ) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_add__nat__number__of]) ).
fof(f_725_2,plain,
! [U_2012,U_2011] :
( ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2011),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2012)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2011,U_2012))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2012,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2011),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2012)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2011)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2012,c_Int_OPls) ) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2011,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2011),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2012)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2012)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2011,c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
fof(f_725_3,plain,
( ! [U_2016,U_2014] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2014),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2016)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2014,U_2016))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2016,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2014),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2016)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2014)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2016,c_Int_OPls) ) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2014,c_Int_OPls) )
& ! [U_2015,U_2013] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2013),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2015)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2013,c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_725_2]) ).
cnf(f_725_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2013),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2015)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2013,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_725_3]) ).
cnf(f_725_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2014),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2016)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2014)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2016,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2014,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_725_3]) ).
cnf(f_725_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2014),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2016)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2014,U_2016))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2016,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2014,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_725_3]) ).
fof(f_726_1,plain,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit0]) ).
fof(f_726_2,plain,
! [U_2018,U_2017] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_2017),c_Int_OBit0(U_2018)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2017,U_2018)),
inference(variable_rename,[status(thm)],[f_726_1]) ).
cnf(f_726_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_2017),c_Int_OBit0(U_2018)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2017,U_2018)),
inference(clausify,[status(thm)],[f_726_2]) ).
fof(f_727_1,plain,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit1]) ).
fof(f_727_2,plain,
! [U_2020,U_2019] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_2019),c_Int_OBit1(U_2020)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2019,U_2020)),
inference(variable_rename,[status(thm)],[f_727_1]) ).
cnf(f_727_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_2019),c_Int_OBit1(U_2020)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2019,U_2020)),
inference(clausify,[status(thm)],[f_727_2]) ).
fof(f_728_1,plain,
! [V_n_2,V_m_2] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
| ( ( V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).
fof(f_728_2,plain,
! [U_2022,U_2021] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2021,U_2022)
| ( ( U_2022 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2021 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2022 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2021 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2022 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2021 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2021 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2021,U_2022) ) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
fof(f_728_3,plain,
( ! [U_2026,U_2024] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2026)
| ( ( U_2026 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2024 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2026 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2024 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2025,U_2023] :
( ( U_2025 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2025 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2023 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2023,U_2025) ) ),
inference(miniscope,[status(thm)],[f_728_2]) ).
cnf(f_728_4,plain,
( U_2023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2023 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2023,U_2025) ),
inference(clausify,[status(thm)],[f_728_3]) ).
cnf(f_728_5,plain,
( U_2025 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2023 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2023,U_2025) ),
inference(clausify,[status(thm)],[f_728_3]) ).
cnf(f_728_6,plain,
( U_2023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2025 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2023,U_2025) ),
inference(clausify,[status(thm)],[f_728_3]) ).
cnf(f_728_7,plain,
( U_2025 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2025 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2023,U_2025) ),
inference(clausify,[status(thm)],[f_728_3]) ).
cnf(f_728_8,plain,
( U_2026 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2024 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2026) ),
inference(clausify,[status(thm)],[f_728_3]) ).
cnf(f_728_9,plain,
( U_2026 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2024 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2026) ),
inference(clausify,[status(thm)],[f_728_3]) ).
fof(f_729_1,plain,
! [V_n_2,V_m_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).
fof(f_729_2,plain,
! [U_2028,U_2027] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2027,U_2028) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2028 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2027 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2028 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2027 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2028 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2027 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2027,U_2028) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
fof(f_729_3,plain,
( ! [U_2032,U_2030] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2030,U_2032) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2032 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2032 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2030 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2031,U_2029] :
( ( U_2031 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2029 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2029,U_2031) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_729_2]) ).
cnf(f_729_4,plain,
( U_2029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2029 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2029,U_2031) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_729_3]) ).
cnf(f_729_5,plain,
( U_2031 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2029 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2029,U_2031) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_729_3]) ).
cnf(f_729_6,plain,
( U_2029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2029,U_2031) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_729_3]) ).
cnf(f_729_7,plain,
( U_2031 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2029,U_2031) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_729_3]) ).
cnf(f_729_8,plain,
( U_2032 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2030 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2030,U_2032) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_729_3]) ).
cnf(f_729_9,plain,
( U_2032 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2030,U_2032) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_729_3]) ).
fof(f_730_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).
fof(f_730_2,plain,
! [U_2034,U_2033] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2033,U_2034))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2034)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2033) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2034)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2033)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2033,U_2034)) ) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
fof(f_730_3,plain,
( ! [U_2038,U_2036] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2036,U_2038))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2038)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2036) ) )
& ! [U_2037,U_2035] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2037)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2035)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2035,U_2037)) ) ),
inference(miniscope,[status(thm)],[f_730_2]) ).
cnf(f_730_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2037)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2035)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2035,U_2037)) ),
inference(clausify,[status(thm)],[f_730_3]) ).
cnf(f_730_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2036)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2036,U_2038)) ),
inference(clausify,[status(thm)],[f_730_3]) ).
cnf(f_730_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2038)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2036,U_2038)) ),
inference(clausify,[status(thm)],[f_730_3]) ).
fof(f_731_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_731_2,plain,
! [U_2040,U_2039] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2039,U_2040))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2040)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2039) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
cnf(f_731_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2039,U_2040))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2040)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2039) ),
inference(clausify,[status(thm)],[f_731_2]) ).
fof(f_732_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| ! [B_k] : V_n_2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) )
& ( ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).
fof(f_732_2,plain,
! [U_2044,U_2043] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2043,U_2044)
| ! [U_2042] : U_2044 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2043,U_2042)) )
& ( ? [U_2041] : U_2044 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2043,U_2041))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2043,U_2044) ) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
fof(f_732_3,plain,
( ! [U_2048,U_2046] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2046,U_2048)
| ! [U_2042] : U_2048 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2046,U_2042)) )
& ! [U_2047,U_2045] :
( ? [U_2041] : U_2047 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2045,U_2041))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2045,U_2047) ) ),
inference(miniscope,[status(thm)],[f_732_2]) ).
fof(f_732_4,plain,
( ! [U_2048,U_2046] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2046,U_2048)
| ! [U_2042] : U_2048 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2046,U_2042)) )
& ! [U_2047,U_2045] :
( U_2047 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2045,sK39(U_2047,U_2045)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2045,U_2047) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2041,sK39(U_2047,U_2045))],[f_732_3]) ).
cnf(f_732_5,plain,
( U_2047 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2045,sK39(U_2047,U_2045)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2045,U_2047) ),
inference(clausify,[status(thm)],[f_732_4]) ).
cnf(f_732_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2046,U_2048)
| U_2048 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2046,U_2042)) ),
inference(clausify,[status(thm)],[f_732_4]) ).
fof(f_733_1,plain,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc2]) ).
fof(f_733_2,plain,
! [U_2050,U_2049] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2049,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2050,U_2049))),
inference(variable_rename,[status(thm)],[f_733_1]) ).
cnf(f_733_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2049,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2050,U_2049))),
inference(clausify,[status(thm)],[f_733_2]) ).
fof(f_734_1,plain,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc1]) ).
fof(f_734_2,plain,
! [U_2052,U_2051] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2051,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2051,U_2052))),
inference(variable_rename,[status(thm)],[f_734_1]) ).
cnf(f_734_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2051,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2051,U_2052))),
inference(clausify,[status(thm)],[f_734_2]) ).
fof(f_735_1,plain,
! [V_za_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).
fof(f_735_2,plain,
! [U_2053] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2053),U_2053),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2053,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2053,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2053),U_2053),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
fof(f_735_3,plain,
( ! [U_2055] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2055),U_2055),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2055,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2054] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2054,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2054),U_2054),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_735_2]) ).
cnf(f_735_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2054,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2054),U_2054),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_735_3]) ).
cnf(f_735_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2055),U_2055),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2055,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_735_3]) ).
fof(f_736_1,plain,
! [V_z,V_z_H,V_w,V_w_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).
fof(f_736_2,plain,
! [U_2059,U_2058,U_2057,U_2056] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2056,U_2058),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2057,U_2059))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2058,U_2059)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2056,U_2057) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
cnf(f_736_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2056,U_2058),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2057,U_2059))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2058,U_2059)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2056,U_2057) ),
inference(clausify,[status(thm)],[f_736_2]) ).
fof(f_737_1,plain,
! [V_za_2,V_wa_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).
fof(f_737_2,plain,
! [U_2061,U_2060] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2060,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2061,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2060,U_2061) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2060,U_2061)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2060,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2061,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
fof(f_737_3,plain,
( ! [U_2065,U_2063] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2063,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2065,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2063,U_2065) )
& ! [U_2064,U_2062] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2062,U_2064)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2062,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2064,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_737_2]) ).
cnf(f_737_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2062,U_2064)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2062,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2064,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_737_3]) ).
cnf(f_737_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2063,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2065,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2063,U_2065) ),
inference(clausify,[status(thm)],[f_737_3]) ).
fof(f_738_1,plain,
! [V_za_2,V_wa_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2) ) ),
inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).
fof(f_738_2,plain,
! [U_2067,U_2066] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2066,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2067)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2066,U_2067) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2066,U_2067)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2066,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2067) ) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
fof(f_738_3,plain,
( ! [U_2071,U_2069] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2069,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2071)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2069,U_2071) )
& ! [U_2070,U_2068] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2068,U_2070)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2068,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2070) ) ),
inference(miniscope,[status(thm)],[f_738_2]) ).
cnf(f_738_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2068,U_2070)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2068,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2070) ),
inference(clausify,[status(thm)],[f_738_3]) ).
cnf(f_738_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2069,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2071)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2069,U_2071) ),
inference(clausify,[status(thm)],[f_738_3]) ).
fof(f_739_1,plain,
! [V_z,V_w] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z) ),
inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).
fof(f_739_2,plain,
! [U_2073,U_2072] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2072,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2073)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2072,U_2073) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
cnf(f_739_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2072,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2073)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2072,U_2073) ),
inference(clausify,[status(thm)],[f_739_2]) ).
fof(f_740_1,plain,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_diff__add__0]) ).
fof(f_740_2,plain,
! [U_2075,U_2074] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2074,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2074,U_2075)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_740_1]) ).
cnf(f_740_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2074,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2074,U_2075)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_740_2]) ).
fof(f_741_1,plain,
! [V_n,V_m] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).
fof(f_741_2,plain,
! [U_2077,U_2076] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2077,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2076,U_2077)) = U_2076
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2076,U_2077) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
cnf(f_741_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2077,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2076,U_2077)) = U_2076
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2076,U_2077) ),
inference(clausify,[status(thm)],[f_741_2]) ).
fof(f_742_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__conv]) ).
fof(f_742_2,plain,
! [U_2080,U_2079,U_2078] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2078,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2079,U_2080))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2078,U_2080),U_2079) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2078,U_2080),U_2079)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2078,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2079,U_2080)) ) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
fof(f_742_3,plain,
( ! [U_2086,U_2084,U_2082] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2082,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2084,U_2086))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2082,U_2086),U_2084) )
& ! [U_2085,U_2083,U_2081] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2081,U_2085),U_2083)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2081,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2083,U_2085)) ) ),
inference(miniscope,[status(thm)],[f_742_2]) ).
cnf(f_742_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2081,U_2085),U_2083)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2081,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2083,U_2085)) ),
inference(clausify,[status(thm)],[f_742_3]) ).
cnf(f_742_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2082,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2084,U_2086))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2082,U_2086),U_2084) ),
inference(clausify,[status(thm)],[f_742_3]) ).
fof(f_743_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2]) ).
fof(f_743_2,plain,
! [U_2089,U_2088,U_2087] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2088,U_2089),U_2087) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2088,U_2087),U_2089)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2087,U_2088) ),
inference(variable_rename,[status(thm)],[f_743_1]) ).
cnf(f_743_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2088,U_2089),U_2087) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2088,U_2087),U_2089)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2087,U_2088) ),
inference(clausify,[status(thm)],[f_743_2]) ).
fof(f_744_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2]) ).
fof(f_744_2,plain,
! [U_2092,U_2091,U_2090] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2091,U_2090),U_2092) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2091,U_2092),U_2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2090,U_2091) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
cnf(f_744_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2091,U_2090),U_2092) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2091,U_2092),U_2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2090,U_2091) ),
inference(clausify,[status(thm)],[f_744_2]) ).
fof(f_745_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc]) ).
fof(f_745_2,plain,
! [U_2095,U_2094,U_2093] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2095,U_2094),U_2093) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2095,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2094,U_2093))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2093,U_2094) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
cnf(f_745_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2095,U_2094),U_2093) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2095,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2094,U_2093))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2093,U_2094) ),
inference(clausify,[status(thm)],[f_745_2]) ).
fof(f_746_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
| V_j_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) )
& ( V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) != V_k_2 ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add]) ).
fof(f_746_2,plain,
! [U_2098,U_2097,U_2096] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2097,U_2096) = U_2098
| U_2097 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2098,U_2096) )
& ( U_2097 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2098,U_2096)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2097,U_2096) != U_2098 ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2096,U_2097) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
cnf(f_746_3,plain,
( U_2097 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2098,U_2096)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2097,U_2096) != U_2098
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2096,U_2097) ),
inference(clausify,[status(thm)],[f_746_2]) ).
cnf(f_746_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2097,U_2096) = U_2098
| U_2097 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2098,U_2096)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2096,U_2097) ),
inference(clausify,[status(thm)],[f_746_2]) ).
fof(f_747_1,plain,
! [V_m,V_n] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2]) ).
fof(f_747_2,plain,
! [U_2100,U_2099] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2100,U_2099),U_2099) = U_2100
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2099,U_2100) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
cnf(f_747_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2100,U_2099),U_2099) = U_2100
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2099,U_2100) ),
inference(clausify,[status(thm)],[f_747_2]) ).
fof(f_748_1,plain,
! [V_i_2,V_j_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__conv2]) ).
fof(f_748_2,plain,
! [U_2103,U_2102,U_2101] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2103,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2102,U_2101))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2103,U_2101),U_2102) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2103,U_2101),U_2102)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2103,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2102,U_2101)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2101,U_2102) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
cnf(f_748_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2103,U_2101),U_2102)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2103,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2102,U_2101))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2101,U_2102) ),
inference(clausify,[status(thm)],[f_748_2]) ).
cnf(f_748_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2103,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2102,U_2101))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2103,U_2101),U_2102)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2101,U_2102) ),
inference(clausify,[status(thm)],[f_748_2]) ).
fof(f_749_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc]) ).
fof(f_749_2,plain,
! [U_2106,U_2105,U_2104] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2106,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2105,U_2104)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2106,U_2105),U_2104)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2104,U_2105) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
cnf(f_749_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2106,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2105,U_2104)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2106,U_2105),U_2104)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2104,U_2105) ),
inference(clausify,[status(thm)],[f_749_2]) ).
fof(f_750_1,plain,
! [V_m,V_n] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse]) ).
fof(f_750_2,plain,
! [U_2108,U_2107] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2107,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2108,U_2107)) = U_2108
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2107,U_2108) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
cnf(f_750_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2107,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2108,U_2107)) = U_2108
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2107,U_2108) ),
inference(clausify,[status(thm)],[f_750_2]) ).
fof(f_751_1,plain,
! [V_m,V_n,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff]) ).
fof(f_751_2,plain,
! [U_2111,U_2110,U_2109] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2111,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2110,U_2111),U_2109))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2109,U_2110) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
cnf(f_751_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2111,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2110,U_2111),U_2109))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2109,U_2110) ),
inference(clausify,[status(thm)],[f_751_2]) ).
fof(f_752_1,plain,
! [V_i_2,V_k_2,V_j_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__conv]) ).
fof(f_752_2,plain,
! [U_2114,U_2113,U_2112] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2112,U_2113),U_2114)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2112,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2114,U_2113)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2112,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2114,U_2113))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2112,U_2113),U_2114) ) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
fof(f_752_3,plain,
( ! [U_2120,U_2118,U_2116] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2116,U_2118),U_2120)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2116,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2120,U_2118)) )
& ! [U_2119,U_2117,U_2115] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2115,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2119,U_2117))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2115,U_2117),U_2119) ) ),
inference(miniscope,[status(thm)],[f_752_2]) ).
cnf(f_752_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2115,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2119,U_2117))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2115,U_2117),U_2119) ),
inference(clausify,[status(thm)],[f_752_3]) ).
cnf(f_752_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2116,U_2118),U_2120)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2116,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2120,U_2118)) ),
inference(clausify,[status(thm)],[f_752_3]) ).
fof(f_753_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__right]) ).
fof(f_753_2,plain,
! [U_2123,U_2122,U_2121] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2123,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2122,U_2121)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2123,U_2121),U_2122)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2121,U_2122) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
cnf(f_753_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2123,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2122,U_2121)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2123,U_2121),U_2122)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2121,U_2122) ),
inference(clausify,[status(thm)],[f_753_2]) ).
fof(f_754_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(f_754_2,plain,
! [U_2124] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2124),U_2124) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_754_1]) ).
cnf(f_754_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2124),U_2124) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_754_2]) ).
fof(f_755_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__add]) ).
fof(f_755_2,plain,
! [U_2126,U_2125] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2125,U_2126)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2125),c_RealDef_Oreal(tc_Nat_Onat,U_2126)),
inference(variable_rename,[status(thm)],[f_755_1]) ).
cnf(f_755_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2125,U_2126)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2125),c_RealDef_Oreal(tc_Nat_Onat,U_2126)),
inference(clausify,[status(thm)],[f_755_2]) ).
fof(f_756_1,plain,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
inference(fof_nnf,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(f_756_2,plain,
! [U_2128,U_2127] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2127,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2128)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2127,U_2128),
inference(variable_rename,[status(thm)],[f_756_1]) ).
cnf(f_756_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2127,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2128)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2127,U_2128),
inference(clausify,[status(thm)],[f_756_2]) ).
fof(f_757_1,plain,
! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_diff__int__def]) ).
fof(f_757_2,plain,
! [U_2130,U_2129] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2129,U_2130) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2129,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2130)),
inference(variable_rename,[status(thm)],[f_757_1]) ).
cnf(f_757_3,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2129,U_2130) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2129,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2130)),
inference(clausify,[status(thm)],[f_757_2]) ).
fof(f_758_1,plain,
! [V_w,V_v,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq]) ).
fof(f_758_2,plain,
! [U_2133,U_2132,U_2131] :
( c_Groups_Ominus__class_Ominus(U_2131,c_Int_Onumber__class_Onumber__of(U_2131,U_2132),c_Int_Onumber__class_Onumber__of(U_2131,U_2133)) = c_Int_Onumber__class_Onumber__of(U_2131,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2132,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2133)))
| ~ class_Int_Onumber__ring(U_2131) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
cnf(f_758_3,plain,
( c_Groups_Ominus__class_Ominus(U_2131,c_Int_Onumber__class_Onumber__of(U_2131,U_2132),c_Int_Onumber__class_Onumber__of(U_2131,U_2133)) = c_Int_Onumber__class_Onumber__of(U_2131,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2132,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2133)))
| ~ class_Int_Onumber__ring(U_2131) ),
inference(clausify,[status(thm)],[f_758_2]) ).
fof(f_759_1,plain,
! [V_z] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__0__less]) ).
fof(f_759_2,plain,
! [U_2134] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2134))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2134) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
cnf(f_759_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2134))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2134) ),
inference(clausify,[status(thm)],[f_759_2]) ).
fof(f_760_1,plain,
! [V_n,V_m] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
| V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__eq__if]) ).
fof(f_760_2,plain,
! [U_2136,U_2135] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2135,U_2136) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2135,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2136))
| U_2135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2135,U_2136) = U_2136
| U_2135 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
fof(f_760_3,plain,
( ! [U_2140,U_2138] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2138,U_2140) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2138,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2140))
| U_2138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2139,U_2137] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2137,U_2139) = U_2139
| U_2137 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_760_2]) ).
cnf(f_760_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2137,U_2139) = U_2139
| U_2137 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_760_3]) ).
cnf(f_760_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2138,U_2140) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2138,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2140))
| U_2138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_760_3]) ).
fof(f_761_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_a_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
| ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).
fof(f_761_2,plain,
! [U_2145,U_2144,U_2143] :
( ( hBOOL(hAPP(U_2143,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2144,U_2145)))
| ? [U_2142] :
( ~ hBOOL(hAPP(U_2143,U_2142))
& U_2144 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2145,U_2142) )
| ( ~ hBOOL(hAPP(U_2143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2144,U_2145) ) )
& ( ( ! [U_2141] :
( hBOOL(hAPP(U_2143,U_2141))
| U_2144 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2145,U_2141) )
& ( hBOOL(hAPP(U_2143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2144,U_2145) ) )
| ~ hBOOL(hAPP(U_2143,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2144,U_2145))) ) ),
inference(variable_rename,[status(thm)],[f_761_1]) ).
fof(f_761_3,plain,
( ! [U_2151,U_2149,U_2147] :
( hBOOL(hAPP(U_2147,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2149,U_2151)))
| ? [U_2142] :
( ~ hBOOL(hAPP(U_2147,U_2142))
& U_2149 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2151,U_2142) )
| ( ~ hBOOL(hAPP(U_2147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2149,U_2151) ) )
& ! [U_2150,U_2148,U_2146] :
( ( ! [U_2141] :
( hBOOL(hAPP(U_2146,U_2141))
| U_2148 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2150,U_2141) )
& ( hBOOL(hAPP(U_2146,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2148,U_2150) ) )
| ~ hBOOL(hAPP(U_2146,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2148,U_2150))) ) ),
inference(miniscope,[status(thm)],[f_761_2]) ).
fof(f_761_4,plain,
( ! [U_2151,U_2149,U_2147] :
( hBOOL(hAPP(U_2147,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2149,U_2151)))
| ( ~ hBOOL(hAPP(U_2147,sK40(U_2151,U_2149,U_2147)))
& U_2149 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2151,sK40(U_2151,U_2149,U_2147)) )
| ( ~ hBOOL(hAPP(U_2147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2149,U_2151) ) )
& ! [U_2150,U_2148,U_2146] :
( ( ! [U_2141] :
( hBOOL(hAPP(U_2146,U_2141))
| U_2148 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2150,U_2141) )
& ( hBOOL(hAPP(U_2146,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2148,U_2150) ) )
| ~ hBOOL(hAPP(U_2146,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2148,U_2150))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2142,sK40(U_2151,U_2149,U_2147))],[f_761_3]) ).
cnf(f_761_5,plain,
( hBOOL(hAPP(U_2146,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2148,U_2150)
| ~ hBOOL(hAPP(U_2146,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2148,U_2150))) ),
inference(clausify,[status(thm)],[f_761_4]) ).
cnf(f_761_6,plain,
( hBOOL(hAPP(U_2146,U_2141))
| U_2148 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2150,U_2141)
| ~ hBOOL(hAPP(U_2146,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2148,U_2150))) ),
inference(clausify,[status(thm)],[f_761_4]) ).
cnf(f_761_7,plain,
( U_2149 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2151,sK40(U_2151,U_2149,U_2147))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2149,U_2151)
| hBOOL(hAPP(U_2147,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2149,U_2151))) ),
inference(clausify,[status(thm)],[f_761_4]) ).
cnf(f_761_8,plain,
( ~ hBOOL(hAPP(U_2147,sK40(U_2151,U_2149,U_2147)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2149,U_2151)
| hBOOL(hAPP(U_2147,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2149,U_2151))) ),
inference(clausify,[status(thm)],[f_761_4]) ).
cnf(f_761_9,plain,
( U_2149 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2151,sK40(U_2151,U_2149,U_2147))
| ~ hBOOL(hAPP(U_2147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2147,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2149,U_2151))) ),
inference(clausify,[status(thm)],[f_761_4]) ).
cnf(f_761_10,plain,
( ~ hBOOL(hAPP(U_2147,sK40(U_2151,U_2149,U_2147)))
| ~ hBOOL(hAPP(U_2147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2147,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2149,U_2151))) ),
inference(clausify,[status(thm)],[f_761_4]) ).
fof(f_762_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_a_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
| ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(f_762_2,plain,
! [U_2156,U_2155,U_2154] :
( ( hBOOL(hAPP(U_2154,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2155,U_2156)))
| ? [U_2153] :
( ~ hBOOL(hAPP(U_2154,U_2153))
& U_2155 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2156,U_2153) )
| ( ~ hBOOL(hAPP(U_2154,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2155,U_2156) ) )
& ( ( ! [U_2152] :
( hBOOL(hAPP(U_2154,U_2152))
| U_2155 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2156,U_2152) )
& ( hBOOL(hAPP(U_2154,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2155,U_2156) ) )
| ~ hBOOL(hAPP(U_2154,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2155,U_2156))) ) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
( ! [U_2162,U_2160,U_2158] :
( hBOOL(hAPP(U_2158,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2160,U_2162)))
| ? [U_2153] :
( ~ hBOOL(hAPP(U_2158,U_2153))
& U_2160 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2162,U_2153) )
| ( ~ hBOOL(hAPP(U_2158,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2160,U_2162) ) )
& ! [U_2161,U_2159,U_2157] :
( ( ! [U_2152] :
( hBOOL(hAPP(U_2157,U_2152))
| U_2159 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2161,U_2152) )
& ( hBOOL(hAPP(U_2157,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2159,U_2161) ) )
| ~ hBOOL(hAPP(U_2157,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2159,U_2161))) ) ),
inference(miniscope,[status(thm)],[f_762_2]) ).
fof(f_762_4,plain,
( ! [U_2162,U_2160,U_2158] :
( hBOOL(hAPP(U_2158,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2160,U_2162)))
| ( ~ hBOOL(hAPP(U_2158,sK41(U_2162,U_2160,U_2158)))
& U_2160 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2162,sK41(U_2162,U_2160,U_2158)) )
| ( ~ hBOOL(hAPP(U_2158,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2160,U_2162) ) )
& ! [U_2161,U_2159,U_2157] :
( ( ! [U_2152] :
( hBOOL(hAPP(U_2157,U_2152))
| U_2159 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2161,U_2152) )
& ( hBOOL(hAPP(U_2157,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2159,U_2161) ) )
| ~ hBOOL(hAPP(U_2157,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2159,U_2161))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2153,sK41(U_2162,U_2160,U_2158))],[f_762_3]) ).
cnf(f_762_5,plain,
( hBOOL(hAPP(U_2157,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2159,U_2161)
| ~ hBOOL(hAPP(U_2157,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2159,U_2161))) ),
inference(clausify,[status(thm)],[f_762_4]) ).
cnf(f_762_6,plain,
( hBOOL(hAPP(U_2157,U_2152))
| U_2159 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2161,U_2152)
| ~ hBOOL(hAPP(U_2157,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2159,U_2161))) ),
inference(clausify,[status(thm)],[f_762_4]) ).
cnf(f_762_7,plain,
( U_2160 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2162,sK41(U_2162,U_2160,U_2158))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2160,U_2162)
| hBOOL(hAPP(U_2158,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2160,U_2162))) ),
inference(clausify,[status(thm)],[f_762_4]) ).
cnf(f_762_8,plain,
( ~ hBOOL(hAPP(U_2158,sK41(U_2162,U_2160,U_2158)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2160,U_2162)
| hBOOL(hAPP(U_2158,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2160,U_2162))) ),
inference(clausify,[status(thm)],[f_762_4]) ).
cnf(f_762_9,plain,
( U_2160 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2162,sK41(U_2162,U_2160,U_2158))
| ~ hBOOL(hAPP(U_2158,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2158,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2160,U_2162))) ),
inference(clausify,[status(thm)],[f_762_4]) ).
cnf(f_762_10,plain,
( ~ hBOOL(hAPP(U_2158,sK41(U_2162,U_2160,U_2158)))
| ~ hBOOL(hAPP(U_2158,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2158,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2160,U_2162))) ),
inference(clausify,[status(thm)],[f_762_4]) ).
fof(f_763_1,plain,
! [V_m,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1]) ).
fof(f_763_2,plain,
! [U_2165,U_2164,U_2163] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2165,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2164,U_2163))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2165,U_2163),c_Nat_OSuc(U_2164))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2163,U_2164) ),
inference(variable_rename,[status(thm)],[f_763_1]) ).
cnf(f_763_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2165,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2164,U_2163))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2165,U_2163),c_Nat_OSuc(U_2164))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2163,U_2164) ),
inference(clausify,[status(thm)],[f_763_2]) ).
fof(f_764_1,plain,
! [V_m,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2]) ).
fof(f_764_2,plain,
! [U_2168,U_2167,U_2166] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2167,U_2166)),U_2168) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2167),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2166,U_2168))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2166,U_2167) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
cnf(f_764_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2167,U_2166)),U_2168) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2167),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2166,U_2168))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2166,U_2167) ),
inference(clausify,[status(thm)],[f_764_2]) ).
fof(f_765_1,plain,
! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))),
inference(fof_nnf,[status(thm)],[fact_complex__mod__triangle__sub]) ).
fof(f_765_2,plain,
! [U_2170,U_2169] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2169),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2169,U_2170)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2170))),
inference(variable_rename,[status(thm)],[f_765_1]) ).
cnf(f_765_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2169),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2169,U_2170)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2170))),
inference(clausify,[status(thm)],[f_765_2]) ).
fof(f_766_1,plain,
! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)),
inference(fof_nnf,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).
fof(f_766_2,plain,
! [U_2172,U_2171] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2171,U_2172)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2171)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2172)),
inference(variable_rename,[status(thm)],[f_766_1]) ).
cnf(f_766_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2171,U_2172)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2171)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2172)),
inference(clausify,[status(thm)],[f_766_2]) ).
fof(f_767_1,plain,
! [V_w,V_v] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),
inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I6_J]) ).
fof(f_767_2,plain,
! [U_2174,U_2173] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2173),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2174)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2173,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2174))),
inference(variable_rename,[status(thm)],[f_767_1]) ).
cnf(f_767_3,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2173),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2174)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2173,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2174))),
inference(clausify,[status(thm)],[f_767_2]) ).
fof(f_768_1,plain,
! [V_n] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),V_n),
inference(fof_nnf,[status(thm)],[fact_Suc3__eq__add__3]) ).
fof(f_768_2,plain,
! [U_2175] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(U_2175))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),U_2175),
inference(variable_rename,[status(thm)],[f_768_1]) ).
cnf(f_768_3,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(U_2175))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),U_2175),
inference(clausify,[status(thm)],[f_768_2]) ).
fof(f_769_1,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(fof_nnf,[status(thm)],[fact_nat__1__add__1]) ).
cnf(f_769_2,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(clausify,[status(thm)],[f_769_1]) ).
fof(f_770_1,plain,
! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n) = c_Nat_OSuc(c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_add__2__eq__Suc]) ).
fof(f_770_2,plain,
! [U_2176] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_2176) = c_Nat_OSuc(c_Nat_OSuc(U_2176)),
inference(variable_rename,[status(thm)],[f_770_1]) ).
cnf(f_770_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_2176) = c_Nat_OSuc(c_Nat_OSuc(U_2176)),
inference(clausify,[status(thm)],[f_770_2]) ).
fof(f_771_1,plain,
! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_add__2__eq__Suc_H]) ).
fof(f_771_2,plain,
! [U_2177] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2177,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(U_2177)),
inference(variable_rename,[status(thm)],[f_771_1]) ).
cnf(f_771_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2177,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(U_2177)),
inference(clausify,[status(thm)],[f_771_2]) ).
fof(f_772_1,plain,
! [V_v,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J]) ).
fof(f_772_2,plain,
! [U_2179,U_2178] :
( c_Groups_Ominus__class_Ominus(U_2178,c_Int_Onumber__class_Onumber__of(U_2178,U_2179),c_Groups_Oone__class_Oone(U_2178)) = c_Int_Onumber__class_Onumber__of(U_2178,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2179,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_2178) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
cnf(f_772_3,plain,
( c_Groups_Ominus__class_Ominus(U_2178,c_Int_Onumber__class_Onumber__of(U_2178,U_2179),c_Groups_Oone__class_Oone(U_2178)) = c_Int_Onumber__class_Onumber__of(U_2178,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2179,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_2178) ),
inference(clausify,[status(thm)],[f_772_2]) ).
fof(f_773_1,plain,
! [V_w,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J]) ).
fof(f_773_2,plain,
! [U_2181,U_2180] :
( c_Groups_Ominus__class_Ominus(U_2180,c_Groups_Oone__class_Oone(U_2180),c_Int_Onumber__class_Onumber__of(U_2180,U_2181)) = c_Int_Onumber__class_Onumber__of(U_2180,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2181)))
| ~ class_Int_Onumber__ring(U_2180) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
cnf(f_773_3,plain,
( c_Groups_Ominus__class_Ominus(U_2180,c_Groups_Oone__class_Oone(U_2180),c_Int_Onumber__class_Onumber__of(U_2180,U_2181)) = c_Int_Onumber__class_Onumber__of(U_2180,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2181)))
| ~ class_Int_Onumber__ring(U_2180) ),
inference(clausify,[status(thm)],[f_773_2]) ).
fof(f_774_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add]) ).
fof(f_774_2,plain,
! [U_2186,U_2185,U_2184,U_2183,U_2182] :
( c_Groups_Ominus__class_Ominus(U_2182,c_Groups_Oplus__class_Oplus(U_2182,U_2183,U_2184),c_Groups_Oplus__class_Oplus(U_2182,U_2185,U_2186)) = c_Groups_Oplus__class_Oplus(U_2182,c_Groups_Ominus__class_Ominus(U_2182,U_2183,U_2185),c_Groups_Ominus__class_Ominus(U_2182,U_2184,U_2186))
| ~ class_Groups_Oab__group__add(U_2182) ),
inference(variable_rename,[status(thm)],[f_774_1]) ).
cnf(f_774_3,plain,
( c_Groups_Ominus__class_Ominus(U_2182,c_Groups_Oplus__class_Oplus(U_2182,U_2183,U_2184),c_Groups_Oplus__class_Oplus(U_2182,U_2185,U_2186)) = c_Groups_Oplus__class_Oplus(U_2182,c_Groups_Ominus__class_Ominus(U_2182,U_2183,U_2185),c_Groups_Ominus__class_Ominus(U_2182,U_2184,U_2186))
| ~ class_Groups_Oab__group__add(U_2182) ),
inference(clausify,[status(thm)],[f_774_2]) ).
fof(f_775_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(fof_nnf,[status(thm)],[fact_less__one__imp__sqr__less__one]) ).
fof(f_775_2,plain,
! [U_2187] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2187,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2187),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
cnf(f_775_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2187,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2187),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_775_2]) ).
fof(f_776_1,plain,
! [V_a,V_b] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_real__average__minus__second]) ).
fof(f_776_2,plain,
! [U_2189,U_2188] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2188,U_2189),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2189) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2188,U_2189),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[f_776_1]) ).
cnf(f_776_3,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2188,U_2189),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2189) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2188,U_2189),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_776_2]) ).
fof(f_777_1,plain,
! [V_x] :
( V_x = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_int__pos__lt__two__imp__zero__or__one]) ).
fof(f_777_2,plain,
! [U_2190] :
( U_2190 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2190 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2190,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2190) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
cnf(f_777_3,plain,
( U_2190 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2190 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2190,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2190) ),
inference(clausify,[status(thm)],[f_777_2]) ).
fof(f_778_1,plain,
! [V_x] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x,
inference(fof_nnf,[status(thm)],[fact_real__sum__of__halves]) ).
fof(f_778_2,plain,
! [U_2191] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2191,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2191,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = U_2191,
inference(variable_rename,[status(thm)],[f_778_1]) ).
cnf(f_778_3,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2191,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2191,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = U_2191,
inference(clausify,[status(thm)],[f_778_2]) ).
fof(f_779_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__mono]) ).
fof(f_779_2,plain,
! [U_2195,U_2194,U_2193,U_2192] :
( c_Orderings_Oord__class_Oless(U_2192,c_Power_Opower__class_Opower(U_2192,U_2193,U_2195),c_Power_Opower__class_Opower(U_2192,U_2194,U_2195))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2195)
| ~ c_Orderings_Oord__class_Oless__eq(U_2192,c_Groups_Ozero__class_Ozero(U_2192),U_2193)
| ~ c_Orderings_Oord__class_Oless(U_2192,U_2193,U_2194)
| ~ class_Rings_Olinordered__semidom(U_2192) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
cnf(f_779_3,plain,
( c_Orderings_Oord__class_Oless(U_2192,c_Power_Opower__class_Opower(U_2192,U_2193,U_2195),c_Power_Opower__class_Opower(U_2192,U_2194,U_2195))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2195)
| ~ c_Orderings_Oord__class_Oless__eq(U_2192,c_Groups_Ozero__class_Ozero(U_2192),U_2193)
| ~ c_Orderings_Oord__class_Oless(U_2192,U_2193,U_2194)
| ~ class_Rings_Olinordered__semidom(U_2192) ),
inference(clausify,[status(thm)],[f_779_2]) ).
fof(f_780_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
inference(fof_nnf,[status(thm)],[fact_nat__add__commute]) ).
fof(f_780_2,plain,
! [U_2197,U_2196] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2196,U_2197) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2197,U_2196),
inference(variable_rename,[status(thm)],[f_780_1]) ).
cnf(f_780_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2196,U_2197) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2197,U_2196),
inference(clausify,[status(thm)],[f_780_2]) ).
fof(f_781_1,plain,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__commute]) ).
fof(f_781_2,plain,
! [U_2200,U_2199,U_2198] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2198,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2199,U_2200)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2199,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2198,U_2200)),
inference(variable_rename,[status(thm)],[f_781_1]) ).
cnf(f_781_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2198,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2199,U_2200)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2199,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2198,U_2200)),
inference(clausify,[status(thm)],[f_781_2]) ).
fof(f_782_1,plain,
! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
inference(fof_nnf,[status(thm)],[fact_nat__add__assoc]) ).
fof(f_782_2,plain,
! [U_2203,U_2202,U_2201] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2201,U_2202),U_2203) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2201,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2202,U_2203)),
inference(variable_rename,[status(thm)],[f_782_1]) ).
cnf(f_782_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2201,U_2202),U_2203) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2201,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2202,U_2203)),
inference(clausify,[status(thm)],[f_782_2]) ).
fof(f_783_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).
fof(f_783_2,plain,
! [U_2206,U_2205,U_2204] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2204,U_2205) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2204,U_2206)
| U_2205 != U_2206 )
& ( U_2205 = U_2206
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2204,U_2205) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2204,U_2206) ) ),
inference(variable_rename,[status(thm)],[f_783_1]) ).
fof(f_783_3,plain,
( ! [U_2212,U_2210] :
( ! [U_2208] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2208,U_2210) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2208,U_2212)
| U_2210 != U_2212 )
& ! [U_2211,U_2209] :
( ! [U_2207] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2207,U_2209) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2207,U_2211)
| U_2209 = U_2211 ) ),
inference(miniscope,[status(thm)],[f_783_2]) ).
cnf(f_783_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2207,U_2209) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2207,U_2211)
| U_2209 = U_2211 ),
inference(clausify,[status(thm)],[f_783_3]) ).
cnf(f_783_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2208,U_2210) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2208,U_2212)
| U_2210 != U_2212 ),
inference(clausify,[status(thm)],[f_783_3]) ).
fof(f_784_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).
fof(f_784_2,plain,
! [U_2215,U_2214,U_2213] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2213,U_2214) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2215,U_2214)
| U_2213 != U_2215 )
& ( U_2213 = U_2215
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2213,U_2214) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2215,U_2214) ) ),
inference(variable_rename,[status(thm)],[f_784_1]) ).
fof(f_784_3,plain,
( ! [U_2221,U_2219,U_2217] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2219) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2221,U_2219)
| U_2217 != U_2221 )
& ! [U_2220,U_2218,U_2216] :
( U_2216 = U_2220
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2216,U_2218) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2220,U_2218) ) ),
inference(miniscope,[status(thm)],[f_784_2]) ).
cnf(f_784_4,plain,
( U_2216 = U_2220
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2216,U_2218) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2220,U_2218) ),
inference(clausify,[status(thm)],[f_784_3]) ).
cnf(f_784_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2219) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2221,U_2219)
| U_2217 != U_2221 ),
inference(clausify,[status(thm)],[f_784_3]) ).
fof(f_785_1,plain,
! [V_n,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__power__not__zero]) ).
fof(f_785_2,plain,
! [U_2224,U_2223,U_2222] :
( c_Power_Opower__class_Opower(U_2222,U_2223,U_2224) != c_Groups_Ozero__class_Ozero(U_2222)
| U_2223 = c_Groups_Ozero__class_Ozero(U_2222)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2222) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
cnf(f_785_3,plain,
( c_Power_Opower__class_Opower(U_2222,U_2223,U_2224) != c_Groups_Ozero__class_Ozero(U_2222)
| U_2223 = c_Groups_Ozero__class_Ozero(U_2222)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2222) ),
inference(clausify,[status(thm)],[f_785_2]) ).
fof(f_786_1,plain,
! [V_n,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one]) ).
fof(f_786_2,plain,
! [U_2226,U_2225] :
( c_Power_Opower__class_Opower(U_2225,c_Groups_Oone__class_Oone(U_2225),U_2226) = c_Groups_Oone__class_Oone(U_2225)
| ~ class_Groups_Omonoid__mult(U_2225) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
cnf(f_786_3,plain,
( c_Power_Opower__class_Opower(U_2225,c_Groups_Oone__class_Oone(U_2225),U_2226) = c_Groups_Oone__class_Oone(U_2225)
| ~ class_Groups_Omonoid__mult(U_2225) ),
inference(clausify,[status(thm)],[f_786_2]) ).
fof(f_787_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__divide]) ).
fof(f_787_2,plain,
! [U_2230,U_2229,U_2228,U_2227] :
( c_Power_Opower__class_Opower(U_2227,c_Rings_Oinverse__class_Odivide(U_2227,U_2228,U_2229),U_2230) = c_Rings_Oinverse__class_Odivide(U_2227,c_Power_Opower__class_Opower(U_2227,U_2228,U_2230),c_Power_Opower__class_Opower(U_2227,U_2229,U_2230))
| ~ class_Fields_Ofield__inverse__zero(U_2227) ),
inference(variable_rename,[status(thm)],[f_787_1]) ).
cnf(f_787_3,plain,
( c_Power_Opower__class_Opower(U_2227,c_Rings_Oinverse__class_Odivide(U_2227,U_2228,U_2229),U_2230) = c_Rings_Oinverse__class_Odivide(U_2227,c_Power_Opower__class_Opower(U_2227,U_2228,U_2230),c_Power_Opower__class_Opower(U_2227,U_2229,U_2230))
| ~ class_Fields_Ofield__inverse__zero(U_2227) ),
inference(clausify,[status(thm)],[f_787_2]) ).
fof(f_788_1,plain,
! [V_n,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__abs]) ).
fof(f_788_2,plain,
! [U_2233,U_2232,U_2231] :
( c_Groups_Oabs__class_Oabs(U_2231,c_Power_Opower__class_Opower(U_2231,U_2232,U_2233)) = c_Power_Opower__class_Opower(U_2231,c_Groups_Oabs__class_Oabs(U_2231,U_2232),U_2233)
| ~ class_Rings_Olinordered__idom(U_2231) ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
cnf(f_788_3,plain,
( c_Groups_Oabs__class_Oabs(U_2231,c_Power_Opower__class_Opower(U_2231,U_2232,U_2233)) = c_Power_Opower__class_Opower(U_2231,c_Groups_Oabs__class_Oabs(U_2231,U_2232),U_2233)
| ~ class_Rings_Olinordered__idom(U_2231) ),
inference(clausify,[status(thm)],[f_788_2]) ).
fof(f_789_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one__right]) ).
fof(f_789_2,plain,
! [U_2235,U_2234] :
( c_Power_Opower__class_Opower(U_2234,U_2235,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2235
| ~ class_Groups_Omonoid__mult(U_2234) ),
inference(variable_rename,[status(thm)],[f_789_1]) ).
cnf(f_789_3,plain,
( c_Power_Opower__class_Opower(U_2234,U_2235,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2235
| ~ class_Groups_Omonoid__mult(U_2234) ),
inference(clausify,[status(thm)],[f_789_2]) ).
fof(f_790_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mono]) ).
fof(f_790_2,plain,
! [U_2239,U_2238,U_2237,U_2236] :
( c_Orderings_Oord__class_Oless__eq(U_2236,c_Power_Opower__class_Opower(U_2236,U_2237,U_2239),c_Power_Opower__class_Opower(U_2236,U_2238,U_2239))
| ~ c_Orderings_Oord__class_Oless__eq(U_2236,c_Groups_Ozero__class_Ozero(U_2236),U_2237)
| ~ c_Orderings_Oord__class_Oless__eq(U_2236,U_2237,U_2238)
| ~ class_Rings_Olinordered__semidom(U_2236) ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
cnf(f_790_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2236,c_Power_Opower__class_Opower(U_2236,U_2237,U_2239),c_Power_Opower__class_Opower(U_2236,U_2238,U_2239))
| ~ c_Orderings_Oord__class_Oless__eq(U_2236,c_Groups_Ozero__class_Ozero(U_2236),U_2237)
| ~ c_Orderings_Oord__class_Oless__eq(U_2236,U_2237,U_2238)
| ~ class_Rings_Olinordered__semidom(U_2236) ),
inference(clausify,[status(thm)],[f_790_2]) ).
fof(f_791_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power]) ).
fof(f_791_2,plain,
! [U_2242,U_2241,U_2240] :
( c_Orderings_Oord__class_Oless__eq(U_2240,c_Groups_Ozero__class_Ozero(U_2240),c_Power_Opower__class_Opower(U_2240,U_2241,U_2242))
| ~ c_Orderings_Oord__class_Oless__eq(U_2240,c_Groups_Ozero__class_Ozero(U_2240),U_2241)
| ~ class_Rings_Olinordered__semidom(U_2240) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
cnf(f_791_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2240,c_Groups_Ozero__class_Ozero(U_2240),c_Power_Opower__class_Opower(U_2240,U_2241,U_2242))
| ~ c_Orderings_Oord__class_Oless__eq(U_2240,c_Groups_Ozero__class_Ozero(U_2240),U_2241)
| ~ class_Rings_Olinordered__semidom(U_2240) ),
inference(clausify,[status(thm)],[f_791_2]) ).
fof(f_792_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power]) ).
fof(f_792_2,plain,
! [U_2245,U_2244,U_2243] :
( c_Orderings_Oord__class_Oless(U_2243,c_Groups_Ozero__class_Ozero(U_2243),c_Power_Opower__class_Opower(U_2243,U_2244,U_2245))
| ~ c_Orderings_Oord__class_Oless(U_2243,c_Groups_Ozero__class_Ozero(U_2243),U_2244)
| ~ class_Rings_Olinordered__semidom(U_2243) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
cnf(f_792_3,plain,
( c_Orderings_Oord__class_Oless(U_2243,c_Groups_Ozero__class_Ozero(U_2243),c_Power_Opower__class_Opower(U_2243,U_2244,U_2245))
| ~ c_Orderings_Oord__class_Oless(U_2243,c_Groups_Ozero__class_Ozero(U_2243),U_2244)
| ~ class_Rings_Olinordered__semidom(U_2243) ),
inference(clausify,[status(thm)],[f_792_2]) ).
fof(f_793_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__le__power]) ).
fof(f_793_2,plain,
! [U_2248,U_2247,U_2246] :
( c_Orderings_Oord__class_Oless__eq(U_2246,c_Groups_Oone__class_Oone(U_2246),c_Power_Opower__class_Opower(U_2246,U_2247,U_2248))
| ~ c_Orderings_Oord__class_Oless__eq(U_2246,c_Groups_Oone__class_Oone(U_2246),U_2247)
| ~ class_Rings_Olinordered__semidom(U_2246) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
cnf(f_793_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2246,c_Groups_Oone__class_Oone(U_2246),c_Power_Opower__class_Opower(U_2246,U_2247,U_2248))
| ~ c_Orderings_Oord__class_Oless__eq(U_2246,c_Groups_Oone__class_Oone(U_2246),U_2247)
| ~ class_Rings_Olinordered__semidom(U_2246) ),
inference(clausify,[status(thm)],[f_793_2]) ).
fof(f_794_1,plain,
! [V_n_2,V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).
fof(f_794_2,plain,
! [U_2251,U_2250,U_2249] :
( ( ( c_Power_Opower__class_Opower(U_2249,U_2250,U_2251) = c_Groups_Ozero__class_Ozero(U_2249)
| U_2251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2250 != c_Groups_Ozero__class_Ozero(U_2249) )
& ( ( U_2251 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2250 = c_Groups_Ozero__class_Ozero(U_2249) )
| c_Power_Opower__class_Opower(U_2249,U_2250,U_2251) != c_Groups_Ozero__class_Ozero(U_2249) ) )
| ~ class_Rings_Ozero__neq__one(U_2249)
| ~ class_Rings_Ono__zero__divisors(U_2249)
| ~ class_Rings_Omult__zero(U_2249)
| ~ class_Power_Opower(U_2249) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
cnf(f_794_3,plain,
( U_2250 = c_Groups_Ozero__class_Ozero(U_2249)
| c_Power_Opower__class_Opower(U_2249,U_2250,U_2251) != c_Groups_Ozero__class_Ozero(U_2249)
| ~ class_Rings_Ozero__neq__one(U_2249)
| ~ class_Rings_Ono__zero__divisors(U_2249)
| ~ class_Rings_Omult__zero(U_2249)
| ~ class_Power_Opower(U_2249) ),
inference(clausify,[status(thm)],[f_794_2]) ).
cnf(f_794_4,plain,
( U_2251 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(U_2249,U_2250,U_2251) != c_Groups_Ozero__class_Ozero(U_2249)
| ~ class_Rings_Ozero__neq__one(U_2249)
| ~ class_Rings_Ono__zero__divisors(U_2249)
| ~ class_Rings_Omult__zero(U_2249)
| ~ class_Power_Opower(U_2249) ),
inference(clausify,[status(thm)],[f_794_2]) ).
cnf(f_794_5,plain,
( c_Power_Opower__class_Opower(U_2249,U_2250,U_2251) = c_Groups_Ozero__class_Ozero(U_2249)
| U_2251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2250 != c_Groups_Ozero__class_Ozero(U_2249)
| ~ class_Rings_Ozero__neq__one(U_2249)
| ~ class_Rings_Ono__zero__divisors(U_2249)
| ~ class_Rings_Omult__zero(U_2249)
| ~ class_Power_Opower(U_2249) ),
inference(clausify,[status(thm)],[f_794_2]) ).
fof(f_795_1,plain,
! [V_n_2,V_m_2,V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,V_m_2) = c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| c_Power_Opower__class_Opower(T_a,V_a_2,V_m_2) != c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).
fof(f_795_2,plain,
! [U_2255,U_2254,U_2253,U_2252] :
( ( ( c_Power_Opower__class_Opower(U_2252,U_2253,U_2254) = c_Power_Opower__class_Opower(U_2252,U_2253,U_2255)
| U_2254 != U_2255 )
& ( U_2254 = U_2255
| c_Power_Opower__class_Opower(U_2252,U_2253,U_2254) != c_Power_Opower__class_Opower(U_2252,U_2253,U_2255) ) )
| ~ c_Orderings_Oord__class_Oless(U_2252,c_Groups_Oone__class_Oone(U_2252),U_2253)
| ~ class_Rings_Olinordered__semidom(U_2252) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
cnf(f_795_3,plain,
( U_2254 = U_2255
| c_Power_Opower__class_Opower(U_2252,U_2253,U_2254) != c_Power_Opower__class_Opower(U_2252,U_2253,U_2255)
| ~ c_Orderings_Oord__class_Oless(U_2252,c_Groups_Oone__class_Oone(U_2252),U_2253)
| ~ class_Rings_Olinordered__semidom(U_2252) ),
inference(clausify,[status(thm)],[f_795_2]) ).
cnf(f_795_4,plain,
( c_Power_Opower__class_Opower(U_2252,U_2253,U_2254) = c_Power_Opower__class_Opower(U_2252,U_2253,U_2255)
| U_2254 != U_2255
| ~ c_Orderings_Oord__class_Oless(U_2252,c_Groups_Oone__class_Oone(U_2252),U_2253)
| ~ class_Rings_Olinordered__semidom(U_2252) ),
inference(clausify,[status(thm)],[f_795_2]) ).
fof(f_796_1,plain,
! [V_n,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0__Suc]) ).
fof(f_796_2,plain,
! [U_2257,U_2256] :
( c_Power_Opower__class_Opower(U_2256,c_Groups_Ozero__class_Ozero(U_2256),c_Nat_OSuc(U_2257)) = c_Groups_Ozero__class_Ozero(U_2256)
| ~ class_Rings_Osemiring__0(U_2256)
| ~ class_Power_Opower(U_2256) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
cnf(f_796_3,plain,
( c_Power_Opower__class_Opower(U_2256,c_Groups_Ozero__class_Ozero(U_2256),c_Nat_OSuc(U_2257)) = c_Groups_Ozero__class_Ozero(U_2256)
| ~ class_Rings_Osemiring__0(U_2256)
| ~ class_Power_Opower(U_2256) ),
inference(clausify,[status(thm)],[f_796_2]) ).
fof(f_797_1,plain,
! [V_n,V_a,V_b,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide]) ).
fof(f_797_2,plain,
! [U_2261,U_2260,U_2259,U_2258] :
( c_Power_Opower__class_Opower(U_2258,c_Rings_Oinverse__class_Odivide(U_2258,U_2260,U_2259),U_2261) = c_Rings_Oinverse__class_Odivide(U_2258,c_Power_Opower__class_Opower(U_2258,U_2260,U_2261),c_Power_Opower__class_Opower(U_2258,U_2259,U_2261))
| U_2259 = c_Groups_Ozero__class_Ozero(U_2258)
| ~ class_Fields_Ofield(U_2258) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
cnf(f_797_3,plain,
( c_Power_Opower__class_Opower(U_2258,c_Rings_Oinverse__class_Odivide(U_2258,U_2260,U_2259),U_2261) = c_Rings_Oinverse__class_Odivide(U_2258,c_Power_Opower__class_Opower(U_2258,U_2260,U_2261),c_Power_Opower__class_Opower(U_2258,U_2259,U_2261))
| U_2259 = c_Groups_Ozero__class_Ozero(U_2258)
| ~ class_Fields_Ofield(U_2258) ),
inference(clausify,[status(thm)],[f_797_2]) ).
fof(f_798_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0]) ).
fof(f_798_2,plain,
! [U_2263,U_2262] :
( c_Power_Opower__class_Opower(U_2262,U_2263,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2262)
| ~ class_Power_Opower(U_2262) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
cnf(f_798_3,plain,
( c_Power_Opower__class_Opower(U_2262,U_2263,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2262)
| ~ class_Power_Opower(U_2262) ),
inference(clausify,[status(thm)],[f_798_2]) ).
fof(f_799_1,plain,
! [V_n,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one__over]) ).
fof(f_799_2,plain,
! [U_2266,U_2265,U_2264] :
( c_Rings_Oinverse__class_Odivide(U_2264,c_Groups_Oone__class_Oone(U_2264),c_Power_Opower__class_Opower(U_2264,U_2265,U_2266)) = c_Power_Opower__class_Opower(U_2264,c_Rings_Oinverse__class_Odivide(U_2264,c_Groups_Oone__class_Oone(U_2264),U_2265),U_2266)
| ~ class_Fields_Ofield__inverse__zero(U_2264) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
cnf(f_799_3,plain,
( c_Rings_Oinverse__class_Odivide(U_2264,c_Groups_Oone__class_Oone(U_2264),c_Power_Opower__class_Opower(U_2264,U_2265,U_2266)) = c_Power_Opower__class_Opower(U_2264,c_Rings_Oinverse__class_Odivide(U_2264,c_Groups_Oone__class_Oone(U_2264),U_2265),U_2266)
| ~ class_Fields_Ofield__inverse__zero(U_2264) ),
inference(clausify,[status(thm)],[f_799_2]) ).
fof(f_800_1,plain,
! [V_x] :
( V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one]) ).
fof(f_800_2,plain,
! [U_2267] :
( U_2267 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2267,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
cnf(f_800_3,plain,
( U_2267 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2267,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_800_2]) ).
fof(f_801_1,plain,
! [V_n,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)) = c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__power__minus]) ).
fof(f_801_2,plain,
! [U_2270,U_2269,U_2268] :
( c_Groups_Oabs__class_Oabs(U_2268,c_Power_Opower__class_Opower(U_2268,c_Groups_Ouminus__class_Ouminus(U_2268,U_2269),U_2270)) = c_Groups_Oabs__class_Oabs(U_2268,c_Power_Opower__class_Opower(U_2268,U_2269,U_2270))
| ~ class_Rings_Olinordered__idom(U_2268) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
cnf(f_801_3,plain,
( c_Groups_Oabs__class_Oabs(U_2268,c_Power_Opower__class_Opower(U_2268,c_Groups_Ouminus__class_Ouminus(U_2268,U_2269),U_2270)) = c_Groups_Oabs__class_Oabs(U_2268,c_Power_Opower__class_Opower(U_2268,U_2269,U_2270))
| ~ class_Rings_Olinordered__idom(U_2268) ),
inference(clausify,[status(thm)],[f_801_2]) ).
fof(f_802_1,plain,
! [V_m_2,V_x_2] :
( ( c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( V_x_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_m_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff]) ).
fof(f_802_2,plain,
! [U_2272,U_2271] :
( ( c_Power_Opower__class_Opower(tc_Nat_Onat,U_2271,U_2272) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_2271 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2272 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_2271 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,U_2271,U_2272) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
fof(f_802_3,plain,
( ! [U_2276,U_2274] :
( c_Power_Opower__class_Opower(tc_Nat_Onat,U_2274,U_2276) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_2274 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2276 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2275,U_2273] :
( U_2273 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,U_2273,U_2275) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_802_2]) ).
cnf(f_802_4,plain,
( U_2273 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,U_2273,U_2275) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_802_3]) ).
cnf(f_802_5,plain,
( U_2276 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,U_2274,U_2276) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_802_3]) ).
cnf(f_802_6,plain,
( U_2274 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Power_Opower__class_Opower(tc_Nat_Onat,U_2274,U_2276) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_802_3]) ).
fof(f_803_1,plain,
! [V_n] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_power__Suc__0]) ).
fof(f_803_2,plain,
! [U_2277] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2277) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_803_1]) ).
cnf(f_803_3,plain,
c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2277) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_803_2]) ).
fof(f_804_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).
fof(f_804_2,plain,
! [U_2279,U_2278] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2278,U_2279))
| ( U_2279 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2278) ) )
& ( U_2279 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2278)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2278,U_2279)) ) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
fof(f_804_3,plain,
( ! [U_2283,U_2281] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2281,U_2283))
| ( U_2283 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2281) ) )
& ! [U_2282,U_2280] :
( U_2282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2280)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2280,U_2282)) ) ),
inference(miniscope,[status(thm)],[f_804_2]) ).
cnf(f_804_4,plain,
( U_2282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2280)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2280,U_2282)) ),
inference(clausify,[status(thm)],[f_804_3]) ).
cnf(f_804_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2281)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2281,U_2283)) ),
inference(clausify,[status(thm)],[f_804_3]) ).
cnf(f_804_6,plain,
( U_2283 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2281,U_2283)) ),
inference(clausify,[status(thm)],[f_804_3]) ).
fof(f_805_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
& V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq]) ).
fof(f_805_2,plain,
! [U_2285,U_2284] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2284,U_2285))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2284)
& U_2285 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2284)
| U_2285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2284,U_2285)) ) ),
inference(variable_rename,[status(thm)],[f_805_1]) ).
fof(f_805_3,plain,
( ! [U_2289,U_2287] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2287,U_2289))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2287)
& U_2289 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2288,U_2286] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2286)
| U_2288 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2286,U_2288)) ) ),
inference(miniscope,[status(thm)],[f_805_2]) ).
cnf(f_805_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2286)
| U_2288 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2286,U_2288)) ),
inference(clausify,[status(thm)],[f_805_3]) ).
cnf(f_805_5,plain,
( U_2289 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2287,U_2289)) ),
inference(clausify,[status(thm)],[f_805_3]) ).
cnf(f_805_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2287)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2287,U_2289)) ),
inference(clausify,[status(thm)],[f_805_3]) ).
fof(f_806_1,plain,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i) ),
inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less]) ).
fof(f_806_2,plain,
! [U_2292,U_2291,U_2290] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2291,U_2292)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,U_2290,U_2291),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2290,U_2292))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2290) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
cnf(f_806_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2291,U_2292)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,U_2290,U_2291),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2290,U_2292))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2290) ),
inference(clausify,[status(thm)],[f_806_2]) ).
fof(f_807_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base]) ).
fof(f_807_2,plain,
! [U_2296,U_2295,U_2294,U_2293] :
( c_Orderings_Oord__class_Oless(U_2293,U_2294,U_2296)
| ~ c_Orderings_Oord__class_Oless__eq(U_2293,c_Groups_Ozero__class_Ozero(U_2293),U_2296)
| ~ c_Orderings_Oord__class_Oless(U_2293,c_Power_Opower__class_Opower(U_2293,U_2294,U_2295),c_Power_Opower__class_Opower(U_2293,U_2296,U_2295))
| ~ class_Rings_Olinordered__semidom(U_2293) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
cnf(f_807_3,plain,
( c_Orderings_Oord__class_Oless(U_2293,U_2294,U_2296)
| ~ c_Orderings_Oord__class_Oless__eq(U_2293,c_Groups_Ozero__class_Ozero(U_2293),U_2296)
| ~ c_Orderings_Oord__class_Oless(U_2293,c_Power_Opower__class_Opower(U_2293,U_2294,U_2295),c_Power_Opower__class_Opower(U_2293,U_2296,U_2295))
| ~ class_Rings_Olinordered__semidom(U_2293) ),
inference(clausify,[status(thm)],[f_807_2]) ).
fof(f_808_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)),c_Power_Opower__class_Opower(T_a,V_b,c_Nat_OSuc(V_n)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base]) ).
fof(f_808_2,plain,
! [U_2300,U_2299,U_2298,U_2297] :
( c_Orderings_Oord__class_Oless__eq(U_2297,U_2298,U_2300)
| ~ c_Orderings_Oord__class_Oless__eq(U_2297,c_Groups_Ozero__class_Ozero(U_2297),U_2300)
| ~ c_Orderings_Oord__class_Oless__eq(U_2297,c_Power_Opower__class_Opower(U_2297,U_2298,c_Nat_OSuc(U_2299)),c_Power_Opower__class_Opower(U_2297,U_2300,c_Nat_OSuc(U_2299)))
| ~ class_Rings_Olinordered__semidom(U_2297) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
cnf(f_808_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2297,U_2298,U_2300)
| ~ c_Orderings_Oord__class_Oless__eq(U_2297,c_Groups_Ozero__class_Ozero(U_2297),U_2300)
| ~ c_Orderings_Oord__class_Oless__eq(U_2297,c_Power_Opower__class_Opower(U_2297,U_2298,c_Nat_OSuc(U_2299)),c_Power_Opower__class_Opower(U_2297,U_2300,c_Nat_OSuc(U_2299)))
| ~ class_Rings_Olinordered__semidom(U_2297) ),
inference(clausify,[status(thm)],[f_808_2]) ).
fof(f_809_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) != c_Power_Opower__class_Opower(T_a,V_b,c_Nat_OSuc(V_n))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__base]) ).
fof(f_809_2,plain,
! [U_2304,U_2303,U_2302,U_2301] :
( U_2302 = U_2304
| ~ c_Orderings_Oord__class_Oless__eq(U_2301,c_Groups_Ozero__class_Ozero(U_2301),U_2304)
| ~ c_Orderings_Oord__class_Oless__eq(U_2301,c_Groups_Ozero__class_Ozero(U_2301),U_2302)
| c_Power_Opower__class_Opower(U_2301,U_2302,c_Nat_OSuc(U_2303)) != c_Power_Opower__class_Opower(U_2301,U_2304,c_Nat_OSuc(U_2303))
| ~ class_Rings_Olinordered__semidom(U_2301) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
cnf(f_809_3,plain,
( U_2302 = U_2304
| ~ c_Orderings_Oord__class_Oless__eq(U_2301,c_Groups_Ozero__class_Ozero(U_2301),U_2304)
| ~ c_Orderings_Oord__class_Oless__eq(U_2301,c_Groups_Ozero__class_Ozero(U_2301),U_2302)
| c_Power_Opower__class_Opower(U_2301,U_2302,c_Nat_OSuc(U_2303)) != c_Power_Opower__class_Opower(U_2301,U_2304,c_Nat_OSuc(U_2303))
| ~ class_Rings_Olinordered__semidom(U_2301) ),
inference(clausify,[status(thm)],[f_809_2]) ).
fof(f_810_1,plain,
! [V_n,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Oone__class_Oone(T_a)
| V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0__left]) ).
fof(f_810_2,plain,
! [U_2306,U_2305] :
( ( ( c_Power_Opower__class_Opower(U_2305,c_Groups_Ozero__class_Ozero(U_2305),U_2306) = c_Groups_Ozero__class_Ozero(U_2305)
| U_2306 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Power_Opower__class_Opower(U_2305,c_Groups_Ozero__class_Ozero(U_2305),U_2306) = c_Groups_Oone__class_Oone(U_2305)
| U_2306 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_2305)
| ~ class_Power_Opower(U_2305) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
cnf(f_810_3,plain,
( c_Power_Opower__class_Opower(U_2305,c_Groups_Ozero__class_Ozero(U_2305),U_2306) = c_Groups_Oone__class_Oone(U_2305)
| U_2306 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_2305)
| ~ class_Power_Opower(U_2305) ),
inference(clausify,[status(thm)],[f_810_2]) ).
cnf(f_810_4,plain,
( c_Power_Opower__class_Opower(U_2305,c_Groups_Ozero__class_Ozero(U_2305),U_2306) = c_Groups_Ozero__class_Ozero(U_2305)
| U_2306 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_2305)
| ~ class_Power_Opower(U_2305) ),
inference(clausify,[status(thm)],[f_810_2]) ).
fof(f_811_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs]) ).
fof(f_811_2,plain,
! [U_2309,U_2308,U_2307] :
( c_Orderings_Oord__class_Oless__eq(U_2307,c_Groups_Ozero__class_Ozero(U_2307),c_Power_Opower__class_Opower(U_2307,c_Groups_Oabs__class_Oabs(U_2307,U_2308),U_2309))
| ~ class_Rings_Olinordered__idom(U_2307) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
cnf(f_811_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2307,c_Groups_Ozero__class_Ozero(U_2307),c_Power_Opower__class_Opower(U_2307,c_Groups_Oabs__class_Oabs(U_2307,U_2308),U_2309))
| ~ class_Rings_Olinordered__idom(U_2307) ),
inference(clausify,[status(thm)],[f_811_2]) ).
fof(f_812_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__gt1]) ).
fof(f_812_2,plain,
! [U_2312,U_2311,U_2310] :
( c_Orderings_Oord__class_Oless(U_2310,c_Groups_Oone__class_Oone(U_2310),c_Power_Opower__class_Opower(U_2310,U_2311,c_Nat_OSuc(U_2312)))
| ~ c_Orderings_Oord__class_Oless(U_2310,c_Groups_Oone__class_Oone(U_2310),U_2311)
| ~ class_Rings_Olinordered__semidom(U_2310) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
cnf(f_812_3,plain,
( c_Orderings_Oord__class_Oless(U_2310,c_Groups_Oone__class_Oone(U_2310),c_Power_Opower__class_Opower(U_2310,U_2311,c_Nat_OSuc(U_2312)))
| ~ c_Orderings_Oord__class_Oless(U_2310,c_Groups_Oone__class_Oone(U_2310),U_2311)
| ~ class_Rings_Olinordered__semidom(U_2310) ),
inference(clausify,[status(thm)],[f_812_2]) ).
fof(f_813_1,plain,
! [V_ra_2,V_a_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff]) ).
fof(f_813_2,plain,
! [U_2316,U_2315,U_2314,U_2313] :
( ( ( c_Orderings_Oord__class_Oless(U_2313,c_Groups_Oabs__class_Oabs(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2314,U_2315)),U_2316)
| ~ c_Orderings_Oord__class_Oless(U_2313,U_2314,c_Groups_Oplus__class_Oplus(U_2313,U_2315,U_2316))
| ~ c_Orderings_Oord__class_Oless(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2315,U_2316),U_2314) )
& ( ( c_Orderings_Oord__class_Oless(U_2313,U_2314,c_Groups_Oplus__class_Oplus(U_2313,U_2315,U_2316))
& c_Orderings_Oord__class_Oless(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2315,U_2316),U_2314) )
| ~ c_Orderings_Oord__class_Oless(U_2313,c_Groups_Oabs__class_Oabs(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2314,U_2315)),U_2316) ) )
| ~ class_Rings_Olinordered__idom(U_2313) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
cnf(f_813_3,plain,
( c_Orderings_Oord__class_Oless(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2315,U_2316),U_2314)
| ~ c_Orderings_Oord__class_Oless(U_2313,c_Groups_Oabs__class_Oabs(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2314,U_2315)),U_2316)
| ~ class_Rings_Olinordered__idom(U_2313) ),
inference(clausify,[status(thm)],[f_813_2]) ).
cnf(f_813_4,plain,
( c_Orderings_Oord__class_Oless(U_2313,U_2314,c_Groups_Oplus__class_Oplus(U_2313,U_2315,U_2316))
| ~ c_Orderings_Oord__class_Oless(U_2313,c_Groups_Oabs__class_Oabs(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2314,U_2315)),U_2316)
| ~ class_Rings_Olinordered__idom(U_2313) ),
inference(clausify,[status(thm)],[f_813_2]) ).
cnf(f_813_5,plain,
( c_Orderings_Oord__class_Oless(U_2313,c_Groups_Oabs__class_Oabs(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2314,U_2315)),U_2316)
| ~ c_Orderings_Oord__class_Oless(U_2313,U_2314,c_Groups_Oplus__class_Oplus(U_2313,U_2315,U_2316))
| ~ c_Orderings_Oord__class_Oless(U_2313,c_Groups_Ominus__class_Ominus(U_2313,U_2315,U_2316),U_2314)
| ~ class_Rings_Olinordered__idom(U_2313) ),
inference(clausify,[status(thm)],[f_813_2]) ).
fof(f_814_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).
fof(f_814_2,plain,
! [U_2320,U_2319,U_2318,U_2317] :
( ( ( c_Orderings_Oord__class_Oless(U_2317,c_Power_Opower__class_Opower(U_2317,U_2318,U_2319),c_Power_Opower__class_Opower(U_2317,U_2318,U_2320))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2320) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2320)
| ~ c_Orderings_Oord__class_Oless(U_2317,c_Power_Opower__class_Opower(U_2317,U_2318,U_2319),c_Power_Opower__class_Opower(U_2317,U_2318,U_2320)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2317,c_Groups_Oone__class_Oone(U_2317),U_2318)
| ~ class_Rings_Olinordered__semidom(U_2317) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
cnf(f_814_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2320)
| ~ c_Orderings_Oord__class_Oless(U_2317,c_Power_Opower__class_Opower(U_2317,U_2318,U_2319),c_Power_Opower__class_Opower(U_2317,U_2318,U_2320))
| ~ c_Orderings_Oord__class_Oless(U_2317,c_Groups_Oone__class_Oone(U_2317),U_2318)
| ~ class_Rings_Olinordered__semidom(U_2317) ),
inference(clausify,[status(thm)],[f_814_2]) ).
cnf(f_814_4,plain,
( c_Orderings_Oord__class_Oless(U_2317,c_Power_Opower__class_Opower(U_2317,U_2318,U_2319),c_Power_Opower__class_Opower(U_2317,U_2318,U_2320))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2320)
| ~ c_Orderings_Oord__class_Oless(U_2317,c_Groups_Oone__class_Oone(U_2317),U_2318)
| ~ class_Rings_Olinordered__semidom(U_2317) ),
inference(clausify,[status(thm)],[f_814_2]) ).
fof(f_815_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp]) ).
fof(f_815_2,plain,
! [U_2324,U_2323,U_2322,U_2321] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2323,U_2324)
| ~ c_Orderings_Oord__class_Oless(U_2321,c_Power_Opower__class_Opower(U_2321,U_2322,U_2323),c_Power_Opower__class_Opower(U_2321,U_2322,U_2324))
| ~ c_Orderings_Oord__class_Oless(U_2321,c_Groups_Oone__class_Oone(U_2321),U_2322)
| ~ class_Rings_Olinordered__semidom(U_2321) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
cnf(f_815_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2323,U_2324)
| ~ c_Orderings_Oord__class_Oless(U_2321,c_Power_Opower__class_Opower(U_2321,U_2322,U_2323),c_Power_Opower__class_Opower(U_2321,U_2322,U_2324))
| ~ c_Orderings_Oord__class_Oless(U_2321,c_Groups_Oone__class_Oone(U_2321),U_2322)
| ~ class_Rings_Olinordered__semidom(U_2321) ),
inference(clausify,[status(thm)],[f_815_2]) ).
fof(f_816_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing]) ).
fof(f_816_2,plain,
! [U_2328,U_2327,U_2326,U_2325] :
( c_Orderings_Oord__class_Oless(U_2325,c_Power_Opower__class_Opower(U_2325,U_2328,U_2326),c_Power_Opower__class_Opower(U_2325,U_2328,U_2327))
| ~ c_Orderings_Oord__class_Oless(U_2325,c_Groups_Oone__class_Oone(U_2325),U_2328)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2326,U_2327)
| ~ class_Rings_Olinordered__semidom(U_2325) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
cnf(f_816_3,plain,
( c_Orderings_Oord__class_Oless(U_2325,c_Power_Opower__class_Opower(U_2325,U_2328,U_2326),c_Power_Opower__class_Opower(U_2325,U_2328,U_2327))
| ~ c_Orderings_Oord__class_Oless(U_2325,c_Groups_Oone__class_Oone(U_2325),U_2328)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2326,U_2327)
| ~ class_Rings_Olinordered__semidom(U_2325) ),
inference(clausify,[status(thm)],[f_816_2]) ).
fof(f_817_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing]) ).
fof(f_817_2,plain,
! [U_2332,U_2331,U_2330,U_2329] :
( c_Orderings_Oord__class_Oless__eq(U_2329,c_Power_Opower__class_Opower(U_2329,U_2332,U_2330),c_Power_Opower__class_Opower(U_2329,U_2332,U_2331))
| ~ c_Orderings_Oord__class_Oless__eq(U_2329,c_Groups_Oone__class_Oone(U_2329),U_2332)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2330,U_2331)
| ~ class_Rings_Olinordered__semidom(U_2329) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
cnf(f_817_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2329,c_Power_Opower__class_Opower(U_2329,U_2332,U_2330),c_Power_Opower__class_Opower(U_2329,U_2332,U_2331))
| ~ c_Orderings_Oord__class_Oless__eq(U_2329,c_Groups_Oone__class_Oone(U_2329),U_2332)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2330,U_2331)
| ~ class_Rings_Olinordered__semidom(U_2329) ),
inference(clausify,[status(thm)],[f_817_2]) ).
fof(f_818_1,plain,
! [V_wa_2,V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff__number__of]) ).
fof(f_818_2,plain,
! [U_2335,U_2334,U_2333] :
( ( ( c_Power_Opower__class_Opower(U_2333,U_2334,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335)) = c_Groups_Ozero__class_Ozero(U_2333)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2334 != c_Groups_Ozero__class_Ozero(U_2333) )
& ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2334 = c_Groups_Ozero__class_Ozero(U_2333) )
| c_Power_Opower__class_Opower(U_2333,U_2334,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335)) != c_Groups_Ozero__class_Ozero(U_2333) ) )
| ~ class_Rings_Ozero__neq__one(U_2333)
| ~ class_Rings_Ono__zero__divisors(U_2333)
| ~ class_Rings_Omult__zero(U_2333)
| ~ class_Power_Opower(U_2333) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
cnf(f_818_3,plain,
( U_2334 = c_Groups_Ozero__class_Ozero(U_2333)
| c_Power_Opower__class_Opower(U_2333,U_2334,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335)) != c_Groups_Ozero__class_Ozero(U_2333)
| ~ class_Rings_Ozero__neq__one(U_2333)
| ~ class_Rings_Ono__zero__divisors(U_2333)
| ~ class_Rings_Omult__zero(U_2333)
| ~ class_Power_Opower(U_2333) ),
inference(clausify,[status(thm)],[f_818_2]) ).
cnf(f_818_4,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(U_2333,U_2334,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335)) != c_Groups_Ozero__class_Ozero(U_2333)
| ~ class_Rings_Ozero__neq__one(U_2333)
| ~ class_Rings_Ono__zero__divisors(U_2333)
| ~ class_Rings_Omult__zero(U_2333)
| ~ class_Power_Opower(U_2333) ),
inference(clausify,[status(thm)],[f_818_2]) ).
cnf(f_818_5,plain,
( c_Power_Opower__class_Opower(U_2333,U_2334,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335)) = c_Groups_Ozero__class_Ozero(U_2333)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2334 != c_Groups_Ozero__class_Ozero(U_2333)
| ~ class_Rings_Ozero__neq__one(U_2333)
| ~ class_Rings_Ono__zero__divisors(U_2333)
| ~ class_Rings_Omult__zero(U_2333)
| ~ class_Power_Opower(U_2333) ),
inference(clausify,[status(thm)],[f_818_2]) ).
fof(f_819_1,plain,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i) ),
inference(fof_nnf,[status(thm)],[fact_nat__one__le__power]) ).
fof(f_819_2,plain,
! [U_2337,U_2336] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2336,U_2337))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2336) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
cnf(f_819_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2336,U_2337))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2336) ),
inference(clausify,[status(thm)],[f_819_2]) ).
fof(f_820_1,plain,
! [V_wa_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
& c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq__number__of]) ).
fof(f_820_2,plain,
! [U_2339,U_2338] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2338,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2339)))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2338)
& c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2339) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2338)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2339) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2338,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2339))) ) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
fof(f_820_3,plain,
( ! [U_2343,U_2341] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2341,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2343)))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2341)
& c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2343) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2342,U_2340] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2340)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2342) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2340,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2342))) ) ),
inference(miniscope,[status(thm)],[f_820_2]) ).
cnf(f_820_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2340)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2342) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2340,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2342))) ),
inference(clausify,[status(thm)],[f_820_3]) ).
cnf(f_820_5,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2343) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2341,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2343))) ),
inference(clausify,[status(thm)],[f_820_3]) ).
cnf(f_820_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2341)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2341,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2343))) ),
inference(clausify,[status(thm)],[f_820_3]) ).
fof(f_821_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one]) ).
fof(f_821_2,plain,
! [U_2346,U_2345,U_2344] :
( c_Orderings_Oord__class_Oless(U_2344,c_Power_Opower__class_Opower(U_2344,U_2345,c_Nat_OSuc(U_2346)),c_Groups_Oone__class_Oone(U_2344))
| ~ c_Orderings_Oord__class_Oless(U_2344,U_2345,c_Groups_Oone__class_Oone(U_2344))
| ~ c_Orderings_Oord__class_Oless(U_2344,c_Groups_Ozero__class_Ozero(U_2344),U_2345)
| ~ class_Rings_Olinordered__semidom(U_2344) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
cnf(f_821_3,plain,
( c_Orderings_Oord__class_Oless(U_2344,c_Power_Opower__class_Opower(U_2344,U_2345,c_Nat_OSuc(U_2346)),c_Groups_Oone__class_Oone(U_2344))
| ~ c_Orderings_Oord__class_Oless(U_2344,U_2345,c_Groups_Oone__class_Oone(U_2344))
| ~ c_Orderings_Oord__class_Oless(U_2344,c_Groups_Ozero__class_Ozero(U_2344),U_2345)
| ~ class_Rings_Olinordered__semidom(U_2344) ),
inference(clausify,[status(thm)],[f_821_2]) ).
fof(f_822_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing]) ).
fof(f_822_2,plain,
! [U_2350,U_2349,U_2348,U_2347] :
( c_Orderings_Oord__class_Oless(U_2347,c_Power_Opower__class_Opower(U_2347,U_2350,U_2349),c_Power_Opower__class_Opower(U_2347,U_2350,U_2348))
| ~ c_Orderings_Oord__class_Oless(U_2347,U_2350,c_Groups_Oone__class_Oone(U_2347))
| ~ c_Orderings_Oord__class_Oless(U_2347,c_Groups_Ozero__class_Ozero(U_2347),U_2350)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2348,U_2349)
| ~ class_Rings_Olinordered__semidom(U_2347) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
cnf(f_822_3,plain,
( c_Orderings_Oord__class_Oless(U_2347,c_Power_Opower__class_Opower(U_2347,U_2350,U_2349),c_Power_Opower__class_Opower(U_2347,U_2350,U_2348))
| ~ c_Orderings_Oord__class_Oless(U_2347,U_2350,c_Groups_Oone__class_Oone(U_2347))
| ~ c_Orderings_Oord__class_Oless(U_2347,c_Groups_Ozero__class_Ozero(U_2347),U_2350)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2348,U_2349)
| ~ class_Rings_Olinordered__semidom(U_2347) ),
inference(clausify,[status(thm)],[f_822_2]) ).
fof(f_823_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Power_Opower__class_Opower(T_a,V_b,V_n)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base]) ).
fof(f_823_2,plain,
! [U_2354,U_2353,U_2352,U_2351] :
( U_2352 = U_2354
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(U_2351,c_Groups_Ozero__class_Ozero(U_2351),U_2354)
| ~ c_Orderings_Oord__class_Oless__eq(U_2351,c_Groups_Ozero__class_Ozero(U_2351),U_2352)
| c_Power_Opower__class_Opower(U_2351,U_2352,U_2353) != c_Power_Opower__class_Opower(U_2351,U_2354,U_2353)
| ~ class_Rings_Olinordered__semidom(U_2351) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
cnf(f_823_3,plain,
( U_2352 = U_2354
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(U_2351,c_Groups_Ozero__class_Ozero(U_2351),U_2354)
| ~ c_Orderings_Oord__class_Oless__eq(U_2351,c_Groups_Ozero__class_Ozero(U_2351),U_2352)
| c_Power_Opower__class_Opower(U_2351,U_2352,U_2353) != c_Power_Opower__class_Opower(U_2351,U_2354,U_2353)
| ~ class_Rings_Olinordered__semidom(U_2351) ),
inference(clausify,[status(thm)],[f_823_2]) ).
fof(f_824_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__decreasing]) ).
fof(f_824_2,plain,
! [U_2358,U_2357,U_2356,U_2355] :
( c_Orderings_Oord__class_Oless__eq(U_2355,c_Power_Opower__class_Opower(U_2355,U_2358,U_2357),c_Power_Opower__class_Opower(U_2355,U_2358,U_2356))
| ~ c_Orderings_Oord__class_Oless__eq(U_2355,U_2358,c_Groups_Oone__class_Oone(U_2355))
| ~ c_Orderings_Oord__class_Oless__eq(U_2355,c_Groups_Ozero__class_Ozero(U_2355),U_2358)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2356,U_2357)
| ~ class_Rings_Olinordered__semidom(U_2355) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
cnf(f_824_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2355,c_Power_Opower__class_Opower(U_2355,U_2358,U_2357),c_Power_Opower__class_Opower(U_2355,U_2358,U_2356))
| ~ c_Orderings_Oord__class_Oless__eq(U_2355,U_2358,c_Groups_Oone__class_Oone(U_2355))
| ~ c_Orderings_Oord__class_Oless__eq(U_2355,c_Groups_Ozero__class_Ozero(U_2355),U_2358)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2356,U_2357)
| ~ class_Rings_Olinordered__semidom(U_2355) ),
inference(clausify,[status(thm)],[f_824_2]) ).
fof(f_825_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp]) ).
fof(f_825_2,plain,
! [U_2362,U_2361,U_2360,U_2359] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2361,U_2362)
| ~ c_Orderings_Oord__class_Oless__eq(U_2359,c_Power_Opower__class_Opower(U_2359,U_2360,U_2361),c_Power_Opower__class_Opower(U_2359,U_2360,U_2362))
| ~ c_Orderings_Oord__class_Oless(U_2359,c_Groups_Oone__class_Oone(U_2359),U_2360)
| ~ class_Rings_Olinordered__semidom(U_2359) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
cnf(f_825_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2361,U_2362)
| ~ c_Orderings_Oord__class_Oless__eq(U_2359,c_Power_Opower__class_Opower(U_2359,U_2360,U_2361),c_Power_Opower__class_Opower(U_2359,U_2360,U_2362))
| ~ c_Orderings_Oord__class_Oless(U_2359,c_Groups_Oone__class_Oone(U_2359),U_2360)
| ~ class_Rings_Olinordered__semidom(U_2359) ),
inference(clausify,[status(thm)],[f_825_2]) ).
fof(f_826_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).
fof(f_826_2,plain,
! [U_2366,U_2365,U_2364,U_2363] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2363,c_Power_Opower__class_Opower(U_2363,U_2364,U_2365),c_Power_Opower__class_Opower(U_2363,U_2364,U_2366))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2365,U_2366) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2365,U_2366)
| ~ c_Orderings_Oord__class_Oless__eq(U_2363,c_Power_Opower__class_Opower(U_2363,U_2364,U_2365),c_Power_Opower__class_Opower(U_2363,U_2364,U_2366)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2363,c_Groups_Oone__class_Oone(U_2363),U_2364)
| ~ class_Rings_Olinordered__semidom(U_2363) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
cnf(f_826_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2365,U_2366)
| ~ c_Orderings_Oord__class_Oless__eq(U_2363,c_Power_Opower__class_Opower(U_2363,U_2364,U_2365),c_Power_Opower__class_Opower(U_2363,U_2364,U_2366))
| ~ c_Orderings_Oord__class_Oless(U_2363,c_Groups_Oone__class_Oone(U_2363),U_2364)
| ~ class_Rings_Olinordered__semidom(U_2363) ),
inference(clausify,[status(thm)],[f_826_2]) ).
cnf(f_826_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2363,c_Power_Opower__class_Opower(U_2363,U_2364,U_2365),c_Power_Opower__class_Opower(U_2363,U_2364,U_2366))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2365,U_2366)
| ~ c_Orderings_Oord__class_Oless(U_2363,c_Groups_Oone__class_Oone(U_2363),U_2364)
| ~ class_Rings_Olinordered__semidom(U_2363) ),
inference(clausify,[status(thm)],[f_826_2]) ).
fof(f_827_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__less__power]) ).
fof(f_827_2,plain,
! [U_2369,U_2368,U_2367] :
( c_Orderings_Oord__class_Oless(U_2367,c_Groups_Oone__class_Oone(U_2367),c_Power_Opower__class_Opower(U_2367,U_2368,U_2369))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2369)
| ~ c_Orderings_Oord__class_Oless(U_2367,c_Groups_Oone__class_Oone(U_2367),U_2368)
| ~ class_Rings_Olinordered__semidom(U_2367) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
cnf(f_827_3,plain,
( c_Orderings_Oord__class_Oless(U_2367,c_Groups_Oone__class_Oone(U_2367),c_Power_Opower__class_Opower(U_2367,U_2368,U_2369))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2369)
| ~ c_Orderings_Oord__class_Oless(U_2367,c_Groups_Oone__class_Oone(U_2367),U_2368)
| ~ class_Rings_Olinordered__semidom(U_2367) ),
inference(clausify,[status(thm)],[f_827_2]) ).
fof(f_828_1,plain,
! [V_w,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0__left__number__of]) ).
fof(f_828_2,plain,
! [U_2371,U_2370] :
( ( ( c_Power_Opower__class_Opower(U_2370,c_Groups_Ozero__class_Ozero(U_2370),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2371)) = c_Groups_Ozero__class_Ozero(U_2370)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2371) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Power_Opower__class_Opower(U_2370,c_Groups_Ozero__class_Ozero(U_2370),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2371)) = c_Groups_Oone__class_Oone(U_2370)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2371) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_2370)
| ~ class_Power_Opower(U_2370) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
cnf(f_828_3,plain,
( c_Power_Opower__class_Opower(U_2370,c_Groups_Ozero__class_Ozero(U_2370),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2371)) = c_Groups_Oone__class_Oone(U_2370)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2371) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_2370)
| ~ class_Power_Opower(U_2370) ),
inference(clausify,[status(thm)],[f_828_2]) ).
cnf(f_828_4,plain,
( c_Power_Opower__class_Opower(U_2370,c_Groups_Ozero__class_Ozero(U_2370),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2371)) = c_Groups_Ozero__class_Ozero(U_2370)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2371) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_2370)
| ~ class_Power_Opower(U_2370) ),
inference(clausify,[status(thm)],[f_828_2]) ).
fof(f_829_1,plain,
! [V_m,V_n,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__diff]) ).
fof(f_829_2,plain,
! [U_2375,U_2374,U_2373,U_2372] :
( c_Power_Opower__class_Opower(U_2372,U_2373,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2375,U_2374)) = c_Rings_Oinverse__class_Odivide(U_2372,c_Power_Opower__class_Opower(U_2372,U_2373,U_2375),c_Power_Opower__class_Opower(U_2372,U_2373,U_2374))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2374,U_2375)
| U_2373 = c_Groups_Ozero__class_Ozero(U_2372)
| ~ class_Fields_Ofield(U_2372) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
cnf(f_829_3,plain,
( c_Power_Opower__class_Opower(U_2372,U_2373,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2375,U_2374)) = c_Rings_Oinverse__class_Odivide(U_2372,c_Power_Opower__class_Opower(U_2372,U_2373,U_2375),c_Power_Opower__class_Opower(U_2372,U_2373,U_2374))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2374,U_2375)
| U_2373 = c_Groups_Ozero__class_Ozero(U_2372)
| ~ class_Fields_Ofield(U_2372) ),
inference(clausify,[status(thm)],[f_829_2]) ).
fof(f_830_1,plain,
! [V_z] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z,
inference(fof_nnf,[status(thm)],[fact_csqrt]) ).
fof(f_830_2,plain,
! [U_2376] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(U_2376),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2376,
inference(variable_rename,[status(thm)],[f_830_1]) ).
cnf(f_830_3,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(U_2376),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2376,
inference(clausify,[status(thm)],[f_830_2]) ).
fof(f_831_1,plain,
! [V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_831_2,plain,
! [U_2378,U_2377] :
( c_Power_Opower__class_Opower(U_2377,U_2378,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2377)
| ~ class_Rings_Ocomm__semiring__1(U_2377) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
cnf(f_831_3,plain,
( c_Power_Opower__class_Opower(U_2377,U_2378,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2377)
| ~ class_Rings_Ocomm__semiring__1(U_2377) ),
inference(clausify,[status(thm)],[f_831_2]) ).
fof(f_832_1,plain,
! [V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_832_2,plain,
! [U_2381,U_2380,U_2379] :
( c_Groups_Oplus__class_Oplus(U_2379,U_2380,U_2381) = c_Groups_Oplus__class_Oplus(U_2379,U_2381,U_2380)
| ~ class_Rings_Ocomm__semiring__1(U_2379) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
cnf(f_832_3,plain,
( c_Groups_Oplus__class_Oplus(U_2379,U_2380,U_2381) = c_Groups_Oplus__class_Oplus(U_2379,U_2381,U_2380)
| ~ class_Rings_Ocomm__semiring__1(U_2379) ),
inference(clausify,[status(thm)],[f_832_2]) ).
fof(f_833_1,plain,
! [V_d,V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_833_2,plain,
! [U_2385,U_2384,U_2383,U_2382] :
( c_Groups_Oplus__class_Oplus(U_2382,U_2383,c_Groups_Oplus__class_Oplus(U_2382,U_2384,U_2385)) = c_Groups_Oplus__class_Oplus(U_2382,U_2384,c_Groups_Oplus__class_Oplus(U_2382,U_2383,U_2385))
| ~ class_Rings_Ocomm__semiring__1(U_2382) ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
cnf(f_833_3,plain,
( c_Groups_Oplus__class_Oplus(U_2382,U_2383,c_Groups_Oplus__class_Oplus(U_2382,U_2384,U_2385)) = c_Groups_Oplus__class_Oplus(U_2382,U_2384,c_Groups_Oplus__class_Oplus(U_2382,U_2383,U_2385))
| ~ class_Rings_Ocomm__semiring__1(U_2382) ),
inference(clausify,[status(thm)],[f_833_2]) ).
fof(f_834_1,plain,
! [V_d,V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_834_2,plain,
! [U_2389,U_2388,U_2387,U_2386] :
( c_Groups_Oplus__class_Oplus(U_2386,U_2387,c_Groups_Oplus__class_Oplus(U_2386,U_2388,U_2389)) = c_Groups_Oplus__class_Oplus(U_2386,c_Groups_Oplus__class_Oplus(U_2386,U_2387,U_2388),U_2389)
| ~ class_Rings_Ocomm__semiring__1(U_2386) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
cnf(f_834_3,plain,
( c_Groups_Oplus__class_Oplus(U_2386,U_2387,c_Groups_Oplus__class_Oplus(U_2386,U_2388,U_2389)) = c_Groups_Oplus__class_Oplus(U_2386,c_Groups_Oplus__class_Oplus(U_2386,U_2387,U_2388),U_2389)
| ~ class_Rings_Ocomm__semiring__1(U_2386) ),
inference(clausify,[status(thm)],[f_834_2]) ).
fof(f_835_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_835_2,plain,
! [U_2393,U_2392,U_2391,U_2390] :
( c_Groups_Oplus__class_Oplus(U_2390,c_Groups_Oplus__class_Oplus(U_2390,U_2391,U_2392),U_2393) = c_Groups_Oplus__class_Oplus(U_2390,U_2391,c_Groups_Oplus__class_Oplus(U_2390,U_2392,U_2393))
| ~ class_Rings_Ocomm__semiring__1(U_2390) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
cnf(f_835_3,plain,
( c_Groups_Oplus__class_Oplus(U_2390,c_Groups_Oplus__class_Oplus(U_2390,U_2391,U_2392),U_2393) = c_Groups_Oplus__class_Oplus(U_2390,U_2391,c_Groups_Oplus__class_Oplus(U_2390,U_2392,U_2393))
| ~ class_Rings_Ocomm__semiring__1(U_2390) ),
inference(clausify,[status(thm)],[f_835_2]) ).
fof(f_836_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_836_2,plain,
! [U_2397,U_2396,U_2395,U_2394] :
( c_Groups_Oplus__class_Oplus(U_2394,c_Groups_Oplus__class_Oplus(U_2394,U_2395,U_2396),U_2397) = c_Groups_Oplus__class_Oplus(U_2394,c_Groups_Oplus__class_Oplus(U_2394,U_2395,U_2397),U_2396)
| ~ class_Rings_Ocomm__semiring__1(U_2394) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
cnf(f_836_3,plain,
( c_Groups_Oplus__class_Oplus(U_2394,c_Groups_Oplus__class_Oplus(U_2394,U_2395,U_2396),U_2397) = c_Groups_Oplus__class_Oplus(U_2394,c_Groups_Oplus__class_Oplus(U_2394,U_2395,U_2397),U_2396)
| ~ class_Rings_Ocomm__semiring__1(U_2394) ),
inference(clausify,[status(thm)],[f_836_2]) ).
fof(f_837_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_837_2,plain,
! [U_2402,U_2401,U_2400,U_2399,U_2398] :
( c_Groups_Oplus__class_Oplus(U_2398,c_Groups_Oplus__class_Oplus(U_2398,U_2399,U_2400),c_Groups_Oplus__class_Oplus(U_2398,U_2401,U_2402)) = c_Groups_Oplus__class_Oplus(U_2398,c_Groups_Oplus__class_Oplus(U_2398,U_2399,U_2401),c_Groups_Oplus__class_Oplus(U_2398,U_2400,U_2402))
| ~ class_Rings_Ocomm__semiring__1(U_2398) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
cnf(f_837_3,plain,
( c_Groups_Oplus__class_Oplus(U_2398,c_Groups_Oplus__class_Oplus(U_2398,U_2399,U_2400),c_Groups_Oplus__class_Oplus(U_2398,U_2401,U_2402)) = c_Groups_Oplus__class_Oplus(U_2398,c_Groups_Oplus__class_Oplus(U_2398,U_2399,U_2401),c_Groups_Oplus__class_Oplus(U_2398,U_2400,U_2402))
| ~ class_Rings_Ocomm__semiring__1(U_2398) ),
inference(clausify,[status(thm)],[f_837_2]) ).
fof(f_838_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_b_2 != c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).
fof(f_838_2,plain,
! [U_2405,U_2404,U_2403] :
( ( ( U_2404 = c_Groups_Oplus__class_Oplus(U_2403,U_2404,U_2405)
| U_2405 != c_Groups_Ozero__class_Ozero(U_2403) )
& ( U_2405 = c_Groups_Ozero__class_Ozero(U_2403)
| U_2404 != c_Groups_Oplus__class_Oplus(U_2403,U_2404,U_2405) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2403) ),
inference(variable_rename,[status(thm)],[f_838_1]) ).
cnf(f_838_3,plain,
( U_2405 = c_Groups_Ozero__class_Ozero(U_2403)
| U_2404 != c_Groups_Oplus__class_Oplus(U_2403,U_2404,U_2405)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2403) ),
inference(clausify,[status(thm)],[f_838_2]) ).
cnf(f_838_4,plain,
( U_2404 = c_Groups_Oplus__class_Oplus(U_2403,U_2404,U_2405)
| U_2405 != c_Groups_Ozero__class_Ozero(U_2403)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2403) ),
inference(clausify,[status(thm)],[f_838_2]) ).
fof(f_839_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_839_2,plain,
! [U_2407,U_2406] :
( c_Groups_Oplus__class_Oplus(U_2406,U_2407,c_Groups_Ozero__class_Ozero(U_2406)) = U_2407
| ~ class_Rings_Ocomm__semiring__1(U_2406) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
cnf(f_839_3,plain,
( c_Groups_Oplus__class_Oplus(U_2406,U_2407,c_Groups_Ozero__class_Ozero(U_2406)) = U_2407
| ~ class_Rings_Ocomm__semiring__1(U_2406) ),
inference(clausify,[status(thm)],[f_839_2]) ).
fof(f_840_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_840_2,plain,
! [U_2409,U_2408] :
( c_Groups_Oplus__class_Oplus(U_2408,c_Groups_Ozero__class_Ozero(U_2408),U_2409) = U_2409
| ~ class_Rings_Ocomm__semiring__1(U_2408) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
cnf(f_840_3,plain,
( c_Groups_Oplus__class_Oplus(U_2408,c_Groups_Ozero__class_Ozero(U_2408),U_2409) = U_2409
| ~ class_Rings_Ocomm__semiring__1(U_2408) ),
inference(clausify,[status(thm)],[f_840_2]) ).
fof(f_841_1,plain,
! [V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_841_2,plain,
! [U_2411,U_2410] :
( c_Power_Opower__class_Opower(U_2410,U_2411,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2411
| ~ class_Rings_Ocomm__semiring__1(U_2410) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
cnf(f_841_3,plain,
( c_Power_Opower__class_Opower(U_2410,U_2411,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2411
| ~ class_Rings_Ocomm__semiring__1(U_2410) ),
inference(clausify,[status(thm)],[f_841_2]) ).
fof(f_842_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J]) ).
fof(f_842_2,plain,
! [U_2414,U_2413,U_2412] :
( c_Groups_Ominus__class_Ominus(U_2412,U_2413,U_2414) = c_Groups_Oplus__class_Oplus(U_2412,U_2413,c_Groups_Ouminus__class_Ouminus(U_2412,U_2414))
| ~ class_Rings_Ocomm__ring__1(U_2412) ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
cnf(f_842_3,plain,
( c_Groups_Ominus__class_Ominus(U_2412,U_2413,U_2414) = c_Groups_Oplus__class_Oplus(U_2412,U_2413,c_Groups_Ouminus__class_Ouminus(U_2412,U_2414))
| ~ class_Rings_Ocomm__ring__1(U_2412) ),
inference(clausify,[status(thm)],[f_842_2]) ).
fof(f_843_1,plain,
! [V_x_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
| c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J]) ).
fof(f_843_2,plain,
! [U_2416,U_2415] :
( ( ( c_Int_Onumber__class_Onumber__of(U_2415,U_2416) = c_Groups_Oone__class_Oone(U_2415)
| ~ c_Int_Oiszero(U_2415,c_Int_Onumber__class_Onumber__of(U_2415,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2416,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(U_2415,c_Int_Onumber__class_Onumber__of(U_2415,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2416,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
| c_Int_Onumber__class_Onumber__of(U_2415,U_2416) != c_Groups_Oone__class_Oone(U_2415) ) )
| ~ class_Int_Onumber__ring(U_2415) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
cnf(f_843_3,plain,
( c_Int_Oiszero(U_2415,c_Int_Onumber__class_Onumber__of(U_2415,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2416,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
| c_Int_Onumber__class_Onumber__of(U_2415,U_2416) != c_Groups_Oone__class_Oone(U_2415)
| ~ class_Int_Onumber__ring(U_2415) ),
inference(clausify,[status(thm)],[f_843_2]) ).
cnf(f_843_4,plain,
( c_Int_Onumber__class_Onumber__of(U_2415,U_2416) = c_Groups_Oone__class_Oone(U_2415)
| ~ c_Int_Oiszero(U_2415,c_Int_Onumber__class_Onumber__of(U_2415,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2416,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_2415) ),
inference(clausify,[status(thm)],[f_843_2]) ).
fof(f_844_1,plain,
! [V_y_2,T_a] :
( ( ( c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2))))
| c_Groups_Oone__class_Oone(T_a) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J]) ).
fof(f_844_2,plain,
! [U_2418,U_2417] :
( ( ( c_Groups_Oone__class_Oone(U_2417) = c_Int_Onumber__class_Onumber__of(U_2417,U_2418)
| ~ c_Int_Oiszero(U_2417,c_Int_Onumber__class_Onumber__of(U_2417,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2418)))) )
& ( c_Int_Oiszero(U_2417,c_Int_Onumber__class_Onumber__of(U_2417,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2418))))
| c_Groups_Oone__class_Oone(U_2417) != c_Int_Onumber__class_Onumber__of(U_2417,U_2418) ) )
| ~ class_Int_Onumber__ring(U_2417) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
cnf(f_844_3,plain,
( c_Int_Oiszero(U_2417,c_Int_Onumber__class_Onumber__of(U_2417,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2418))))
| c_Groups_Oone__class_Oone(U_2417) != c_Int_Onumber__class_Onumber__of(U_2417,U_2418)
| ~ class_Int_Onumber__ring(U_2417) ),
inference(clausify,[status(thm)],[f_844_2]) ).
cnf(f_844_4,plain,
( c_Groups_Oone__class_Oone(U_2417) = c_Int_Onumber__class_Onumber__of(U_2417,U_2418)
| ~ c_Int_Oiszero(U_2417,c_Int_Onumber__class_Onumber__of(U_2417,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2418))))
| ~ class_Int_Onumber__ring(U_2417) ),
inference(clausify,[status(thm)],[f_844_2]) ).
fof(f_845_1,plain,
! [V_za_2,T_a] :
( ( ( c_Int_Oiszero(T_a,V_za_2)
| V_za_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_za_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Int_Oiszero(T_a,V_za_2) ) )
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__def]) ).
fof(f_845_2,plain,
! [U_2420,U_2419] :
( ( ( c_Int_Oiszero(U_2419,U_2420)
| U_2420 != c_Groups_Ozero__class_Ozero(U_2419) )
& ( U_2420 = c_Groups_Ozero__class_Ozero(U_2419)
| ~ c_Int_Oiszero(U_2419,U_2420) ) )
| ~ class_Rings_Osemiring__1(U_2419) ),
inference(variable_rename,[status(thm)],[f_845_1]) ).
cnf(f_845_3,plain,
( U_2420 = c_Groups_Ozero__class_Ozero(U_2419)
| ~ c_Int_Oiszero(U_2419,U_2420)
| ~ class_Rings_Osemiring__1(U_2419) ),
inference(clausify,[status(thm)],[f_845_2]) ).
cnf(f_845_4,plain,
( c_Int_Oiszero(U_2419,U_2420)
| U_2420 != c_Groups_Ozero__class_Ozero(U_2419)
| ~ class_Rings_Osemiring__1(U_2419) ),
inference(clausify,[status(thm)],[f_845_2]) ).
fof(f_846_1,plain,
! [T_a] :
( c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__0]) ).
fof(f_846_2,plain,
! [U_2421] :
( c_Int_Oiszero(U_2421,c_Groups_Ozero__class_Ozero(U_2421))
| ~ class_Rings_Osemiring__1(U_2421) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
cnf(f_846_3,plain,
( c_Int_Oiszero(U_2421,c_Groups_Ozero__class_Ozero(U_2421))
| ~ class_Rings_Osemiring__1(U_2421) ),
inference(clausify,[status(thm)],[f_846_2]) ).
fof(f_847_1,plain,
! [T_a] :
( ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__iszero__1]) ).
fof(f_847_2,plain,
! [U_2422] :
( ~ c_Int_Oiszero(U_2422,c_Groups_Oone__class_Oone(U_2422))
| ~ class_Rings_Osemiring__1(U_2422) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
cnf(f_847_3,plain,
( ~ c_Int_Oiszero(U_2422,c_Groups_Oone__class_Oone(U_2422))
| ~ class_Rings_Osemiring__1(U_2422) ),
inference(clausify,[status(thm)],[f_847_2]) ).
fof(f_848_1,plain,
! [V_w,T_a] :
( ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)))
| ~ class_Int_Oring__char__0(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit1]) ).
fof(f_848_2,plain,
! [U_2424,U_2423] :
( ~ c_Int_Oiszero(U_2423,c_Int_Onumber__class_Onumber__of(U_2423,c_Int_OBit1(U_2424)))
| ~ class_Int_Oring__char__0(U_2423)
| ~ class_Int_Onumber__ring(U_2423) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
cnf(f_848_3,plain,
( ~ c_Int_Oiszero(U_2423,c_Int_Onumber__class_Onumber__of(U_2423,c_Int_OBit1(U_2424)))
| ~ class_Int_Oring__char__0(U_2423)
| ~ class_Int_Onumber__ring(U_2423) ),
inference(clausify,[status(thm)],[f_848_2]) ).
fof(f_849_1,plain,
! [T_a] :
( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0]) ).
fof(f_849_2,plain,
! [U_2425] :
( c_Int_Oiszero(U_2425,c_Int_Onumber__class_Onumber__of(U_2425,c_Int_OPls))
| ~ class_Int_Onumber__ring(U_2425) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
cnf(f_849_3,plain,
( c_Int_Oiszero(U_2425,c_Int_Onumber__class_Onumber__of(U_2425,c_Int_OPls))
| ~ class_Int_Onumber__ring(U_2425) ),
inference(clausify,[status(thm)],[f_849_2]) ).
fof(f_850_1,plain,
! [V_wa_2,T_a] :
( ( ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2)))
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2))) ) )
| ~ class_Int_Oring__char__0(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0]) ).
fof(f_850_2,plain,
! [U_2427,U_2426] :
( ( ( c_Int_Oiszero(U_2426,c_Int_Onumber__class_Onumber__of(U_2426,c_Int_OBit0(U_2427)))
| ~ c_Int_Oiszero(U_2426,c_Int_Onumber__class_Onumber__of(U_2426,U_2427)) )
& ( c_Int_Oiszero(U_2426,c_Int_Onumber__class_Onumber__of(U_2426,U_2427))
| ~ c_Int_Oiszero(U_2426,c_Int_Onumber__class_Onumber__of(U_2426,c_Int_OBit0(U_2427))) ) )
| ~ class_Int_Oring__char__0(U_2426)
| ~ class_Int_Onumber__ring(U_2426) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
cnf(f_850_3,plain,
( c_Int_Oiszero(U_2426,c_Int_Onumber__class_Onumber__of(U_2426,U_2427))
| ~ c_Int_Oiszero(U_2426,c_Int_Onumber__class_Onumber__of(U_2426,c_Int_OBit0(U_2427)))
| ~ class_Int_Oring__char__0(U_2426)
| ~ class_Int_Onumber__ring(U_2426) ),
inference(clausify,[status(thm)],[f_850_2]) ).
cnf(f_850_4,plain,
( c_Int_Oiszero(U_2426,c_Int_Onumber__class_Onumber__of(U_2426,c_Int_OBit0(U_2427)))
| ~ c_Int_Oiszero(U_2426,c_Int_Onumber__class_Onumber__of(U_2426,U_2427))
| ~ class_Int_Oring__char__0(U_2426)
| ~ class_Int_Onumber__ring(U_2426) ),
inference(clausify,[status(thm)],[f_850_2]) ).
fof(f_851_1,plain,
! [T_a] :
( ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__iszero__Numeral1]) ).
fof(f_851_2,plain,
! [U_2428] :
( ~ c_Int_Oiszero(U_2428,c_Int_Onumber__class_Onumber__of(U_2428,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_2428) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
cnf(f_851_3,plain,
( ~ c_Int_Oiszero(U_2428,c_Int_Onumber__class_Onumber__of(U_2428,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_2428) ),
inference(clausify,[status(thm)],[f_851_2]) ).
fof(f_852_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2))))
| c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq]) ).
fof(f_852_2,plain,
! [U_2431,U_2430,U_2429] :
( ( ( c_Int_Onumber__class_Onumber__of(U_2429,U_2430) = c_Int_Onumber__class_Onumber__of(U_2429,U_2431)
| ~ c_Int_Oiszero(U_2429,c_Int_Onumber__class_Onumber__of(U_2429,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2430,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2431)))) )
& ( c_Int_Oiszero(U_2429,c_Int_Onumber__class_Onumber__of(U_2429,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2430,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2431))))
| c_Int_Onumber__class_Onumber__of(U_2429,U_2430) != c_Int_Onumber__class_Onumber__of(U_2429,U_2431) ) )
| ~ class_Int_Onumber__ring(U_2429) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
cnf(f_852_3,plain,
( c_Int_Oiszero(U_2429,c_Int_Onumber__class_Onumber__of(U_2429,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2430,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2431))))
| c_Int_Onumber__class_Onumber__of(U_2429,U_2430) != c_Int_Onumber__class_Onumber__of(U_2429,U_2431)
| ~ class_Int_Onumber__ring(U_2429) ),
inference(clausify,[status(thm)],[f_852_2]) ).
cnf(f_852_4,plain,
( c_Int_Onumber__class_Onumber__of(U_2429,U_2430) = c_Int_Onumber__class_Onumber__of(U_2429,U_2431)
| ~ c_Int_Oiszero(U_2429,c_Int_Onumber__class_Onumber__of(U_2429,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2430,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2431))))
| ~ class_Int_Onumber__ring(U_2429) ),
inference(clausify,[status(thm)],[f_852_2]) ).
fof(f_853_1,plain,
! [V_y_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2))))
| c_Groups_Ozero__class_Ozero(T_a) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J]) ).
fof(f_853_2,plain,
! [U_2433,U_2432] :
( ( ( c_Groups_Ozero__class_Ozero(U_2432) = c_Int_Onumber__class_Onumber__of(U_2432,U_2433)
| ~ c_Int_Oiszero(U_2432,c_Int_Onumber__class_Onumber__of(U_2432,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2433)))) )
& ( c_Int_Oiszero(U_2432,c_Int_Onumber__class_Onumber__of(U_2432,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2433))))
| c_Groups_Ozero__class_Ozero(U_2432) != c_Int_Onumber__class_Onumber__of(U_2432,U_2433) ) )
| ~ class_Int_Onumber__ring(U_2432) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
cnf(f_853_3,plain,
( c_Int_Oiszero(U_2432,c_Int_Onumber__class_Onumber__of(U_2432,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2433))))
| c_Groups_Ozero__class_Ozero(U_2432) != c_Int_Onumber__class_Onumber__of(U_2432,U_2433)
| ~ class_Int_Onumber__ring(U_2432) ),
inference(clausify,[status(thm)],[f_853_2]) ).
cnf(f_853_4,plain,
( c_Groups_Ozero__class_Ozero(U_2432) = c_Int_Onumber__class_Onumber__of(U_2432,U_2433)
| ~ c_Int_Oiszero(U_2432,c_Int_Onumber__class_Onumber__of(U_2432,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2433))))
| ~ class_Int_Onumber__ring(U_2432) ),
inference(clausify,[status(thm)],[f_853_2]) ).
fof(f_854_1,plain,
! [V_x_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
| c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J]) ).
fof(f_854_2,plain,
! [U_2435,U_2434] :
( ( ( c_Int_Onumber__class_Onumber__of(U_2434,U_2435) = c_Groups_Ozero__class_Ozero(U_2434)
| ~ c_Int_Oiszero(U_2434,c_Int_Onumber__class_Onumber__of(U_2434,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2435,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) )
& ( c_Int_Oiszero(U_2434,c_Int_Onumber__class_Onumber__of(U_2434,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2435,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
| c_Int_Onumber__class_Onumber__of(U_2434,U_2435) != c_Groups_Ozero__class_Ozero(U_2434) ) )
| ~ class_Int_Onumber__ring(U_2434) ),
inference(variable_rename,[status(thm)],[f_854_1]) ).
cnf(f_854_3,plain,
( c_Int_Oiszero(U_2434,c_Int_Onumber__class_Onumber__of(U_2434,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2435,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
| c_Int_Onumber__class_Onumber__of(U_2434,U_2435) != c_Groups_Ozero__class_Ozero(U_2434)
| ~ class_Int_Onumber__ring(U_2434) ),
inference(clausify,[status(thm)],[f_854_2]) ).
cnf(f_854_4,plain,
( c_Int_Onumber__class_Onumber__of(U_2434,U_2435) = c_Groups_Ozero__class_Ozero(U_2434)
| ~ c_Int_Oiszero(U_2434,c_Int_Onumber__class_Onumber__of(U_2434,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2435,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_2434) ),
inference(clausify,[status(thm)],[f_854_2]) ).
fof(f_855_1,plain,
! [V_x,V_n] :
( c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__eq]) ).
fof(f_855_2,plain,
! [U_2437,U_2436] :
( c_RComplete_Onatceiling(U_2437) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2436,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2437,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2436),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2436),U_2437) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
cnf(f_855_3,plain,
( c_RComplete_Onatceiling(U_2437) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2436,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2437,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2436),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2436),U_2437) ),
inference(clausify,[status(thm)],[f_855_2]) ).
fof(f_856_1,plain,
! [V_ya,V_xa,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__mult__ge__zero]) ).
fof(f_856_2,plain,
! [U_2441,U_2440,U_2439,U_2438] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2438,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2439,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2440,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2441,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(variable_rename,[status(thm)],[f_856_1]) ).
cnf(f_856_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2438,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2439,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2440,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2441,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(clausify,[status(thm)],[f_856_2]) ).
fof(f_857_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right]) ).
fof(f_857_2,plain,
! [U_2445,U_2444,U_2443,U_2442] :
( c_Groups_Otimes__class_Otimes(U_2442,U_2443,c_Groups_Oplus__class_Oplus(U_2442,U_2444,U_2445)) = c_Groups_Oplus__class_Oplus(U_2442,c_Groups_Otimes__class_Otimes(U_2442,U_2443,U_2444),c_Groups_Otimes__class_Otimes(U_2442,U_2443,U_2445))
| ~ class_RealVector_Oreal__normed__algebra(U_2442) ),
inference(variable_rename,[status(thm)],[f_857_1]) ).
cnf(f_857_3,plain,
( c_Groups_Otimes__class_Otimes(U_2442,U_2443,c_Groups_Oplus__class_Oplus(U_2442,U_2444,U_2445)) = c_Groups_Oplus__class_Oplus(U_2442,c_Groups_Otimes__class_Otimes(U_2442,U_2443,U_2444),c_Groups_Otimes__class_Otimes(U_2442,U_2443,U_2445))
| ~ class_RealVector_Oreal__normed__algebra(U_2442) ),
inference(clausify,[status(thm)],[f_857_2]) ).
fof(f_858_1,plain,
! [V_y,V_x,V_xa,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd]) ).
fof(f_858_2,plain,
! [U_2449,U_2448,U_2447,U_2446] :
( c_Groups_Otimes__class_Otimes(U_2446,U_2447,c_Groups_Oplus__class_Oplus(U_2446,U_2448,U_2449)) = c_Groups_Oplus__class_Oplus(U_2446,c_Groups_Otimes__class_Otimes(U_2446,U_2447,U_2448),c_Groups_Otimes__class_Otimes(U_2446,U_2447,U_2449))
| ~ class_RealVector_Oreal__normed__algebra(U_2446) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
cnf(f_858_3,plain,
( c_Groups_Otimes__class_Otimes(U_2446,U_2447,c_Groups_Oplus__class_Oplus(U_2446,U_2448,U_2449)) = c_Groups_Oplus__class_Oplus(U_2446,c_Groups_Otimes__class_Otimes(U_2446,U_2447,U_2448),c_Groups_Otimes__class_Otimes(U_2446,U_2447,U_2449))
| ~ class_RealVector_Oreal__normed__algebra(U_2446) ),
inference(clausify,[status(thm)],[f_858_2]) ).
fof(f_859_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left]) ).
fof(f_859_2,plain,
! [U_2453,U_2452,U_2451,U_2450] :
( c_Groups_Otimes__class_Otimes(U_2450,c_Groups_Oplus__class_Oplus(U_2450,U_2451,U_2452),U_2453) = c_Groups_Oplus__class_Oplus(U_2450,c_Groups_Otimes__class_Otimes(U_2450,U_2451,U_2453),c_Groups_Otimes__class_Otimes(U_2450,U_2452,U_2453))
| ~ class_RealVector_Oreal__normed__algebra(U_2450) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
cnf(f_859_3,plain,
( c_Groups_Otimes__class_Otimes(U_2450,c_Groups_Oplus__class_Oplus(U_2450,U_2451,U_2452),U_2453) = c_Groups_Oplus__class_Oplus(U_2450,c_Groups_Otimes__class_Otimes(U_2450,U_2451,U_2453),c_Groups_Otimes__class_Otimes(U_2450,U_2452,U_2453))
| ~ class_RealVector_Oreal__normed__algebra(U_2450) ),
inference(clausify,[status(thm)],[f_859_2]) ).
fof(f_860_1,plain,
! [V_ya,V_y,V_x,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd]) ).
fof(f_860_2,plain,
! [U_2457,U_2456,U_2455,U_2454] :
( c_Groups_Otimes__class_Otimes(U_2454,c_Groups_Oplus__class_Oplus(U_2454,U_2455,U_2456),U_2457) = c_Groups_Oplus__class_Oplus(U_2454,c_Groups_Otimes__class_Otimes(U_2454,U_2455,U_2457),c_Groups_Otimes__class_Otimes(U_2454,U_2456,U_2457))
| ~ class_RealVector_Oreal__normed__algebra(U_2454) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
cnf(f_860_3,plain,
( c_Groups_Otimes__class_Otimes(U_2454,c_Groups_Oplus__class_Oplus(U_2454,U_2455,U_2456),U_2457) = c_Groups_Oplus__class_Oplus(U_2454,c_Groups_Otimes__class_Otimes(U_2454,U_2455,U_2457),c_Groups_Otimes__class_Otimes(U_2454,U_2456,U_2457))
| ~ class_RealVector_Oreal__normed__algebra(U_2454) ),
inference(clausify,[status(thm)],[f_860_2]) ).
fof(f_861_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
| ~ class_Rings_Ocomm__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib]) ).
fof(f_861_2,plain,
! [U_2461,U_2460,U_2459,U_2458] :
( c_Groups_Otimes__class_Otimes(U_2458,c_Groups_Oplus__class_Oplus(U_2458,U_2459,U_2460),U_2461) = c_Groups_Oplus__class_Oplus(U_2458,c_Groups_Otimes__class_Otimes(U_2458,U_2459,U_2461),c_Groups_Otimes__class_Otimes(U_2458,U_2460,U_2461))
| ~ class_Rings_Ocomm__semiring(U_2458) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
cnf(f_861_3,plain,
( c_Groups_Otimes__class_Otimes(U_2458,c_Groups_Oplus__class_Oplus(U_2458,U_2459,U_2460),U_2461) = c_Groups_Oplus__class_Oplus(U_2458,c_Groups_Otimes__class_Otimes(U_2458,U_2459,U_2461),c_Groups_Otimes__class_Otimes(U_2458,U_2460,U_2461))
| ~ class_Rings_Ocomm__semiring(U_2458) ),
inference(clausify,[status(thm)],[f_861_2]) ).
fof(f_862_1,plain,
! [V_c,V_b,V_e,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c)
| ~ class_Rings_Osemiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_combine__common__factor]) ).
fof(f_862_2,plain,
! [U_2466,U_2465,U_2464,U_2463,U_2462] :
( c_Groups_Oplus__class_Oplus(U_2462,c_Groups_Otimes__class_Otimes(U_2462,U_2463,U_2464),c_Groups_Oplus__class_Oplus(U_2462,c_Groups_Otimes__class_Otimes(U_2462,U_2465,U_2464),U_2466)) = c_Groups_Oplus__class_Oplus(U_2462,c_Groups_Otimes__class_Otimes(U_2462,c_Groups_Oplus__class_Oplus(U_2462,U_2463,U_2465),U_2464),U_2466)
| ~ class_Rings_Osemiring(U_2462) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
cnf(f_862_3,plain,
( c_Groups_Oplus__class_Oplus(U_2462,c_Groups_Otimes__class_Otimes(U_2462,U_2463,U_2464),c_Groups_Oplus__class_Oplus(U_2462,c_Groups_Otimes__class_Otimes(U_2462,U_2465,U_2464),U_2466)) = c_Groups_Oplus__class_Oplus(U_2462,c_Groups_Otimes__class_Otimes(U_2462,c_Groups_Oplus__class_Oplus(U_2462,U_2463,U_2465),U_2464),U_2466)
| ~ class_Rings_Osemiring(U_2462) ),
inference(clausify,[status(thm)],[f_862_2]) ).
fof(f_863_1,plain,
! [V_w,V_z2,V_z1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w)),
inference(fof_nnf,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(f_863_2,plain,
! [U_2469,U_2468,U_2467] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2467,U_2468),U_2469) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2467,U_2469),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2468,U_2469)),
inference(variable_rename,[status(thm)],[f_863_1]) ).
cnf(f_863_3,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2467,U_2468),U_2469) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2467,U_2469),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2468,U_2469)),
inference(clausify,[status(thm)],[f_863_2]) ).
fof(f_864_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).
fof(f_864_2,plain,
! [U_2472,U_2471,U_2470] :
( ( ( c_Groups_Oplus__class_Oplus(U_2470,c_Groups_Otimes__class_Otimes(U_2470,U_2471,U_2471),c_Groups_Otimes__class_Otimes(U_2470,U_2472,U_2472)) = c_Groups_Ozero__class_Ozero(U_2470)
| U_2472 != c_Groups_Ozero__class_Ozero(U_2470)
| U_2471 != c_Groups_Ozero__class_Ozero(U_2470) )
& ( ( U_2472 = c_Groups_Ozero__class_Ozero(U_2470)
& U_2471 = c_Groups_Ozero__class_Ozero(U_2470) )
| c_Groups_Oplus__class_Oplus(U_2470,c_Groups_Otimes__class_Otimes(U_2470,U_2471,U_2471),c_Groups_Otimes__class_Otimes(U_2470,U_2472,U_2472)) != c_Groups_Ozero__class_Ozero(U_2470) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2470) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
cnf(f_864_3,plain,
( U_2471 = c_Groups_Ozero__class_Ozero(U_2470)
| c_Groups_Oplus__class_Oplus(U_2470,c_Groups_Otimes__class_Otimes(U_2470,U_2471,U_2471),c_Groups_Otimes__class_Otimes(U_2470,U_2472,U_2472)) != c_Groups_Ozero__class_Ozero(U_2470)
| ~ class_Rings_Olinordered__ring__strict(U_2470) ),
inference(clausify,[status(thm)],[f_864_2]) ).
cnf(f_864_4,plain,
( U_2472 = c_Groups_Ozero__class_Ozero(U_2470)
| c_Groups_Oplus__class_Oplus(U_2470,c_Groups_Otimes__class_Otimes(U_2470,U_2471,U_2471),c_Groups_Otimes__class_Otimes(U_2470,U_2472,U_2472)) != c_Groups_Ozero__class_Ozero(U_2470)
| ~ class_Rings_Olinordered__ring__strict(U_2470) ),
inference(clausify,[status(thm)],[f_864_2]) ).
cnf(f_864_5,plain,
( c_Groups_Oplus__class_Oplus(U_2470,c_Groups_Otimes__class_Otimes(U_2470,U_2471,U_2471),c_Groups_Otimes__class_Otimes(U_2470,U_2472,U_2472)) = c_Groups_Ozero__class_Ozero(U_2470)
| U_2472 != c_Groups_Ozero__class_Ozero(U_2470)
| U_2471 != c_Groups_Ozero__class_Ozero(U_2470)
| ~ class_Rings_Olinordered__ring__strict(U_2470) ),
inference(clausify,[status(thm)],[f_864_2]) ).
fof(f_865_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus]) ).
fof(f_865_2,plain,
! [U_2475,U_2474,U_2473] :
( c_Groups_Otimes__class_Otimes(U_2473,c_Groups_Ouminus__class_Ouminus(U_2473,U_2474),U_2475) = c_Groups_Ouminus__class_Ouminus(U_2473,c_Groups_Otimes__class_Otimes(U_2473,U_2474,U_2475))
| ~ class_RealVector_Oreal__normed__algebra(U_2473) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
cnf(f_865_3,plain,
( c_Groups_Otimes__class_Otimes(U_2473,c_Groups_Ouminus__class_Ouminus(U_2473,U_2474),U_2475) = c_Groups_Ouminus__class_Ouminus(U_2473,c_Groups_Otimes__class_Otimes(U_2473,U_2474,U_2475))
| ~ class_RealVector_Oreal__normed__algebra(U_2473) ),
inference(clausify,[status(thm)],[f_865_2]) ).
fof(f_866_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left]) ).
fof(f_866_2,plain,
! [U_2478,U_2477,U_2476] :
( c_Groups_Otimes__class_Otimes(U_2476,c_Groups_Ouminus__class_Ouminus(U_2476,U_2477),U_2478) = c_Groups_Ouminus__class_Ouminus(U_2476,c_Groups_Otimes__class_Otimes(U_2476,U_2477,U_2478))
| ~ class_RealVector_Oreal__normed__algebra(U_2476) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
cnf(f_866_3,plain,
( c_Groups_Otimes__class_Otimes(U_2476,c_Groups_Ouminus__class_Ouminus(U_2476,U_2477),U_2478) = c_Groups_Ouminus__class_Ouminus(U_2476,c_Groups_Otimes__class_Otimes(U_2476,U_2477,U_2478))
| ~ class_RealVector_Oreal__normed__algebra(U_2476) ),
inference(clausify,[status(thm)],[f_866_2]) ).
fof(f_867_1,plain,
! [V_x,V_xa,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus]) ).
fof(f_867_2,plain,
! [U_2481,U_2480,U_2479] :
( c_Groups_Otimes__class_Otimes(U_2479,U_2480,c_Groups_Ouminus__class_Ouminus(U_2479,U_2481)) = c_Groups_Ouminus__class_Ouminus(U_2479,c_Groups_Otimes__class_Otimes(U_2479,U_2480,U_2481))
| ~ class_RealVector_Oreal__normed__algebra(U_2479) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
cnf(f_867_3,plain,
( c_Groups_Otimes__class_Otimes(U_2479,U_2480,c_Groups_Ouminus__class_Ouminus(U_2479,U_2481)) = c_Groups_Ouminus__class_Ouminus(U_2479,c_Groups_Otimes__class_Otimes(U_2479,U_2480,U_2481))
| ~ class_RealVector_Oreal__normed__algebra(U_2479) ),
inference(clausify,[status(thm)],[f_867_2]) ).
fof(f_868_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right]) ).
fof(f_868_2,plain,
! [U_2484,U_2483,U_2482] :
( c_Groups_Otimes__class_Otimes(U_2482,U_2483,c_Groups_Ouminus__class_Ouminus(U_2482,U_2484)) = c_Groups_Ouminus__class_Ouminus(U_2482,c_Groups_Otimes__class_Otimes(U_2482,U_2483,U_2484))
| ~ class_RealVector_Oreal__normed__algebra(U_2482) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
cnf(f_868_3,plain,
( c_Groups_Otimes__class_Otimes(U_2482,U_2483,c_Groups_Ouminus__class_Ouminus(U_2482,U_2484)) = c_Groups_Ouminus__class_Ouminus(U_2482,c_Groups_Otimes__class_Otimes(U_2482,U_2483,U_2484))
| ~ class_RealVector_Oreal__normed__algebra(U_2482) ),
inference(clausify,[status(thm)],[f_868_2]) ).
fof(f_869_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_a_2) = c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2)
| ( V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
& V_a_2 != V_b_2 ) )
& ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 = V_b_2
| c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_a_2) != c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).
fof(f_869_2,plain,
! [U_2487,U_2486,U_2485] :
( ( ( c_Groups_Otimes__class_Otimes(U_2485,U_2486,U_2486) = c_Groups_Otimes__class_Otimes(U_2485,U_2487,U_2487)
| ( U_2486 != c_Groups_Ouminus__class_Ouminus(U_2485,U_2487)
& U_2486 != U_2487 ) )
& ( U_2486 = c_Groups_Ouminus__class_Ouminus(U_2485,U_2487)
| U_2486 = U_2487
| c_Groups_Otimes__class_Otimes(U_2485,U_2486,U_2486) != c_Groups_Otimes__class_Otimes(U_2485,U_2487,U_2487) ) )
| ~ class_Rings_Oidom(U_2485) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
cnf(f_869_3,plain,
( U_2486 = c_Groups_Ouminus__class_Ouminus(U_2485,U_2487)
| U_2486 = U_2487
| c_Groups_Otimes__class_Otimes(U_2485,U_2486,U_2486) != c_Groups_Otimes__class_Otimes(U_2485,U_2487,U_2487)
| ~ class_Rings_Oidom(U_2485) ),
inference(clausify,[status(thm)],[f_869_2]) ).
cnf(f_869_4,plain,
( U_2486 != U_2487
| c_Groups_Otimes__class_Otimes(U_2485,U_2486,U_2486) = c_Groups_Otimes__class_Otimes(U_2485,U_2487,U_2487)
| ~ class_Rings_Oidom(U_2485) ),
inference(clausify,[status(thm)],[f_869_2]) ).
cnf(f_869_5,plain,
( U_2486 != c_Groups_Ouminus__class_Ouminus(U_2485,U_2487)
| c_Groups_Otimes__class_Otimes(U_2485,U_2486,U_2486) = c_Groups_Otimes__class_Otimes(U_2485,U_2487,U_2487)
| ~ class_Rings_Oidom(U_2485) ),
inference(clausify,[status(thm)],[f_869_2]) ).
fof(f_870_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__minus]) ).
fof(f_870_2,plain,
! [U_2490,U_2489,U_2488] :
( c_Groups_Otimes__class_Otimes(U_2488,c_Groups_Ouminus__class_Ouminus(U_2488,U_2489),c_Groups_Ouminus__class_Ouminus(U_2488,U_2490)) = c_Groups_Otimes__class_Otimes(U_2488,U_2489,U_2490)
| ~ class_Rings_Oring(U_2488) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
cnf(f_870_3,plain,
( c_Groups_Otimes__class_Otimes(U_2488,c_Groups_Ouminus__class_Ouminus(U_2488,U_2489),c_Groups_Ouminus__class_Ouminus(U_2488,U_2490)) = c_Groups_Otimes__class_Otimes(U_2488,U_2489,U_2490)
| ~ class_Rings_Oring(U_2488) ),
inference(clausify,[status(thm)],[f_870_2]) ).
fof(f_871_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__commute]) ).
fof(f_871_2,plain,
! [U_2493,U_2492,U_2491] :
( c_Groups_Otimes__class_Otimes(U_2491,c_Groups_Ouminus__class_Ouminus(U_2491,U_2492),U_2493) = c_Groups_Otimes__class_Otimes(U_2491,U_2492,c_Groups_Ouminus__class_Ouminus(U_2491,U_2493))
| ~ class_Rings_Oring(U_2491) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
cnf(f_871_3,plain,
( c_Groups_Otimes__class_Otimes(U_2491,c_Groups_Ouminus__class_Ouminus(U_2491,U_2492),U_2493) = c_Groups_Otimes__class_Otimes(U_2491,U_2492,c_Groups_Ouminus__class_Ouminus(U_2491,U_2493))
| ~ class_Rings_Oring(U_2491) ),
inference(clausify,[status(thm)],[f_871_2]) ).
fof(f_872_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__left]) ).
fof(f_872_2,plain,
! [U_2496,U_2495,U_2494] :
( c_Groups_Ouminus__class_Ouminus(U_2494,c_Groups_Otimes__class_Otimes(U_2494,U_2495,U_2496)) = c_Groups_Otimes__class_Otimes(U_2494,c_Groups_Ouminus__class_Ouminus(U_2494,U_2495),U_2496)
| ~ class_Rings_Oring(U_2494) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
cnf(f_872_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_2494,c_Groups_Otimes__class_Otimes(U_2494,U_2495,U_2496)) = c_Groups_Otimes__class_Otimes(U_2494,c_Groups_Ouminus__class_Ouminus(U_2494,U_2495),U_2496)
| ~ class_Rings_Oring(U_2494) ),
inference(clausify,[status(thm)],[f_872_2]) ).
fof(f_873_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__right]) ).
fof(f_873_2,plain,
! [U_2499,U_2498,U_2497] :
( c_Groups_Ouminus__class_Ouminus(U_2497,c_Groups_Otimes__class_Otimes(U_2497,U_2498,U_2499)) = c_Groups_Otimes__class_Otimes(U_2497,U_2498,c_Groups_Ouminus__class_Ouminus(U_2497,U_2499))
| ~ class_Rings_Oring(U_2497) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
cnf(f_873_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_2497,c_Groups_Otimes__class_Otimes(U_2497,U_2498,U_2499)) = c_Groups_Otimes__class_Otimes(U_2497,U_2498,c_Groups_Ouminus__class_Ouminus(U_2497,U_2499))
| ~ class_Rings_Oring(U_2497) ),
inference(clausify,[status(thm)],[f_873_2]) ).
fof(f_874_1,plain,
! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
inference(fof_nnf,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(f_874_2,plain,
! [U_2500] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_2500)) = U_2500,
inference(variable_rename,[status(thm)],[f_874_1]) ).
cnf(f_874_3,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_2500)) = U_2500,
inference(clausify,[status(thm)],[f_874_2]) ).
fof(f_875_1,plain,
! [V_n,V_m,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__1__mult]) ).
fof(f_875_2,plain,
! [U_2503,U_2502,U_2501] :
( c_Orderings_Oord__class_Oless(U_2501,c_Groups_Oone__class_Oone(U_2501),c_Groups_Otimes__class_Otimes(U_2501,U_2502,U_2503))
| ~ c_Orderings_Oord__class_Oless(U_2501,c_Groups_Oone__class_Oone(U_2501),U_2503)
| ~ c_Orderings_Oord__class_Oless(U_2501,c_Groups_Oone__class_Oone(U_2501),U_2502)
| ~ class_Rings_Olinordered__semidom(U_2501) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
cnf(f_875_3,plain,
( c_Orderings_Oord__class_Oless(U_2501,c_Groups_Oone__class_Oone(U_2501),c_Groups_Otimes__class_Otimes(U_2501,U_2502,U_2503))
| ~ c_Orderings_Oord__class_Oless(U_2501,c_Groups_Oone__class_Oone(U_2501),U_2503)
| ~ c_Orderings_Oord__class_Oless(U_2501,c_Groups_Oone__class_Oone(U_2501),U_2502)
| ~ class_Rings_Olinordered__semidom(U_2501) ),
inference(clausify,[status(thm)],[f_875_2]) ).
fof(f_876_1,plain,
! [V_c,V_b,V_v,T_b] :
( c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c))
| ~ class_Rings_Osemiring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of]) ).
fof(f_876_2,plain,
! [U_2507,U_2506,U_2505,U_2504] :
( c_Groups_Otimes__class_Otimes(U_2504,c_Int_Onumber__class_Onumber__of(U_2504,U_2505),c_Groups_Oplus__class_Oplus(U_2504,U_2506,U_2507)) = c_Groups_Oplus__class_Oplus(U_2504,c_Groups_Otimes__class_Otimes(U_2504,c_Int_Onumber__class_Onumber__of(U_2504,U_2505),U_2506),c_Groups_Otimes__class_Otimes(U_2504,c_Int_Onumber__class_Onumber__of(U_2504,U_2505),U_2507))
| ~ class_Rings_Osemiring(U_2504)
| ~ class_Int_Onumber(U_2504) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
cnf(f_876_3,plain,
( c_Groups_Otimes__class_Otimes(U_2504,c_Int_Onumber__class_Onumber__of(U_2504,U_2505),c_Groups_Oplus__class_Oplus(U_2504,U_2506,U_2507)) = c_Groups_Oplus__class_Oplus(U_2504,c_Groups_Otimes__class_Otimes(U_2504,c_Int_Onumber__class_Onumber__of(U_2504,U_2505),U_2506),c_Groups_Otimes__class_Otimes(U_2504,c_Int_Onumber__class_Onumber__of(U_2504,U_2505),U_2507))
| ~ class_Rings_Osemiring(U_2504)
| ~ class_Int_Onumber(U_2504) ),
inference(clausify,[status(thm)],[f_876_2]) ).
fof(f_877_1,plain,
! [V_v,V_b,V_a,T_b] :
( c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)))
| ~ class_Rings_Osemiring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of]) ).
fof(f_877_2,plain,
! [U_2511,U_2510,U_2509,U_2508] :
( c_Groups_Otimes__class_Otimes(U_2508,c_Groups_Oplus__class_Oplus(U_2508,U_2509,U_2510),c_Int_Onumber__class_Onumber__of(U_2508,U_2511)) = c_Groups_Oplus__class_Oplus(U_2508,c_Groups_Otimes__class_Otimes(U_2508,U_2509,c_Int_Onumber__class_Onumber__of(U_2508,U_2511)),c_Groups_Otimes__class_Otimes(U_2508,U_2510,c_Int_Onumber__class_Onumber__of(U_2508,U_2511)))
| ~ class_Rings_Osemiring(U_2508)
| ~ class_Int_Onumber(U_2508) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
cnf(f_877_3,plain,
( c_Groups_Otimes__class_Otimes(U_2508,c_Groups_Oplus__class_Oplus(U_2508,U_2509,U_2510),c_Int_Onumber__class_Onumber__of(U_2508,U_2511)) = c_Groups_Oplus__class_Oplus(U_2508,c_Groups_Otimes__class_Otimes(U_2508,U_2509,c_Int_Onumber__class_Onumber__of(U_2508,U_2511)),c_Groups_Otimes__class_Otimes(U_2508,U_2510,c_Int_Onumber__class_Onumber__of(U_2508,U_2511)))
| ~ class_Rings_Osemiring(U_2508)
| ~ class_Int_Onumber(U_2508) ),
inference(clausify,[status(thm)],[f_877_2]) ).
fof(f_878_1,plain,
! [V_b,V_a,V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__diff__mult]) ).
fof(f_878_2,plain,
! [U_2516,U_2515,U_2514,U_2513,U_2512] :
( c_Groups_Ominus__class_Ominus(U_2512,c_Groups_Otimes__class_Otimes(U_2512,U_2513,U_2514),c_Groups_Otimes__class_Otimes(U_2512,U_2515,U_2516)) = c_Groups_Oplus__class_Oplus(U_2512,c_Groups_Otimes__class_Otimes(U_2512,U_2513,c_Groups_Ominus__class_Ominus(U_2512,U_2514,U_2516)),c_Groups_Otimes__class_Otimes(U_2512,c_Groups_Ominus__class_Ominus(U_2512,U_2513,U_2515),U_2516))
| ~ class_Rings_Oring(U_2512) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
cnf(f_878_3,plain,
( c_Groups_Ominus__class_Ominus(U_2512,c_Groups_Otimes__class_Otimes(U_2512,U_2513,U_2514),c_Groups_Otimes__class_Otimes(U_2512,U_2515,U_2516)) = c_Groups_Oplus__class_Oplus(U_2512,c_Groups_Otimes__class_Otimes(U_2512,U_2513,c_Groups_Ominus__class_Ominus(U_2512,U_2514,U_2516)),c_Groups_Otimes__class_Otimes(U_2512,c_Groups_Ominus__class_Ominus(U_2512,U_2513,U_2515),U_2516))
| ~ class_Rings_Oring(U_2512) ),
inference(clausify,[status(thm)],[f_878_2]) ).
fof(f_879_1,plain,
! [V_b,V_a,V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod]) ).
fof(f_879_2,plain,
! [U_2521,U_2520,U_2519,U_2518,U_2517] :
( c_Groups_Ominus__class_Ominus(U_2517,c_Groups_Otimes__class_Otimes(U_2517,U_2518,U_2519),c_Groups_Otimes__class_Otimes(U_2517,U_2520,U_2521)) = c_Groups_Oplus__class_Oplus(U_2517,c_Groups_Oplus__class_Oplus(U_2517,c_Groups_Otimes__class_Otimes(U_2517,c_Groups_Ominus__class_Ominus(U_2517,U_2518,U_2520),c_Groups_Ominus__class_Ominus(U_2517,U_2519,U_2521)),c_Groups_Otimes__class_Otimes(U_2517,c_Groups_Ominus__class_Ominus(U_2517,U_2518,U_2520),U_2521)),c_Groups_Otimes__class_Otimes(U_2517,U_2520,c_Groups_Ominus__class_Ominus(U_2517,U_2519,U_2521)))
| ~ class_RealVector_Oreal__normed__algebra(U_2517) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
cnf(f_879_3,plain,
( c_Groups_Ominus__class_Ominus(U_2517,c_Groups_Otimes__class_Otimes(U_2517,U_2518,U_2519),c_Groups_Otimes__class_Otimes(U_2517,U_2520,U_2521)) = c_Groups_Oplus__class_Oplus(U_2517,c_Groups_Oplus__class_Oplus(U_2517,c_Groups_Otimes__class_Otimes(U_2517,c_Groups_Ominus__class_Ominus(U_2517,U_2518,U_2520),c_Groups_Ominus__class_Ominus(U_2517,U_2519,U_2521)),c_Groups_Otimes__class_Otimes(U_2517,c_Groups_Ominus__class_Ominus(U_2517,U_2518,U_2520),U_2521)),c_Groups_Otimes__class_Otimes(U_2517,U_2520,c_Groups_Ominus__class_Ominus(U_2517,U_2519,U_2521)))
| ~ class_RealVector_Oreal__normed__algebra(U_2517) ),
inference(clausify,[status(thm)],[f_879_2]) ).
fof(f_880_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)
| V_c_2 != c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_d_2) )
& ( V_c_2 = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_d_2)
| c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) != c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2) ) )
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).
fof(f_880_2,plain,
! [U_2527,U_2526,U_2525,U_2524,U_2523,U_2522] :
( ( ( c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,U_2523,U_2524),U_2525) = c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,U_2526,U_2524),U_2527)
| U_2525 != c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,c_Groups_Ominus__class_Ominus(U_2522,U_2526,U_2523),U_2524),U_2527) )
& ( U_2525 = c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,c_Groups_Ominus__class_Ominus(U_2522,U_2526,U_2523),U_2524),U_2527)
| c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,U_2523,U_2524),U_2525) != c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,U_2526,U_2524),U_2527) ) )
| ~ class_Rings_Oring(U_2522) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
cnf(f_880_3,plain,
( U_2525 = c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,c_Groups_Ominus__class_Ominus(U_2522,U_2526,U_2523),U_2524),U_2527)
| c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,U_2523,U_2524),U_2525) != c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,U_2526,U_2524),U_2527)
| ~ class_Rings_Oring(U_2522) ),
inference(clausify,[status(thm)],[f_880_2]) ).
cnf(f_880_4,plain,
( c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,U_2523,U_2524),U_2525) = c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,U_2526,U_2524),U_2527)
| U_2525 != c_Groups_Oplus__class_Oplus(U_2522,c_Groups_Otimes__class_Otimes(U_2522,c_Groups_Ominus__class_Ominus(U_2522,U_2526,U_2523),U_2524),U_2527)
| ~ class_Rings_Oring(U_2522) ),
inference(clausify,[status(thm)],[f_880_2]) ).
fof(f_881_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)
| c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_e_2),V_c_2) != V_d_2 )
& ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_e_2),V_c_2) = V_d_2
| c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) != c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2) ) )
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).
fof(f_881_2,plain,
! [U_2533,U_2532,U_2531,U_2530,U_2529,U_2528] :
( ( ( c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,U_2529,U_2530),U_2531) = c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,U_2532,U_2530),U_2533)
| c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,c_Groups_Ominus__class_Ominus(U_2528,U_2529,U_2532),U_2530),U_2531) != U_2533 )
& ( c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,c_Groups_Ominus__class_Ominus(U_2528,U_2529,U_2532),U_2530),U_2531) = U_2533
| c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,U_2529,U_2530),U_2531) != c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,U_2532,U_2530),U_2533) ) )
| ~ class_Rings_Oring(U_2528) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
cnf(f_881_3,plain,
( c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,c_Groups_Ominus__class_Ominus(U_2528,U_2529,U_2532),U_2530),U_2531) = U_2533
| c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,U_2529,U_2530),U_2531) != c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,U_2532,U_2530),U_2533)
| ~ class_Rings_Oring(U_2528) ),
inference(clausify,[status(thm)],[f_881_2]) ).
cnf(f_881_4,plain,
( c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,U_2529,U_2530),U_2531) = c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,U_2532,U_2530),U_2533)
| c_Groups_Oplus__class_Oplus(U_2528,c_Groups_Otimes__class_Otimes(U_2528,c_Groups_Ominus__class_Ominus(U_2528,U_2529,U_2532),U_2530),U_2531) != U_2533
| ~ class_Rings_Oring(U_2528) ),
inference(clausify,[status(thm)],[f_881_2]) ).
fof(f_882_1,plain,
! [V_c,V_b,V_v,T_b] :
( c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c))
| ~ class_Rings_Oring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of]) ).
fof(f_882_2,plain,
! [U_2537,U_2536,U_2535,U_2534] :
( c_Groups_Otimes__class_Otimes(U_2534,c_Int_Onumber__class_Onumber__of(U_2534,U_2535),c_Groups_Ominus__class_Ominus(U_2534,U_2536,U_2537)) = c_Groups_Ominus__class_Ominus(U_2534,c_Groups_Otimes__class_Otimes(U_2534,c_Int_Onumber__class_Onumber__of(U_2534,U_2535),U_2536),c_Groups_Otimes__class_Otimes(U_2534,c_Int_Onumber__class_Onumber__of(U_2534,U_2535),U_2537))
| ~ class_Rings_Oring(U_2534)
| ~ class_Int_Onumber(U_2534) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
cnf(f_882_3,plain,
( c_Groups_Otimes__class_Otimes(U_2534,c_Int_Onumber__class_Onumber__of(U_2534,U_2535),c_Groups_Ominus__class_Ominus(U_2534,U_2536,U_2537)) = c_Groups_Ominus__class_Ominus(U_2534,c_Groups_Otimes__class_Otimes(U_2534,c_Int_Onumber__class_Onumber__of(U_2534,U_2535),U_2536),c_Groups_Otimes__class_Otimes(U_2534,c_Int_Onumber__class_Onumber__of(U_2534,U_2535),U_2537))
| ~ class_Rings_Oring(U_2534)
| ~ class_Int_Onumber(U_2534) ),
inference(clausify,[status(thm)],[f_882_2]) ).
fof(f_883_1,plain,
! [V_v,V_b,V_a,T_b] :
( c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)))
| ~ class_Rings_Oring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of]) ).
fof(f_883_2,plain,
! [U_2541,U_2540,U_2539,U_2538] :
( c_Groups_Otimes__class_Otimes(U_2538,c_Groups_Ominus__class_Ominus(U_2538,U_2539,U_2540),c_Int_Onumber__class_Onumber__of(U_2538,U_2541)) = c_Groups_Ominus__class_Ominus(U_2538,c_Groups_Otimes__class_Otimes(U_2538,U_2539,c_Int_Onumber__class_Onumber__of(U_2538,U_2541)),c_Groups_Otimes__class_Otimes(U_2538,U_2540,c_Int_Onumber__class_Onumber__of(U_2538,U_2541)))
| ~ class_Rings_Oring(U_2538)
| ~ class_Int_Onumber(U_2538) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
cnf(f_883_3,plain,
( c_Groups_Otimes__class_Otimes(U_2538,c_Groups_Ominus__class_Ominus(U_2538,U_2539,U_2540),c_Int_Onumber__class_Onumber__of(U_2538,U_2541)) = c_Groups_Ominus__class_Ominus(U_2538,c_Groups_Otimes__class_Otimes(U_2538,U_2539,c_Int_Onumber__class_Onumber__of(U_2538,U_2541)),c_Groups_Otimes__class_Otimes(U_2538,U_2540,c_Int_Onumber__class_Onumber__of(U_2538,U_2541)))
| ~ class_Rings_Oring(U_2538)
| ~ class_Int_Onumber(U_2538) ),
inference(clausify,[status(thm)],[f_883_2]) ).
fof(f_884_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
| c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) != V_b_2 )
& ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_b_2
| V_a_2 != c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).
fof(f_884_2,plain,
! [U_2545,U_2544,U_2543,U_2542] :
( ( ( U_2544 = c_Rings_Oinverse__class_Odivide(U_2542,U_2545,U_2543)
| c_Groups_Otimes__class_Otimes(U_2542,U_2544,U_2543) != U_2545 )
& ( c_Groups_Otimes__class_Otimes(U_2542,U_2544,U_2543) = U_2545
| U_2544 != c_Rings_Oinverse__class_Odivide(U_2542,U_2545,U_2543) ) )
| U_2543 = c_Groups_Ozero__class_Ozero(U_2542)
| ~ class_Rings_Odivision__ring(U_2542) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
cnf(f_884_3,plain,
( c_Groups_Otimes__class_Otimes(U_2542,U_2544,U_2543) = U_2545
| U_2544 != c_Rings_Oinverse__class_Odivide(U_2542,U_2545,U_2543)
| U_2543 = c_Groups_Ozero__class_Ozero(U_2542)
| ~ class_Rings_Odivision__ring(U_2542) ),
inference(clausify,[status(thm)],[f_884_2]) ).
cnf(f_884_4,plain,
( U_2544 = c_Rings_Oinverse__class_Odivide(U_2542,U_2545,U_2543)
| c_Groups_Otimes__class_Otimes(U_2542,U_2544,U_2543) != U_2545
| U_2543 = c_Groups_Ozero__class_Ozero(U_2542)
| ~ class_Rings_Odivision__ring(U_2542) ),
inference(clausify,[status(thm)],[f_884_2]) ).
fof(f_885_1,plain,
! [V_a_2,V_b_2,V_c_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
| V_b_2 != c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) )
& ( V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)
| c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) != V_a_2 ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).
fof(f_885_2,plain,
! [U_2549,U_2548,U_2547,U_2546] :
( ( ( c_Rings_Oinverse__class_Odivide(U_2546,U_2548,U_2547) = U_2549
| U_2548 != c_Groups_Otimes__class_Otimes(U_2546,U_2549,U_2547) )
& ( U_2548 = c_Groups_Otimes__class_Otimes(U_2546,U_2549,U_2547)
| c_Rings_Oinverse__class_Odivide(U_2546,U_2548,U_2547) != U_2549 ) )
| U_2547 = c_Groups_Ozero__class_Ozero(U_2546)
| ~ class_Rings_Odivision__ring(U_2546) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
cnf(f_885_3,plain,
( U_2548 = c_Groups_Otimes__class_Otimes(U_2546,U_2549,U_2547)
| c_Rings_Oinverse__class_Odivide(U_2546,U_2548,U_2547) != U_2549
| U_2547 = c_Groups_Ozero__class_Ozero(U_2546)
| ~ class_Rings_Odivision__ring(U_2546) ),
inference(clausify,[status(thm)],[f_885_2]) ).
cnf(f_885_4,plain,
( c_Rings_Oinverse__class_Odivide(U_2546,U_2548,U_2547) = U_2549
| U_2548 != c_Groups_Otimes__class_Otimes(U_2546,U_2549,U_2547)
| U_2547 = c_Groups_Ozero__class_Ozero(U_2546)
| ~ class_Rings_Odivision__ring(U_2546) ),
inference(clausify,[status(thm)],[f_885_2]) ).
fof(f_886_1,plain,
! [V_a,V_b,V_c,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a
| V_b != c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__imp]) ).
fof(f_886_2,plain,
! [U_2553,U_2552,U_2551,U_2550] :
( c_Rings_Oinverse__class_Odivide(U_2550,U_2552,U_2551) = U_2553
| U_2552 != c_Groups_Otimes__class_Otimes(U_2550,U_2553,U_2551)
| U_2551 = c_Groups_Ozero__class_Ozero(U_2550)
| ~ class_Rings_Odivision__ring(U_2550) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
cnf(f_886_3,plain,
( c_Rings_Oinverse__class_Odivide(U_2550,U_2552,U_2551) = U_2553
| U_2552 != c_Groups_Otimes__class_Otimes(U_2550,U_2553,U_2551)
| U_2551 = c_Groups_Ozero__class_Ozero(U_2550)
| ~ class_Rings_Odivision__ring(U_2550) ),
inference(clausify,[status(thm)],[f_886_2]) ).
fof(f_887_1,plain,
! [V_b,V_a,V_c,T_a] :
( V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)
| c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) != V_b
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__imp]) ).
fof(f_887_2,plain,
! [U_2557,U_2556,U_2555,U_2554] :
( U_2556 = c_Rings_Oinverse__class_Odivide(U_2554,U_2557,U_2555)
| c_Groups_Otimes__class_Otimes(U_2554,U_2556,U_2555) != U_2557
| U_2555 = c_Groups_Ozero__class_Ozero(U_2554)
| ~ class_Rings_Odivision__ring(U_2554) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
cnf(f_887_3,plain,
( U_2556 = c_Rings_Oinverse__class_Odivide(U_2554,U_2557,U_2555)
| c_Groups_Otimes__class_Otimes(U_2554,U_2556,U_2555) != U_2557
| U_2555 = c_Groups_Ozero__class_Ozero(U_2554)
| ~ class_Rings_Odivision__ring(U_2554) ),
inference(clausify,[status(thm)],[f_887_2]) ).
fof(f_888_1,plain,
! [V_c_2,V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) != V_b_2
& V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_b_2
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
| V_a_2 != c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) ) )
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).
fof(f_888_2,plain,
! [U_2561,U_2560,U_2559,U_2558] :
( ( ( U_2559 = c_Rings_Oinverse__class_Odivide(U_2558,U_2560,U_2561)
| ( U_2559 != c_Groups_Ozero__class_Ozero(U_2558)
& U_2561 = c_Groups_Ozero__class_Ozero(U_2558) )
| ( c_Groups_Otimes__class_Otimes(U_2558,U_2559,U_2561) != U_2560
& U_2561 != c_Groups_Ozero__class_Ozero(U_2558) ) )
& ( ( ( U_2559 = c_Groups_Ozero__class_Ozero(U_2558)
| U_2561 != c_Groups_Ozero__class_Ozero(U_2558) )
& ( c_Groups_Otimes__class_Otimes(U_2558,U_2559,U_2561) = U_2560
| U_2561 = c_Groups_Ozero__class_Ozero(U_2558) ) )
| U_2559 != c_Rings_Oinverse__class_Odivide(U_2558,U_2560,U_2561) ) )
| ~ class_Fields_Ofield__inverse__zero(U_2558) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
cnf(f_888_3,plain,
( c_Groups_Otimes__class_Otimes(U_2558,U_2559,U_2561) = U_2560
| U_2561 = c_Groups_Ozero__class_Ozero(U_2558)
| U_2559 != c_Rings_Oinverse__class_Odivide(U_2558,U_2560,U_2561)
| ~ class_Fields_Ofield__inverse__zero(U_2558) ),
inference(clausify,[status(thm)],[f_888_2]) ).
cnf(f_888_4,plain,
( U_2559 = c_Groups_Ozero__class_Ozero(U_2558)
| U_2561 != c_Groups_Ozero__class_Ozero(U_2558)
| U_2559 != c_Rings_Oinverse__class_Odivide(U_2558,U_2560,U_2561)
| ~ class_Fields_Ofield__inverse__zero(U_2558) ),
inference(clausify,[status(thm)],[f_888_2]) ).
cnf(f_888_5,plain,
( U_2561 = c_Groups_Ozero__class_Ozero(U_2558)
| U_2561 != c_Groups_Ozero__class_Ozero(U_2558)
| U_2559 = c_Rings_Oinverse__class_Odivide(U_2558,U_2560,U_2561)
| ~ class_Fields_Ofield__inverse__zero(U_2558) ),
inference(clausify,[status(thm)],[f_888_2]) ).
cnf(f_888_6,plain,
( U_2559 != c_Groups_Ozero__class_Ozero(U_2558)
| U_2561 != c_Groups_Ozero__class_Ozero(U_2558)
| U_2559 = c_Rings_Oinverse__class_Odivide(U_2558,U_2560,U_2561)
| ~ class_Fields_Ofield__inverse__zero(U_2558) ),
inference(clausify,[status(thm)],[f_888_2]) ).
cnf(f_888_7,plain,
( U_2561 = c_Groups_Ozero__class_Ozero(U_2558)
| c_Groups_Otimes__class_Otimes(U_2558,U_2559,U_2561) != U_2560
| U_2559 = c_Rings_Oinverse__class_Odivide(U_2558,U_2560,U_2561)
| ~ class_Fields_Ofield__inverse__zero(U_2558) ),
inference(clausify,[status(thm)],[f_888_2]) ).
cnf(f_888_8,plain,
( U_2559 != c_Groups_Ozero__class_Ozero(U_2558)
| c_Groups_Otimes__class_Otimes(U_2558,U_2559,U_2561) != U_2560
| U_2559 = c_Rings_Oinverse__class_Odivide(U_2558,U_2560,U_2561)
| ~ class_Fields_Ofield__inverse__zero(U_2558) ),
inference(clausify,[status(thm)],[f_888_2]) ).
fof(f_889_1,plain,
! [V_a_2,V_c_2,V_b_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 != c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)
& V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
| c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) != V_a_2 ) )
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).
fof(f_889_2,plain,
! [U_2565,U_2564,U_2563,U_2562] :
( ( ( c_Rings_Oinverse__class_Odivide(U_2562,U_2563,U_2564) = U_2565
| ( U_2565 != c_Groups_Ozero__class_Ozero(U_2562)
& U_2564 = c_Groups_Ozero__class_Ozero(U_2562) )
| ( U_2563 != c_Groups_Otimes__class_Otimes(U_2562,U_2565,U_2564)
& U_2564 != c_Groups_Ozero__class_Ozero(U_2562) ) )
& ( ( ( U_2565 = c_Groups_Ozero__class_Ozero(U_2562)
| U_2564 != c_Groups_Ozero__class_Ozero(U_2562) )
& ( U_2563 = c_Groups_Otimes__class_Otimes(U_2562,U_2565,U_2564)
| U_2564 = c_Groups_Ozero__class_Ozero(U_2562) ) )
| c_Rings_Oinverse__class_Odivide(U_2562,U_2563,U_2564) != U_2565 ) )
| ~ class_Fields_Ofield__inverse__zero(U_2562) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
cnf(f_889_3,plain,
( U_2563 = c_Groups_Otimes__class_Otimes(U_2562,U_2565,U_2564)
| U_2564 = c_Groups_Ozero__class_Ozero(U_2562)
| c_Rings_Oinverse__class_Odivide(U_2562,U_2563,U_2564) != U_2565
| ~ class_Fields_Ofield__inverse__zero(U_2562) ),
inference(clausify,[status(thm)],[f_889_2]) ).
cnf(f_889_4,plain,
( U_2565 = c_Groups_Ozero__class_Ozero(U_2562)
| U_2564 != c_Groups_Ozero__class_Ozero(U_2562)
| c_Rings_Oinverse__class_Odivide(U_2562,U_2563,U_2564) != U_2565
| ~ class_Fields_Ofield__inverse__zero(U_2562) ),
inference(clausify,[status(thm)],[f_889_2]) ).
cnf(f_889_5,plain,
( U_2564 = c_Groups_Ozero__class_Ozero(U_2562)
| U_2564 != c_Groups_Ozero__class_Ozero(U_2562)
| c_Rings_Oinverse__class_Odivide(U_2562,U_2563,U_2564) = U_2565
| ~ class_Fields_Ofield__inverse__zero(U_2562) ),
inference(clausify,[status(thm)],[f_889_2]) ).
cnf(f_889_6,plain,
( U_2565 != c_Groups_Ozero__class_Ozero(U_2562)
| U_2564 != c_Groups_Ozero__class_Ozero(U_2562)
| c_Rings_Oinverse__class_Odivide(U_2562,U_2563,U_2564) = U_2565
| ~ class_Fields_Ofield__inverse__zero(U_2562) ),
inference(clausify,[status(thm)],[f_889_2]) ).
cnf(f_889_7,plain,
( U_2564 = c_Groups_Ozero__class_Ozero(U_2562)
| U_2563 != c_Groups_Otimes__class_Otimes(U_2562,U_2565,U_2564)
| c_Rings_Oinverse__class_Odivide(U_2562,U_2563,U_2564) = U_2565
| ~ class_Fields_Ofield__inverse__zero(U_2562) ),
inference(clausify,[status(thm)],[f_889_2]) ).
cnf(f_889_8,plain,
( U_2565 != c_Groups_Ozero__class_Ozero(U_2562)
| U_2563 != c_Groups_Otimes__class_Otimes(U_2562,U_2565,U_2564)
| c_Rings_Oinverse__class_Odivide(U_2562,U_2563,U_2564) = U_2565
| ~ class_Fields_Ofield__inverse__zero(U_2562) ),
inference(clausify,[status(thm)],[f_889_2]) ).
fof(f_890_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right]) ).
fof(f_890_2,plain,
! [U_2569,U_2568,U_2567,U_2566] :
( c_Rings_Oinverse__class_Odivide(U_2566,c_Groups_Otimes__class_Otimes(U_2566,U_2568,U_2567),c_Groups_Otimes__class_Otimes(U_2566,U_2569,U_2567)) = c_Rings_Oinverse__class_Odivide(U_2566,U_2568,U_2569)
| U_2567 = c_Groups_Ozero__class_Ozero(U_2566)
| ~ class_Fields_Ofield__inverse__zero(U_2566) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
cnf(f_890_3,plain,
( c_Rings_Oinverse__class_Odivide(U_2566,c_Groups_Otimes__class_Otimes(U_2566,U_2568,U_2567),c_Groups_Otimes__class_Otimes(U_2566,U_2569,U_2567)) = c_Rings_Oinverse__class_Odivide(U_2566,U_2568,U_2569)
| U_2567 = c_Groups_Ozero__class_Ozero(U_2566)
| ~ class_Fields_Ofield__inverse__zero(U_2566) ),
inference(clausify,[status(thm)],[f_890_2]) ).
fof(f_891_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left]) ).
fof(f_891_2,plain,
! [U_2573,U_2572,U_2571,U_2570] :
( c_Rings_Oinverse__class_Odivide(U_2570,c_Groups_Otimes__class_Otimes(U_2570,U_2571,U_2572),c_Groups_Otimes__class_Otimes(U_2570,U_2571,U_2573)) = c_Rings_Oinverse__class_Odivide(U_2570,U_2572,U_2573)
| U_2571 = c_Groups_Ozero__class_Ozero(U_2570)
| ~ class_Fields_Ofield__inverse__zero(U_2570) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
cnf(f_891_3,plain,
( c_Rings_Oinverse__class_Odivide(U_2570,c_Groups_Otimes__class_Otimes(U_2570,U_2571,U_2572),c_Groups_Otimes__class_Otimes(U_2570,U_2571,U_2573)) = c_Rings_Oinverse__class_Odivide(U_2570,U_2572,U_2573)
| U_2571 = c_Groups_Ozero__class_Ozero(U_2570)
| ~ class_Fields_Ofield__inverse__zero(U_2570) ),
inference(clausify,[status(thm)],[f_891_2]) ).
fof(f_892_1,plain,
! [V_wa_2,V_x_2,V_za_2,V_y_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)
| c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_za_2) != c_Groups_Otimes__class_Otimes(T_a,V_wa_2,V_y_2) )
& ( c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_za_2) = c_Groups_Otimes__class_Otimes(T_a,V_wa_2,V_y_2)
| c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) != c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2) ) )
| V_za_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).
fof(f_892_2,plain,
! [U_2578,U_2577,U_2576,U_2575,U_2574] :
( ( ( c_Rings_Oinverse__class_Odivide(U_2574,U_2577,U_2575) = c_Rings_Oinverse__class_Odivide(U_2574,U_2578,U_2576)
| c_Groups_Otimes__class_Otimes(U_2574,U_2577,U_2576) != c_Groups_Otimes__class_Otimes(U_2574,U_2578,U_2575) )
& ( c_Groups_Otimes__class_Otimes(U_2574,U_2577,U_2576) = c_Groups_Otimes__class_Otimes(U_2574,U_2578,U_2575)
| c_Rings_Oinverse__class_Odivide(U_2574,U_2577,U_2575) != c_Rings_Oinverse__class_Odivide(U_2574,U_2578,U_2576) ) )
| U_2576 = c_Groups_Ozero__class_Ozero(U_2574)
| U_2575 = c_Groups_Ozero__class_Ozero(U_2574)
| ~ class_Fields_Ofield(U_2574) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
cnf(f_892_3,plain,
( c_Groups_Otimes__class_Otimes(U_2574,U_2577,U_2576) = c_Groups_Otimes__class_Otimes(U_2574,U_2578,U_2575)
| c_Rings_Oinverse__class_Odivide(U_2574,U_2577,U_2575) != c_Rings_Oinverse__class_Odivide(U_2574,U_2578,U_2576)
| U_2576 = c_Groups_Ozero__class_Ozero(U_2574)
| U_2575 = c_Groups_Ozero__class_Ozero(U_2574)
| ~ class_Fields_Ofield(U_2574) ),
inference(clausify,[status(thm)],[f_892_2]) ).
cnf(f_892_4,plain,
( c_Rings_Oinverse__class_Odivide(U_2574,U_2577,U_2575) = c_Rings_Oinverse__class_Odivide(U_2574,U_2578,U_2576)
| c_Groups_Otimes__class_Otimes(U_2574,U_2577,U_2576) != c_Groups_Otimes__class_Otimes(U_2574,U_2578,U_2575)
| U_2576 = c_Groups_Ozero__class_Ozero(U_2574)
| U_2575 = c_Groups_Ozero__class_Ozero(U_2574)
| ~ class_Fields_Ofield(U_2574) ),
inference(clausify,[status(thm)],[f_892_2]) ).
fof(f_893_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2) = c_Groups_Oone__class_Oone(T_a)
| ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
& V_x_2 != c_Groups_Oone__class_Oone(T_a) ) )
& ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_x_2 = c_Groups_Oone__class_Oone(T_a)
| c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).
fof(f_893_2,plain,
! [U_2580,U_2579] :
( ( ( c_Groups_Otimes__class_Otimes(U_2579,U_2580,U_2580) = c_Groups_Oone__class_Oone(U_2579)
| ( U_2580 != c_Groups_Ouminus__class_Ouminus(U_2579,c_Groups_Oone__class_Oone(U_2579))
& U_2580 != c_Groups_Oone__class_Oone(U_2579) ) )
& ( U_2580 = c_Groups_Ouminus__class_Ouminus(U_2579,c_Groups_Oone__class_Oone(U_2579))
| U_2580 = c_Groups_Oone__class_Oone(U_2579)
| c_Groups_Otimes__class_Otimes(U_2579,U_2580,U_2580) != c_Groups_Oone__class_Oone(U_2579) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_2579) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
cnf(f_893_3,plain,
( U_2580 = c_Groups_Ouminus__class_Ouminus(U_2579,c_Groups_Oone__class_Oone(U_2579))
| U_2580 = c_Groups_Oone__class_Oone(U_2579)
| c_Groups_Otimes__class_Otimes(U_2579,U_2580,U_2580) != c_Groups_Oone__class_Oone(U_2579)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2579) ),
inference(clausify,[status(thm)],[f_893_2]) ).
cnf(f_893_4,plain,
( U_2580 != c_Groups_Oone__class_Oone(U_2579)
| c_Groups_Otimes__class_Otimes(U_2579,U_2580,U_2580) = c_Groups_Oone__class_Oone(U_2579)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2579) ),
inference(clausify,[status(thm)],[f_893_2]) ).
cnf(f_893_5,plain,
( U_2580 != c_Groups_Ouminus__class_Ouminus(U_2579,c_Groups_Oone__class_Oone(U_2579))
| c_Groups_Otimes__class_Otimes(U_2579,U_2580,U_2580) = c_Groups_Oone__class_Oone(U_2579)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2579) ),
inference(clausify,[status(thm)],[f_893_2]) ).
fof(f_894_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult__less]) ).
fof(f_894_2,plain,
! [U_2585,U_2584,U_2583,U_2582,U_2581] :
( c_Orderings_Oord__class_Oless(U_2581,c_Groups_Otimes__class_Otimes(U_2581,c_Groups_Oabs__class_Oabs(U_2581,U_2582),c_Groups_Oabs__class_Oabs(U_2581,U_2584)),c_Groups_Otimes__class_Otimes(U_2581,U_2583,U_2585))
| ~ c_Orderings_Oord__class_Oless(U_2581,c_Groups_Oabs__class_Oabs(U_2581,U_2584),U_2585)
| ~ c_Orderings_Oord__class_Oless(U_2581,c_Groups_Oabs__class_Oabs(U_2581,U_2582),U_2583)
| ~ class_Rings_Olinordered__idom(U_2581) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
cnf(f_894_3,plain,
( c_Orderings_Oord__class_Oless(U_2581,c_Groups_Otimes__class_Otimes(U_2581,c_Groups_Oabs__class_Oabs(U_2581,U_2582),c_Groups_Oabs__class_Oabs(U_2581,U_2584)),c_Groups_Otimes__class_Otimes(U_2581,U_2583,U_2585))
| ~ c_Orderings_Oord__class_Oless(U_2581,c_Groups_Oabs__class_Oabs(U_2581,U_2584),U_2585)
| ~ c_Orderings_Oord__class_Oless(U_2581,c_Groups_Oabs__class_Oabs(U_2581,U_2582),U_2583)
| ~ class_Rings_Olinordered__idom(U_2581) ),
inference(clausify,[status(thm)],[f_894_2]) ).
fof(f_895_1,plain,
! [V_x_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2))
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(f_895_2,plain,
! [U_2586] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2586,U_2586))
| U_2586 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_2586 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2586,U_2586)) ) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
fof(f_895_3,plain,
( ! [U_2588] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2588,U_2588))
| U_2588 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_2587] :
( U_2587 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2587,U_2587)) ) ),
inference(miniscope,[status(thm)],[f_895_2]) ).
cnf(f_895_4,plain,
( U_2587 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2587,U_2587)) ),
inference(clausify,[status(thm)],[f_895_3]) ).
cnf(f_895_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2588,U_2588))
| U_2588 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_895_3]) ).
fof(f_896_1,plain,
! [V_y_2,V_x_2,V_za_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_za_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_za_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_za_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_za_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1]) ).
fof(f_896_2,plain,
! [U_2591,U_2590,U_2589] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2590,U_2589),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2591,U_2589))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2590,U_2591) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2590,U_2591)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2590,U_2589),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2591,U_2589)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2589) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
cnf(f_896_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2590,U_2591)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2590,U_2589),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2591,U_2589))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2589) ),
inference(clausify,[status(thm)],[f_896_2]) ).
cnf(f_896_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2590,U_2589),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2591,U_2589))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2590,U_2591)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2589) ),
inference(clausify,[status(thm)],[f_896_2]) ).
fof(f_897_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__order]) ).
fof(f_897_2,plain,
! [U_2593,U_2592] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2592,U_2593))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2593)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2592) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
cnf(f_897_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2592,U_2593))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2593)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2592) ),
inference(clausify,[status(thm)],[f_897_2]) ).
fof(f_898_1,plain,
! [V_y,V_x,V_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2]) ).
fof(f_898_2,plain,
! [U_2596,U_2595,U_2594] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2594,U_2595),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2594,U_2596))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2595,U_2596)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2594) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
cnf(f_898_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2594,U_2595),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2594,U_2596))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2595,U_2596)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2594) ),
inference(clausify,[status(thm)],[f_898_2]) ).
fof(f_899_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_y_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff]) ).
fof(f_899_2,plain,
! [U_2598,U_2597] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2597,U_2597),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2598,U_2598)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2598 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2597 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_2598 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_2597 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2597,U_2597),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2598,U_2598)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
fof(f_899_3,plain,
( ! [U_2602,U_2600] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2600,U_2600),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2602,U_2602)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2602 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2600 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_2601,U_2599] :
( ( U_2601 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_2599 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2599,U_2599),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2601,U_2601)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_899_2]) ).
cnf(f_899_4,plain,
( U_2599 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2599,U_2599),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2601,U_2601)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_899_3]) ).
cnf(f_899_5,plain,
( U_2601 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2599,U_2599),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2601,U_2601)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_899_3]) ).
cnf(f_899_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2600,U_2600),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2602,U_2602)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2602 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2600 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_899_3]) ).
fof(f_900_1,plain,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u,V_u)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x)),
inference(fof_nnf,[status(thm)],[fact_real__minus__mult__self__le]) ).
fof(f_900_2,plain,
! [U_2604,U_2603] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2603,U_2603)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2604,U_2604)),
inference(variable_rename,[status(thm)],[f_900_1]) ).
cnf(f_900_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2603,U_2603)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2604,U_2604)),
inference(clausify,[status(thm)],[f_900_2]) ).
fof(f_901_1,plain,
! [V_b_2,V_a_2,V_fa_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_a_2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_b_2)),
inference(fof_nnf,[status(thm)],[fact_lemma__MVT]) ).
fof(f_901_2,plain,
! [U_2607,U_2606,U_2605] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_2605,U_2606),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_2605,U_2607),hAPP(U_2605,U_2606)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2607,U_2606)),U_2606)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_2605,U_2607),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_2605,U_2607),hAPP(U_2605,U_2606)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2607,U_2606)),U_2607)),
inference(variable_rename,[status(thm)],[f_901_1]) ).
cnf(f_901_3,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_2605,U_2606),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_2605,U_2607),hAPP(U_2605,U_2606)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2607,U_2606)),U_2606)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_2605,U_2607),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_2605,U_2607),hAPP(U_2605,U_2606)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2607,U_2606)),U_2607)),
inference(clausify,[status(thm)],[f_901_2]) ).
fof(f_902_1,plain,
! [V_x] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__abs2]) ).
fof(f_902_2,plain,
! [U_2608] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2608,U_2608)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2608),
inference(variable_rename,[status(thm)],[f_902_1]) ).
cnf(f_902_3,plain,
c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2608,U_2608)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2608),
inference(clausify,[status(thm)],[f_902_2]) ).
fof(f_903_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right]) ).
fof(f_903_2,plain,
! [U_2612,U_2611,U_2610,U_2609] :
( c_Groups_Otimes__class_Otimes(U_2609,U_2610,c_Groups_Ominus__class_Ominus(U_2609,U_2611,U_2612)) = c_Groups_Ominus__class_Ominus(U_2609,c_Groups_Otimes__class_Otimes(U_2609,U_2610,U_2611),c_Groups_Otimes__class_Otimes(U_2609,U_2610,U_2612))
| ~ class_RealVector_Oreal__normed__algebra(U_2609) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
cnf(f_903_3,plain,
( c_Groups_Otimes__class_Otimes(U_2609,U_2610,c_Groups_Ominus__class_Ominus(U_2609,U_2611,U_2612)) = c_Groups_Ominus__class_Ominus(U_2609,c_Groups_Otimes__class_Otimes(U_2609,U_2610,U_2611),c_Groups_Otimes__class_Otimes(U_2609,U_2610,U_2612))
| ~ class_RealVector_Oreal__normed__algebra(U_2609) ),
inference(clausify,[status(thm)],[f_903_2]) ).
fof(f_904_1,plain,
! [V_y,V_x,V_xa,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff]) ).
fof(f_904_2,plain,
! [U_2616,U_2615,U_2614,U_2613] :
( c_Groups_Otimes__class_Otimes(U_2613,U_2614,c_Groups_Ominus__class_Ominus(U_2613,U_2615,U_2616)) = c_Groups_Ominus__class_Ominus(U_2613,c_Groups_Otimes__class_Otimes(U_2613,U_2614,U_2615),c_Groups_Otimes__class_Otimes(U_2613,U_2614,U_2616))
| ~ class_RealVector_Oreal__normed__algebra(U_2613) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
cnf(f_904_3,plain,
( c_Groups_Otimes__class_Otimes(U_2613,U_2614,c_Groups_Ominus__class_Ominus(U_2613,U_2615,U_2616)) = c_Groups_Ominus__class_Ominus(U_2613,c_Groups_Otimes__class_Otimes(U_2613,U_2614,U_2615),c_Groups_Otimes__class_Otimes(U_2613,U_2614,U_2616))
| ~ class_RealVector_Oreal__normed__algebra(U_2613) ),
inference(clausify,[status(thm)],[f_904_2]) ).
fof(f_905_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left]) ).
fof(f_905_2,plain,
! [U_2620,U_2619,U_2618,U_2617] :
( c_Groups_Otimes__class_Otimes(U_2617,c_Groups_Ominus__class_Ominus(U_2617,U_2618,U_2619),U_2620) = c_Groups_Ominus__class_Ominus(U_2617,c_Groups_Otimes__class_Otimes(U_2617,U_2618,U_2620),c_Groups_Otimes__class_Otimes(U_2617,U_2619,U_2620))
| ~ class_RealVector_Oreal__normed__algebra(U_2617) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
cnf(f_905_3,plain,
( c_Groups_Otimes__class_Otimes(U_2617,c_Groups_Ominus__class_Ominus(U_2617,U_2618,U_2619),U_2620) = c_Groups_Ominus__class_Ominus(U_2617,c_Groups_Otimes__class_Otimes(U_2617,U_2618,U_2620),c_Groups_Otimes__class_Otimes(U_2617,U_2619,U_2620))
| ~ class_RealVector_Oreal__normed__algebra(U_2617) ),
inference(clausify,[status(thm)],[f_905_2]) ).
fof(f_906_1,plain,
! [V_ya,V_y,V_x,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff]) ).
fof(f_906_2,plain,
! [U_2624,U_2623,U_2622,U_2621] :
( c_Groups_Otimes__class_Otimes(U_2621,c_Groups_Ominus__class_Ominus(U_2621,U_2622,U_2623),U_2624) = c_Groups_Ominus__class_Ominus(U_2621,c_Groups_Otimes__class_Otimes(U_2621,U_2622,U_2624),c_Groups_Otimes__class_Otimes(U_2621,U_2623,U_2624))
| ~ class_RealVector_Oreal__normed__algebra(U_2621) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
cnf(f_906_3,plain,
( c_Groups_Otimes__class_Otimes(U_2621,c_Groups_Ominus__class_Ominus(U_2621,U_2622,U_2623),U_2624) = c_Groups_Ominus__class_Ominus(U_2621,c_Groups_Otimes__class_Otimes(U_2621,U_2622,U_2624),c_Groups_Otimes__class_Otimes(U_2621,U_2623,U_2624))
| ~ class_RealVector_Oreal__normed__algebra(U_2621) ),
inference(clausify,[status(thm)],[f_906_2]) ).
fof(f_907_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right]) ).
fof(f_907_2,plain,
! [U_2628,U_2627,U_2626,U_2625] :
( c_Groups_Otimes__class_Otimes(U_2625,U_2626,c_Rings_Oinverse__class_Odivide(U_2625,U_2627,U_2628)) = c_Rings_Oinverse__class_Odivide(U_2625,c_Groups_Otimes__class_Otimes(U_2625,U_2626,U_2627),U_2628)
| ~ class_Rings_Odivision__ring(U_2625) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
cnf(f_907_3,plain,
( c_Groups_Otimes__class_Otimes(U_2625,U_2626,c_Rings_Oinverse__class_Odivide(U_2625,U_2627,U_2628)) = c_Rings_Oinverse__class_Odivide(U_2625,c_Groups_Otimes__class_Otimes(U_2625,U_2626,U_2627),U_2628)
| ~ class_Rings_Odivision__ring(U_2625) ),
inference(clausify,[status(thm)],[f_907_2]) ).
fof(f_908_1,plain,
! [V_w,V_z,V_y,V_x,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq]) ).
fof(f_908_2,plain,
! [U_2633,U_2632,U_2631,U_2630,U_2629] :
( c_Groups_Otimes__class_Otimes(U_2629,c_Rings_Oinverse__class_Odivide(U_2629,U_2630,U_2631),c_Rings_Oinverse__class_Odivide(U_2629,U_2632,U_2633)) = c_Rings_Oinverse__class_Odivide(U_2629,c_Groups_Otimes__class_Otimes(U_2629,U_2630,U_2632),c_Groups_Otimes__class_Otimes(U_2629,U_2631,U_2633))
| ~ class_Fields_Ofield__inverse__zero(U_2629) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
cnf(f_908_3,plain,
( c_Groups_Otimes__class_Otimes(U_2629,c_Rings_Oinverse__class_Odivide(U_2629,U_2630,U_2631),c_Rings_Oinverse__class_Odivide(U_2629,U_2632,U_2633)) = c_Rings_Oinverse__class_Odivide(U_2629,c_Groups_Otimes__class_Otimes(U_2629,U_2630,U_2632),c_Groups_Otimes__class_Otimes(U_2629,U_2631,U_2633))
| ~ class_Fields_Ofield__inverse__zero(U_2629) ),
inference(clausify,[status(thm)],[f_908_2]) ).
fof(f_909_1,plain,
! [V_b_2,V_a_2,V_c_2] :
( ( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel]) ).
fof(f_909_2,plain,
! [U_2636,U_2635,U_2634] :
( ( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2635,U_2634) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2636,U_2634)
| U_2635 != U_2636 )
& ( U_2635 = U_2636
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2635,U_2634) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2636,U_2634) ) )
| U_2634 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
cnf(f_909_3,plain,
( U_2635 = U_2636
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2635,U_2634) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2636,U_2634)
| U_2634 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_909_2]) ).
cnf(f_909_4,plain,
( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2635,U_2634) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2636,U_2634)
| U_2635 != U_2636
| U_2634 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_909_2]) ).
fof(f_910_1,plain,
! [V_b_2,V_a_2,V_c_2] :
( ( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__left__cancel]) ).
fof(f_910_2,plain,
! [U_2639,U_2638,U_2637] :
( ( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2637,U_2638) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2637,U_2639)
| U_2638 != U_2639 )
& ( U_2638 = U_2639
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2637,U_2638) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2637,U_2639) ) )
| U_2637 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
cnf(f_910_3,plain,
( U_2638 = U_2639
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2637,U_2638) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2637,U_2639)
| U_2637 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_910_2]) ).
cnf(f_910_4,plain,
( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2637,U_2638) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2637,U_2639)
| U_2638 != U_2639
| U_2637 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_910_2]) ).
fof(f_911_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult]) ).
fof(f_911_2,plain,
! [U_2642,U_2641,U_2640] :
( c_Groups_Oabs__class_Oabs(U_2640,c_Groups_Otimes__class_Otimes(U_2640,U_2641,U_2642)) = c_Groups_Otimes__class_Otimes(U_2640,c_Groups_Oabs__class_Oabs(U_2640,U_2641),c_Groups_Oabs__class_Oabs(U_2640,U_2642))
| ~ class_Rings_Olinordered__idom(U_2640) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
cnf(f_911_3,plain,
( c_Groups_Oabs__class_Oabs(U_2640,c_Groups_Otimes__class_Otimes(U_2640,U_2641,U_2642)) = c_Groups_Otimes__class_Otimes(U_2640,c_Groups_Oabs__class_Oabs(U_2640,U_2641),c_Groups_Oabs__class_Oabs(U_2640,U_2642))
| ~ class_Rings_Olinordered__idom(U_2640) ),
inference(clausify,[status(thm)],[f_911_2]) ).
fof(f_912_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult__self]) ).
fof(f_912_2,plain,
! [U_2644,U_2643] :
( c_Groups_Otimes__class_Otimes(U_2643,c_Groups_Oabs__class_Oabs(U_2643,U_2644),c_Groups_Oabs__class_Oabs(U_2643,U_2644)) = c_Groups_Otimes__class_Otimes(U_2643,U_2644,U_2644)
| ~ class_Rings_Olinordered__idom(U_2643) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
cnf(f_912_3,plain,
( c_Groups_Otimes__class_Otimes(U_2643,c_Groups_Oabs__class_Oabs(U_2643,U_2644),c_Groups_Oabs__class_Oabs(U_2643,U_2644)) = c_Groups_Otimes__class_Otimes(U_2643,U_2644,U_2644)
| ~ class_Rings_Olinordered__idom(U_2643) ),
inference(clausify,[status(thm)],[f_912_2]) ).
fof(f_913_1,plain,
! [V_s,V_y,V_r,V_x,T_a] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_s))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__mult__less]) ).
fof(f_913_2,plain,
! [U_2649,U_2648,U_2647,U_2646,U_2645] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2645,c_Groups_Otimes__class_Otimes(U_2645,U_2646,U_2648)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2647,U_2649))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2645,U_2648),U_2649)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2645,U_2646),U_2647)
| ~ class_RealVector_Oreal__normed__algebra(U_2645) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
cnf(f_913_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2645,c_Groups_Otimes__class_Otimes(U_2645,U_2646,U_2648)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2647,U_2649))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2645,U_2648),U_2649)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2645,U_2646),U_2647)
| ~ class_RealVector_Oreal__normed__algebra(U_2645) ),
inference(clausify,[status(thm)],[f_913_2]) ).
fof(f_914_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__idem]) ).
fof(f_914_2,plain,
! [U_2652,U_2651,U_2650] :
( c_Groups_Otimes__class_Otimes(U_2650,U_2651,c_Groups_Otimes__class_Otimes(U_2650,U_2651,U_2652)) = c_Groups_Otimes__class_Otimes(U_2650,U_2651,U_2652)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2650) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
cnf(f_914_3,plain,
( c_Groups_Otimes__class_Otimes(U_2650,U_2651,c_Groups_Otimes__class_Otimes(U_2650,U_2651,U_2652)) = c_Groups_Otimes__class_Otimes(U_2650,U_2651,U_2652)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2650) ),
inference(clausify,[status(thm)],[f_914_2]) ).
fof(f_915_1,plain,
! [V_x,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = V_x
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__idem]) ).
fof(f_915_2,plain,
! [U_2654,U_2653] :
( c_Groups_Otimes__class_Otimes(U_2653,U_2654,U_2654) = U_2654
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2653) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
cnf(f_915_3,plain,
( c_Groups_Otimes__class_Otimes(U_2653,U_2654,U_2654) = U_2654
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2653) ),
inference(clausify,[status(thm)],[f_915_2]) ).
fof(f_916_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,V_a) = V_a
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times_Oidem]) ).
fof(f_916_2,plain,
! [U_2656,U_2655] :
( c_Groups_Otimes__class_Otimes(U_2655,U_2656,U_2656) = U_2656
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2655) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
cnf(f_916_3,plain,
( c_Groups_Otimes__class_Otimes(U_2655,U_2656,U_2656) = U_2656
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2655) ),
inference(clausify,[status(thm)],[f_916_2]) ).
fof(f_917_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
| ~ class_Groups_Oab__semigroup__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J]) ).
fof(f_917_2,plain,
! [U_2660,U_2659,U_2658,U_2657] :
( c_Groups_Otimes__class_Otimes(U_2657,c_Groups_Otimes__class_Otimes(U_2657,U_2658,U_2659),U_2660) = c_Groups_Otimes__class_Otimes(U_2657,U_2658,c_Groups_Otimes__class_Otimes(U_2657,U_2659,U_2660))
| ~ class_Groups_Oab__semigroup__mult(U_2657) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
cnf(f_917_3,plain,
( c_Groups_Otimes__class_Otimes(U_2657,c_Groups_Otimes__class_Otimes(U_2657,U_2658,U_2659),U_2660) = c_Groups_Otimes__class_Otimes(U_2657,U_2658,c_Groups_Otimes__class_Otimes(U_2657,U_2659,U_2660))
| ~ class_Groups_Oab__semigroup__mult(U_2657) ),
inference(clausify,[status(thm)],[f_917_2]) ).
fof(f_918_1,plain,
! [V_z,V_w,V_v,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__number__of__left]) ).
fof(f_918_2,plain,
! [U_2664,U_2663,U_2662,U_2661] :
( c_Groups_Otimes__class_Otimes(U_2661,c_Int_Onumber__class_Onumber__of(U_2661,U_2662),c_Groups_Otimes__class_Otimes(U_2661,c_Int_Onumber__class_Onumber__of(U_2661,U_2663),U_2664)) = c_Groups_Otimes__class_Otimes(U_2661,c_Int_Onumber__class_Onumber__of(U_2661,c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2662,U_2663)),U_2664)
| ~ class_Int_Onumber__ring(U_2661) ),
inference(variable_rename,[status(thm)],[f_918_1]) ).
cnf(f_918_3,plain,
( c_Groups_Otimes__class_Otimes(U_2661,c_Int_Onumber__class_Onumber__of(U_2661,U_2662),c_Groups_Otimes__class_Otimes(U_2661,c_Int_Onumber__class_Onumber__of(U_2661,U_2663),U_2664)) = c_Groups_Otimes__class_Otimes(U_2661,c_Int_Onumber__class_Onumber__of(U_2661,c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2662,U_2663)),U_2664)
| ~ class_Int_Onumber__ring(U_2661) ),
inference(clausify,[status(thm)],[f_918_2]) ).
fof(f_919_1,plain,
! [V_w,V_v,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J]) ).
fof(f_919_2,plain,
! [U_2667,U_2666,U_2665] :
( c_Groups_Otimes__class_Otimes(U_2665,c_Int_Onumber__class_Onumber__of(U_2665,U_2666),c_Int_Onumber__class_Onumber__of(U_2665,U_2667)) = c_Int_Onumber__class_Onumber__of(U_2665,c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2666,U_2667))
| ~ class_Int_Onumber__ring(U_2665) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
cnf(f_919_3,plain,
( c_Groups_Otimes__class_Otimes(U_2665,c_Int_Onumber__class_Onumber__of(U_2665,U_2666),c_Int_Onumber__class_Onumber__of(U_2665,U_2667)) = c_Int_Onumber__class_Onumber__of(U_2665,c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2666,U_2667))
| ~ class_Int_Onumber__ring(U_2665) ),
inference(clausify,[status(thm)],[f_919_2]) ).
fof(f_920_1,plain,
! [V_w,V_v,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__mult]) ).
fof(f_920_2,plain,
! [U_2670,U_2669,U_2668] :
( c_Int_Onumber__class_Onumber__of(U_2668,c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2669,U_2670)) = c_Groups_Otimes__class_Otimes(U_2668,c_Int_Onumber__class_Onumber__of(U_2668,U_2669),c_Int_Onumber__class_Onumber__of(U_2668,U_2670))
| ~ class_Int_Onumber__ring(U_2668) ),
inference(variable_rename,[status(thm)],[f_920_1]) ).
cnf(f_920_3,plain,
( c_Int_Onumber__class_Onumber__of(U_2668,c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2669,U_2670)) = c_Groups_Otimes__class_Otimes(U_2668,c_Int_Onumber__class_Onumber__of(U_2668,U_2669),c_Int_Onumber__class_Onumber__of(U_2668,U_2670))
| ~ class_Int_Onumber__ring(U_2668) ),
inference(clausify,[status(thm)],[f_920_2]) ).
fof(f_921_1,plain,
! [V_y,V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))
| ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__mult]) ).
fof(f_921_2,plain,
! [U_2673,U_2672,U_2671] :
( c_RealVector_Onorm__class_Onorm(U_2671,c_Groups_Otimes__class_Otimes(U_2671,U_2672,U_2673)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2671,U_2672),c_RealVector_Onorm__class_Onorm(U_2671,U_2673))
| ~ class_RealVector_Oreal__normed__div__algebra(U_2671) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
cnf(f_921_3,plain,
( c_RealVector_Onorm__class_Onorm(U_2671,c_Groups_Otimes__class_Otimes(U_2671,U_2672,U_2673)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2671,U_2672),c_RealVector_Onorm__class_Onorm(U_2671,U_2673))
| ~ class_RealVector_Oreal__normed__div__algebra(U_2671) ),
inference(clausify,[status(thm)],[f_921_2]) ).
fof(f_922_1,plain,
! [V_z3,V_z2,V_z1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_z2),V_z3) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_z3)),
inference(fof_nnf,[status(thm)],[fact_real__mult__assoc]) ).
fof(f_922_2,plain,
! [U_2676,U_2675,U_2674] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2674,U_2675),U_2676) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2674,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2675,U_2676)),
inference(variable_rename,[status(thm)],[f_922_1]) ).
cnf(f_922_3,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2674,U_2675),U_2676) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2674,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2675,U_2676)),
inference(clausify,[status(thm)],[f_922_2]) ).
fof(f_923_1,plain,
! [V_w,V_z] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_w) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w,V_z),
inference(fof_nnf,[status(thm)],[fact_real__mult__commute]) ).
fof(f_923_2,plain,
! [U_2678,U_2677] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2677,U_2678) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2678,U_2677),
inference(variable_rename,[status(thm)],[f_923_1]) ).
cnf(f_923_3,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2677,U_2678) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2678,U_2677),
inference(clausify,[status(thm)],[f_923_2]) ).
fof(f_924_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__mult]) ).
fof(f_924_2,plain,
! [U_2682,U_2681,U_2680,U_2679] :
( hAPP(c_Polynomial_Opoly(U_2679,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2679),U_2680,U_2681)),U_2682) = c_Groups_Otimes__class_Otimes(U_2679,hAPP(c_Polynomial_Opoly(U_2679,U_2680),U_2682),hAPP(c_Polynomial_Opoly(U_2679,U_2681),U_2682))
| ~ class_Rings_Ocomm__semiring__0(U_2679) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
cnf(f_924_3,plain,
( hAPP(c_Polynomial_Opoly(U_2679,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2679),U_2680,U_2681)),U_2682) = c_Groups_Otimes__class_Otimes(U_2679,hAPP(c_Polynomial_Opoly(U_2679,U_2680),U_2682),hAPP(c_Polynomial_Opoly(U_2679,U_2681),U_2682))
| ~ class_Rings_Ocomm__semiring__0(U_2679) ),
inference(clausify,[status(thm)],[f_924_2]) ).
fof(f_925_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq]) ).
fof(f_925_2,plain,
! [U_2685,U_2684,U_2683] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2683,c_Groups_Otimes__class_Otimes(U_2683,U_2684,U_2685)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2683,U_2684),c_RealVector_Onorm__class_Onorm(U_2683,U_2685)))
| ~ class_RealVector_Oreal__normed__algebra(U_2683) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
cnf(f_925_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2683,c_Groups_Otimes__class_Otimes(U_2683,U_2684,U_2685)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2683,U_2684),c_RealVector_Onorm__class_Onorm(U_2683,U_2685)))
| ~ class_RealVector_Oreal__normed__algebra(U_2683) ),
inference(clausify,[status(thm)],[f_925_2]) ).
fof(f_926_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Omult__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__zero__left]) ).
fof(f_926_2,plain,
! [U_2687,U_2686] :
( c_Groups_Otimes__class_Otimes(U_2686,c_Groups_Ozero__class_Ozero(U_2686),U_2687) = c_Groups_Ozero__class_Ozero(U_2686)
| ~ class_Rings_Omult__zero(U_2686) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
cnf(f_926_3,plain,
( c_Groups_Otimes__class_Otimes(U_2686,c_Groups_Ozero__class_Ozero(U_2686),U_2687) = c_Groups_Ozero__class_Ozero(U_2686)
| ~ class_Rings_Omult__zero(U_2686) ),
inference(clausify,[status(thm)],[f_926_2]) ).
fof(f_927_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Omult__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__zero__right]) ).
fof(f_927_2,plain,
! [U_2689,U_2688] :
( c_Groups_Otimes__class_Otimes(U_2688,U_2689,c_Groups_Ozero__class_Ozero(U_2688)) = c_Groups_Ozero__class_Ozero(U_2688)
| ~ class_Rings_Omult__zero(U_2688) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
cnf(f_927_3,plain,
( c_Groups_Otimes__class_Otimes(U_2688,U_2689,c_Groups_Ozero__class_Ozero(U_2688)) = c_Groups_Ozero__class_Ozero(U_2688)
| ~ class_Rings_Omult__zero(U_2688) ),
inference(clausify,[status(thm)],[f_927_2]) ).
fof(f_928_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
& V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oring__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).
fof(f_928_2,plain,
! [U_2692,U_2691,U_2690] :
( ( ( c_Groups_Otimes__class_Otimes(U_2690,U_2691,U_2692) = c_Groups_Ozero__class_Ozero(U_2690)
| ( U_2692 != c_Groups_Ozero__class_Ozero(U_2690)
& U_2691 != c_Groups_Ozero__class_Ozero(U_2690) ) )
& ( U_2692 = c_Groups_Ozero__class_Ozero(U_2690)
| U_2691 = c_Groups_Ozero__class_Ozero(U_2690)
| c_Groups_Otimes__class_Otimes(U_2690,U_2691,U_2692) != c_Groups_Ozero__class_Ozero(U_2690) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_2690) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
cnf(f_928_3,plain,
( U_2692 = c_Groups_Ozero__class_Ozero(U_2690)
| U_2691 = c_Groups_Ozero__class_Ozero(U_2690)
| c_Groups_Otimes__class_Otimes(U_2690,U_2691,U_2692) != c_Groups_Ozero__class_Ozero(U_2690)
| ~ class_Rings_Oring__no__zero__divisors(U_2690) ),
inference(clausify,[status(thm)],[f_928_2]) ).
cnf(f_928_4,plain,
( U_2691 != c_Groups_Ozero__class_Ozero(U_2690)
| c_Groups_Otimes__class_Otimes(U_2690,U_2691,U_2692) = c_Groups_Ozero__class_Ozero(U_2690)
| ~ class_Rings_Oring__no__zero__divisors(U_2690) ),
inference(clausify,[status(thm)],[f_928_2]) ).
cnf(f_928_5,plain,
( U_2692 != c_Groups_Ozero__class_Ozero(U_2690)
| c_Groups_Otimes__class_Otimes(U_2690,U_2691,U_2692) = c_Groups_Ozero__class_Ozero(U_2690)
| ~ class_Rings_Oring__no__zero__divisors(U_2690) ),
inference(clausify,[status(thm)],[f_928_2]) ).
fof(f_929_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a)
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_no__zero__divisors]) ).
fof(f_929_2,plain,
! [U_2695,U_2694,U_2693] :
( c_Groups_Otimes__class_Otimes(U_2693,U_2694,U_2695) != c_Groups_Ozero__class_Ozero(U_2693)
| U_2695 = c_Groups_Ozero__class_Ozero(U_2693)
| U_2694 = c_Groups_Ozero__class_Ozero(U_2693)
| ~ class_Rings_Ono__zero__divisors(U_2693) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
cnf(f_929_3,plain,
( c_Groups_Otimes__class_Otimes(U_2693,U_2694,U_2695) != c_Groups_Ozero__class_Ozero(U_2693)
| U_2695 = c_Groups_Ozero__class_Ozero(U_2693)
| U_2694 = c_Groups_Ozero__class_Ozero(U_2693)
| ~ class_Rings_Ono__zero__divisors(U_2693) ),
inference(clausify,[status(thm)],[f_929_2]) ).
fof(f_930_1,plain,
! [V_b,V_a,T_a] :
( V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divisors__zero]) ).
fof(f_930_2,plain,
! [U_2698,U_2697,U_2696] :
( U_2698 = c_Groups_Ozero__class_Ozero(U_2696)
| U_2697 = c_Groups_Ozero__class_Ozero(U_2696)
| c_Groups_Otimes__class_Otimes(U_2696,U_2697,U_2698) != c_Groups_Ozero__class_Ozero(U_2696)
| ~ class_Rings_Ono__zero__divisors(U_2696) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
cnf(f_930_3,plain,
( U_2698 = c_Groups_Ozero__class_Ozero(U_2696)
| U_2697 = c_Groups_Ozero__class_Ozero(U_2696)
| c_Groups_Otimes__class_Otimes(U_2696,U_2697,U_2698) != c_Groups_Ozero__class_Ozero(U_2696)
| ~ class_Rings_Ono__zero__divisors(U_2696) ),
inference(clausify,[status(thm)],[f_930_2]) ).
fof(f_931_1,plain,
! [V_b,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left]) ).
fof(f_931_2,plain,
! [U_2700,U_2699] :
( c_Groups_Otimes__class_Otimes(U_2699,c_Groups_Ozero__class_Ozero(U_2699),U_2700) = c_Groups_Ozero__class_Ozero(U_2699)
| ~ class_RealVector_Oreal__normed__algebra(U_2699) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
cnf(f_931_3,plain,
( c_Groups_Otimes__class_Otimes(U_2699,c_Groups_Ozero__class_Ozero(U_2699),U_2700) = c_Groups_Ozero__class_Ozero(U_2699)
| ~ class_RealVector_Oreal__normed__algebra(U_2699) ),
inference(clausify,[status(thm)],[f_931_2]) ).
fof(f_932_1,plain,
! [V_y,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero]) ).
fof(f_932_2,plain,
! [U_2702,U_2701] :
( c_Groups_Otimes__class_Otimes(U_2701,c_Groups_Ozero__class_Ozero(U_2701),U_2702) = c_Groups_Ozero__class_Ozero(U_2701)
| ~ class_RealVector_Oreal__normed__algebra(U_2701) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
cnf(f_932_3,plain,
( c_Groups_Otimes__class_Otimes(U_2701,c_Groups_Ozero__class_Ozero(U_2701),U_2702) = c_Groups_Ozero__class_Ozero(U_2701)
| ~ class_RealVector_Oreal__normed__algebra(U_2701) ),
inference(clausify,[status(thm)],[f_932_2]) ).
fof(f_933_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right]) ).
fof(f_933_2,plain,
! [U_2704,U_2703] :
( c_Groups_Otimes__class_Otimes(U_2703,U_2704,c_Groups_Ozero__class_Ozero(U_2703)) = c_Groups_Ozero__class_Ozero(U_2703)
| ~ class_RealVector_Oreal__normed__algebra(U_2703) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
cnf(f_933_3,plain,
( c_Groups_Otimes__class_Otimes(U_2703,U_2704,c_Groups_Ozero__class_Ozero(U_2703)) = c_Groups_Ozero__class_Ozero(U_2703)
| ~ class_RealVector_Oreal__normed__algebra(U_2703) ),
inference(clausify,[status(thm)],[f_933_2]) ).
fof(f_934_1,plain,
! [V_x,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero]) ).
fof(f_934_2,plain,
! [U_2706,U_2705] :
( c_Groups_Otimes__class_Otimes(U_2705,U_2706,c_Groups_Ozero__class_Ozero(U_2705)) = c_Groups_Ozero__class_Ozero(U_2705)
| ~ class_RealVector_Oreal__normed__algebra(U_2705) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
cnf(f_934_3,plain,
( c_Groups_Otimes__class_Otimes(U_2705,U_2706,c_Groups_Ozero__class_Ozero(U_2705)) = c_Groups_Ozero__class_Ozero(U_2705)
| ~ class_RealVector_Oreal__normed__algebra(U_2705) ),
inference(clausify,[status(thm)],[f_934_2]) ).
fof(f_935_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__square__less__zero]) ).
fof(f_935_2,plain,
! [U_2708,U_2707] :
( ~ c_Orderings_Oord__class_Oless(U_2707,c_Groups_Otimes__class_Otimes(U_2707,U_2708,U_2708),c_Groups_Ozero__class_Ozero(U_2707))
| ~ class_Rings_Olinordered__ring(U_2707) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
cnf(f_935_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2707,c_Groups_Otimes__class_Otimes(U_2707,U_2708,U_2708),c_Groups_Ozero__class_Ozero(U_2707))
| ~ class_Rings_Olinordered__ring(U_2707) ),
inference(clausify,[status(thm)],[f_935_2]) ).
fof(f_936_1,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).
fof(f_936_2,plain,
! [U_2712,U_2711,U_2710,U_2709] :
( ( ( c_Orderings_Oord__class_Oless(U_2709,c_Groups_Otimes__class_Otimes(U_2709,U_2710,U_2711),c_Groups_Otimes__class_Otimes(U_2709,U_2712,U_2711))
| ( ( ~ c_Orderings_Oord__class_Oless(U_2709,U_2712,U_2710)
| ~ c_Orderings_Oord__class_Oless(U_2709,U_2711,c_Groups_Ozero__class_Ozero(U_2709)) )
& ( ~ c_Orderings_Oord__class_Oless(U_2709,U_2710,U_2712)
| ~ c_Orderings_Oord__class_Oless(U_2709,c_Groups_Ozero__class_Ozero(U_2709),U_2711) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_2709,U_2712,U_2710)
& c_Orderings_Oord__class_Oless(U_2709,U_2711,c_Groups_Ozero__class_Ozero(U_2709)) )
| ( c_Orderings_Oord__class_Oless(U_2709,U_2710,U_2712)
& c_Orderings_Oord__class_Oless(U_2709,c_Groups_Ozero__class_Ozero(U_2709),U_2711) )
| ~ c_Orderings_Oord__class_Oless(U_2709,c_Groups_Otimes__class_Otimes(U_2709,U_2710,U_2711),c_Groups_Otimes__class_Otimes(U_2709,U_2712,U_2711)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2709) ),
inference(variable_rename,[status(thm)],[f_936_1]) ).
cnf(f_936_3,plain,
( c_Orderings_Oord__class_Oless(U_2709,U_2711,c_Groups_Ozero__class_Ozero(U_2709))
| c_Orderings_Oord__class_Oless(U_2709,c_Groups_Ozero__class_Ozero(U_2709),U_2711)
| ~ c_Orderings_Oord__class_Oless(U_2709,c_Groups_Otimes__class_Otimes(U_2709,U_2710,U_2711),c_Groups_Otimes__class_Otimes(U_2709,U_2712,U_2711))
| ~ class_Rings_Olinordered__ring__strict(U_2709) ),
inference(clausify,[status(thm)],[f_936_2]) ).
cnf(f_936_4,plain,
( c_Orderings_Oord__class_Oless(U_2709,U_2712,U_2710)
| c_Orderings_Oord__class_Oless(U_2709,c_Groups_Ozero__class_Ozero(U_2709),U_2711)
| ~ c_Orderings_Oord__class_Oless(U_2709,c_Groups_Otimes__class_Otimes(U_2709,U_2710,U_2711),c_Groups_Otimes__class_Otimes(U_2709,U_2712,U_2711))
| ~ class_Rings_Olinordered__ring__strict(U_2709) ),
inference(clausify,[status(thm)],[f_936_2]) ).
cnf(f_936_5,plain,
( c_Orderings_Oord__class_Oless(U_2709,U_2711,c_Groups_Ozero__class_Ozero(U_2709))
| c_Orderings_Oord__class_Oless(U_2709,U_2710,U_2712)
| ~ c_Orderings_Oord__class_Oless(U_2709,c_Groups_Otimes__class_Otimes(U_2709,U_2710,U_2711),c_Groups_Otimes__class_Otimes(U_2709,U_2712,U_2711))
| ~ class_Rings_Olinordered__ring__strict(U_2709) ),
inference(clausify,[status(thm)],[f_936_2]) ).
cnf(f_936_6,plain,
( c_Orderings_Oord__class_Oless(U_2709,U_2712,U_2710)
| c_Orderings_Oord__class_Oless(U_2709,U_2710,U_2712)
| ~ c_Orderings_Oord__class_Oless(U_2709,c_Groups_Otimes__class_Otimes(U_2709,U_2710,U_2711),c_Groups_Otimes__class_Otimes(U_2709,U_2712,U_2711))
| ~ class_Rings_Olinordered__ring__strict(U_2709) ),
inference(clausify,[status(thm)],[f_936_2]) ).
cnf(f_936_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_2709,U_2710,U_2712)
| ~ c_Orderings_Oord__class_Oless(U_2709,c_Groups_Ozero__class_Ozero(U_2709),U_2711)
| c_Orderings_Oord__class_Oless(U_2709,c_Groups_Otimes__class_Otimes(U_2709,U_2710,U_2711),c_Groups_Otimes__class_Otimes(U_2709,U_2712,U_2711))
| ~ class_Rings_Olinordered__ring__strict(U_2709) ),
inference(clausify,[status(thm)],[f_936_2]) ).
cnf(f_936_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_2709,U_2712,U_2710)
| ~ c_Orderings_Oord__class_Oless(U_2709,U_2711,c_Groups_Ozero__class_Ozero(U_2709))
| c_Orderings_Oord__class_Oless(U_2709,c_Groups_Otimes__class_Otimes(U_2709,U_2710,U_2711),c_Groups_Otimes__class_Otimes(U_2709,U_2712,U_2711))
| ~ class_Rings_Olinordered__ring__strict(U_2709) ),
inference(clausify,[status(thm)],[f_936_2]) ).
fof(f_937_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).
fof(f_937_2,plain,
! [U_2716,U_2715,U_2714,U_2713] :
( ( ( c_Orderings_Oord__class_Oless(U_2713,c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2715),c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2716))
| ( ( ~ c_Orderings_Oord__class_Oless(U_2713,U_2716,U_2715)
| ~ c_Orderings_Oord__class_Oless(U_2713,U_2714,c_Groups_Ozero__class_Ozero(U_2713)) )
& ( ~ c_Orderings_Oord__class_Oless(U_2713,U_2715,U_2716)
| ~ c_Orderings_Oord__class_Oless(U_2713,c_Groups_Ozero__class_Ozero(U_2713),U_2714) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_2713,U_2716,U_2715)
& c_Orderings_Oord__class_Oless(U_2713,U_2714,c_Groups_Ozero__class_Ozero(U_2713)) )
| ( c_Orderings_Oord__class_Oless(U_2713,U_2715,U_2716)
& c_Orderings_Oord__class_Oless(U_2713,c_Groups_Ozero__class_Ozero(U_2713),U_2714) )
| ~ c_Orderings_Oord__class_Oless(U_2713,c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2715),c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2716)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2713) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
cnf(f_937_3,plain,
( c_Orderings_Oord__class_Oless(U_2713,U_2714,c_Groups_Ozero__class_Ozero(U_2713))
| c_Orderings_Oord__class_Oless(U_2713,c_Groups_Ozero__class_Ozero(U_2713),U_2714)
| ~ c_Orderings_Oord__class_Oless(U_2713,c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2715),c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2716))
| ~ class_Rings_Olinordered__ring__strict(U_2713) ),
inference(clausify,[status(thm)],[f_937_2]) ).
cnf(f_937_4,plain,
( c_Orderings_Oord__class_Oless(U_2713,U_2716,U_2715)
| c_Orderings_Oord__class_Oless(U_2713,c_Groups_Ozero__class_Ozero(U_2713),U_2714)
| ~ c_Orderings_Oord__class_Oless(U_2713,c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2715),c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2716))
| ~ class_Rings_Olinordered__ring__strict(U_2713) ),
inference(clausify,[status(thm)],[f_937_2]) ).
cnf(f_937_5,plain,
( c_Orderings_Oord__class_Oless(U_2713,U_2714,c_Groups_Ozero__class_Ozero(U_2713))
| c_Orderings_Oord__class_Oless(U_2713,U_2715,U_2716)
| ~ c_Orderings_Oord__class_Oless(U_2713,c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2715),c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2716))
| ~ class_Rings_Olinordered__ring__strict(U_2713) ),
inference(clausify,[status(thm)],[f_937_2]) ).
cnf(f_937_6,plain,
( c_Orderings_Oord__class_Oless(U_2713,U_2716,U_2715)
| c_Orderings_Oord__class_Oless(U_2713,U_2715,U_2716)
| ~ c_Orderings_Oord__class_Oless(U_2713,c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2715),c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2716))
| ~ class_Rings_Olinordered__ring__strict(U_2713) ),
inference(clausify,[status(thm)],[f_937_2]) ).
cnf(f_937_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_2713,U_2715,U_2716)
| ~ c_Orderings_Oord__class_Oless(U_2713,c_Groups_Ozero__class_Ozero(U_2713),U_2714)
| c_Orderings_Oord__class_Oless(U_2713,c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2715),c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2716))
| ~ class_Rings_Olinordered__ring__strict(U_2713) ),
inference(clausify,[status(thm)],[f_937_2]) ).
cnf(f_937_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_2713,U_2716,U_2715)
| ~ c_Orderings_Oord__class_Oless(U_2713,U_2714,c_Groups_Ozero__class_Ozero(U_2713))
| c_Orderings_Oord__class_Oless(U_2713,c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2715),c_Groups_Otimes__class_Otimes(U_2713,U_2714,U_2716))
| ~ class_Rings_Olinordered__ring__strict(U_2713) ),
inference(clausify,[status(thm)],[f_937_2]) ).
fof(f_938_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).
fof(f_938_2,plain,
! [U_2720,U_2719,U_2718,U_2717] :
( ( ( c_Orderings_Oord__class_Oless(U_2717,c_Groups_Otimes__class_Otimes(U_2717,U_2718,U_2719),c_Groups_Otimes__class_Otimes(U_2717,U_2718,U_2720))
| ~ c_Orderings_Oord__class_Oless(U_2717,U_2719,U_2720) )
& ( c_Orderings_Oord__class_Oless(U_2717,U_2719,U_2720)
| ~ c_Orderings_Oord__class_Oless(U_2717,c_Groups_Otimes__class_Otimes(U_2717,U_2718,U_2719),c_Groups_Otimes__class_Otimes(U_2717,U_2718,U_2720)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2717,c_Groups_Ozero__class_Ozero(U_2717),U_2718)
| ~ class_Rings_Olinordered__ring__strict(U_2717) ),
inference(variable_rename,[status(thm)],[f_938_1]) ).
cnf(f_938_3,plain,
( c_Orderings_Oord__class_Oless(U_2717,U_2719,U_2720)
| ~ c_Orderings_Oord__class_Oless(U_2717,c_Groups_Otimes__class_Otimes(U_2717,U_2718,U_2719),c_Groups_Otimes__class_Otimes(U_2717,U_2718,U_2720))
| ~ c_Orderings_Oord__class_Oless(U_2717,c_Groups_Ozero__class_Ozero(U_2717),U_2718)
| ~ class_Rings_Olinordered__ring__strict(U_2717) ),
inference(clausify,[status(thm)],[f_938_2]) ).
cnf(f_938_4,plain,
( c_Orderings_Oord__class_Oless(U_2717,c_Groups_Otimes__class_Otimes(U_2717,U_2718,U_2719),c_Groups_Otimes__class_Otimes(U_2717,U_2718,U_2720))
| ~ c_Orderings_Oord__class_Oless(U_2717,U_2719,U_2720)
| ~ c_Orderings_Oord__class_Oless(U_2717,c_Groups_Ozero__class_Ozero(U_2717),U_2718)
| ~ class_Rings_Olinordered__ring__strict(U_2717) ),
inference(clausify,[status(thm)],[f_938_2]) ).
fof(f_939_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__pos]) ).
fof(f_939_2,plain,
! [U_2723,U_2722,U_2721] :
( c_Orderings_Oord__class_Oless(U_2721,c_Groups_Ozero__class_Ozero(U_2721),c_Groups_Otimes__class_Otimes(U_2721,U_2722,U_2723))
| ~ c_Orderings_Oord__class_Oless(U_2721,c_Groups_Ozero__class_Ozero(U_2721),U_2723)
| ~ c_Orderings_Oord__class_Oless(U_2721,c_Groups_Ozero__class_Ozero(U_2721),U_2722)
| ~ class_Rings_Olinordered__semiring__strict(U_2721) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
cnf(f_939_3,plain,
( c_Orderings_Oord__class_Oless(U_2721,c_Groups_Ozero__class_Ozero(U_2721),c_Groups_Otimes__class_Otimes(U_2721,U_2722,U_2723))
| ~ c_Orderings_Oord__class_Oless(U_2721,c_Groups_Ozero__class_Ozero(U_2721),U_2723)
| ~ c_Orderings_Oord__class_Oless(U_2721,c_Groups_Ozero__class_Ozero(U_2721),U_2722)
| ~ class_Rings_Olinordered__semiring__strict(U_2721) ),
inference(clausify,[status(thm)],[f_939_2]) ).
fof(f_940_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__neg]) ).
fof(f_940_2,plain,
! [U_2726,U_2725,U_2724] :
( c_Orderings_Oord__class_Oless(U_2724,c_Groups_Otimes__class_Otimes(U_2724,U_2725,U_2726),c_Groups_Ozero__class_Ozero(U_2724))
| ~ c_Orderings_Oord__class_Oless(U_2724,U_2726,c_Groups_Ozero__class_Ozero(U_2724))
| ~ c_Orderings_Oord__class_Oless(U_2724,c_Groups_Ozero__class_Ozero(U_2724),U_2725)
| ~ class_Rings_Olinordered__semiring__strict(U_2724) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
cnf(f_940_3,plain,
( c_Orderings_Oord__class_Oless(U_2724,c_Groups_Otimes__class_Otimes(U_2724,U_2725,U_2726),c_Groups_Ozero__class_Ozero(U_2724))
| ~ c_Orderings_Oord__class_Oless(U_2724,U_2726,c_Groups_Ozero__class_Ozero(U_2724))
| ~ c_Orderings_Oord__class_Oless(U_2724,c_Groups_Ozero__class_Ozero(U_2724),U_2725)
| ~ class_Rings_Olinordered__semiring__strict(U_2724) ),
inference(clausify,[status(thm)],[f_940_2]) ).
fof(f_941_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2]) ).
fof(f_941_2,plain,
! [U_2729,U_2728,U_2727] :
( c_Orderings_Oord__class_Oless(U_2727,c_Groups_Otimes__class_Otimes(U_2727,U_2729,U_2728),c_Groups_Ozero__class_Ozero(U_2727))
| ~ c_Orderings_Oord__class_Oless(U_2727,U_2729,c_Groups_Ozero__class_Ozero(U_2727))
| ~ c_Orderings_Oord__class_Oless(U_2727,c_Groups_Ozero__class_Ozero(U_2727),U_2728)
| ~ class_Rings_Olinordered__semiring__strict(U_2727) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
cnf(f_941_3,plain,
( c_Orderings_Oord__class_Oless(U_2727,c_Groups_Otimes__class_Otimes(U_2727,U_2729,U_2728),c_Groups_Ozero__class_Ozero(U_2727))
| ~ c_Orderings_Oord__class_Oless(U_2727,U_2729,c_Groups_Ozero__class_Ozero(U_2727))
| ~ c_Orderings_Oord__class_Oless(U_2727,c_Groups_Ozero__class_Ozero(U_2727),U_2728)
| ~ class_Rings_Olinordered__semiring__strict(U_2727) ),
inference(clausify,[status(thm)],[f_941_2]) ).
fof(f_942_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos]) ).
fof(f_942_2,plain,
! [U_2732,U_2731,U_2730] :
( c_Orderings_Oord__class_Oless(U_2730,c_Groups_Ozero__class_Ozero(U_2730),U_2732)
| ~ c_Orderings_Oord__class_Oless(U_2730,c_Groups_Ozero__class_Ozero(U_2730),U_2731)
| ~ c_Orderings_Oord__class_Oless(U_2730,c_Groups_Ozero__class_Ozero(U_2730),c_Groups_Otimes__class_Otimes(U_2730,U_2731,U_2732))
| ~ class_Rings_Olinordered__semiring__strict(U_2730) ),
inference(variable_rename,[status(thm)],[f_942_1]) ).
cnf(f_942_3,plain,
( c_Orderings_Oord__class_Oless(U_2730,c_Groups_Ozero__class_Ozero(U_2730),U_2732)
| ~ c_Orderings_Oord__class_Oless(U_2730,c_Groups_Ozero__class_Ozero(U_2730),U_2731)
| ~ c_Orderings_Oord__class_Oless(U_2730,c_Groups_Ozero__class_Ozero(U_2730),c_Groups_Otimes__class_Otimes(U_2730,U_2731,U_2732))
| ~ class_Rings_Olinordered__semiring__strict(U_2730) ),
inference(clausify,[status(thm)],[f_942_2]) ).
fof(f_943_1,plain,
! [V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2]) ).
fof(f_943_2,plain,
! [U_2735,U_2734,U_2733] :
( c_Orderings_Oord__class_Oless(U_2733,c_Groups_Ozero__class_Ozero(U_2733),U_2734)
| ~ c_Orderings_Oord__class_Oless(U_2733,c_Groups_Ozero__class_Ozero(U_2733),U_2735)
| ~ c_Orderings_Oord__class_Oless(U_2733,c_Groups_Ozero__class_Ozero(U_2733),c_Groups_Otimes__class_Otimes(U_2733,U_2734,U_2735))
| ~ class_Rings_Olinordered__semiring__strict(U_2733) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
cnf(f_943_3,plain,
( c_Orderings_Oord__class_Oless(U_2733,c_Groups_Ozero__class_Ozero(U_2733),U_2734)
| ~ c_Orderings_Oord__class_Oless(U_2733,c_Groups_Ozero__class_Ozero(U_2733),U_2735)
| ~ c_Orderings_Oord__class_Oless(U_2733,c_Groups_Ozero__class_Ozero(U_2733),c_Groups_Otimes__class_Otimes(U_2733,U_2734,U_2735))
| ~ class_Rings_Olinordered__semiring__strict(U_2733) ),
inference(clausify,[status(thm)],[f_943_2]) ).
fof(f_944_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).
fof(f_944_2,plain,
! [U_2739,U_2738,U_2737,U_2736] :
( ( ( c_Orderings_Oord__class_Oless(U_2736,c_Groups_Otimes__class_Otimes(U_2736,U_2737,U_2738),c_Groups_Otimes__class_Otimes(U_2736,U_2737,U_2739))
| ~ c_Orderings_Oord__class_Oless(U_2736,U_2739,U_2738) )
& ( c_Orderings_Oord__class_Oless(U_2736,U_2739,U_2738)
| ~ c_Orderings_Oord__class_Oless(U_2736,c_Groups_Otimes__class_Otimes(U_2736,U_2737,U_2738),c_Groups_Otimes__class_Otimes(U_2736,U_2737,U_2739)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2736,U_2737,c_Groups_Ozero__class_Ozero(U_2736))
| ~ class_Rings_Olinordered__ring__strict(U_2736) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
cnf(f_944_3,plain,
( c_Orderings_Oord__class_Oless(U_2736,U_2739,U_2738)
| ~ c_Orderings_Oord__class_Oless(U_2736,c_Groups_Otimes__class_Otimes(U_2736,U_2737,U_2738),c_Groups_Otimes__class_Otimes(U_2736,U_2737,U_2739))
| ~ c_Orderings_Oord__class_Oless(U_2736,U_2737,c_Groups_Ozero__class_Ozero(U_2736))
| ~ class_Rings_Olinordered__ring__strict(U_2736) ),
inference(clausify,[status(thm)],[f_944_2]) ).
cnf(f_944_4,plain,
( c_Orderings_Oord__class_Oless(U_2736,c_Groups_Otimes__class_Otimes(U_2736,U_2737,U_2738),c_Groups_Otimes__class_Otimes(U_2736,U_2737,U_2739))
| ~ c_Orderings_Oord__class_Oless(U_2736,U_2739,U_2738)
| ~ c_Orderings_Oord__class_Oless(U_2736,U_2737,c_Groups_Ozero__class_Ozero(U_2736))
| ~ class_Rings_Olinordered__ring__strict(U_2736) ),
inference(clausify,[status(thm)],[f_944_2]) ).
fof(f_945_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__neg__pos]) ).
fof(f_945_2,plain,
! [U_2742,U_2741,U_2740] :
( c_Orderings_Oord__class_Oless(U_2740,c_Groups_Otimes__class_Otimes(U_2740,U_2741,U_2742),c_Groups_Ozero__class_Ozero(U_2740))
| ~ c_Orderings_Oord__class_Oless(U_2740,c_Groups_Ozero__class_Ozero(U_2740),U_2742)
| ~ c_Orderings_Oord__class_Oless(U_2740,U_2741,c_Groups_Ozero__class_Ozero(U_2740))
| ~ class_Rings_Olinordered__semiring__strict(U_2740) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
cnf(f_945_3,plain,
( c_Orderings_Oord__class_Oless(U_2740,c_Groups_Otimes__class_Otimes(U_2740,U_2741,U_2742),c_Groups_Ozero__class_Ozero(U_2740))
| ~ c_Orderings_Oord__class_Oless(U_2740,c_Groups_Ozero__class_Ozero(U_2740),U_2742)
| ~ c_Orderings_Oord__class_Oless(U_2740,U_2741,c_Groups_Ozero__class_Ozero(U_2740))
| ~ class_Rings_Olinordered__semiring__strict(U_2740) ),
inference(clausify,[status(thm)],[f_945_2]) ).
fof(f_946_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__neg__neg]) ).
fof(f_946_2,plain,
! [U_2745,U_2744,U_2743] :
( c_Orderings_Oord__class_Oless(U_2743,c_Groups_Ozero__class_Ozero(U_2743),c_Groups_Otimes__class_Otimes(U_2743,U_2744,U_2745))
| ~ c_Orderings_Oord__class_Oless(U_2743,U_2745,c_Groups_Ozero__class_Ozero(U_2743))
| ~ c_Orderings_Oord__class_Oless(U_2743,U_2744,c_Groups_Ozero__class_Ozero(U_2743))
| ~ class_Rings_Olinordered__ring__strict(U_2743) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
cnf(f_946_3,plain,
( c_Orderings_Oord__class_Oless(U_2743,c_Groups_Ozero__class_Ozero(U_2743),c_Groups_Otimes__class_Otimes(U_2743,U_2744,U_2745))
| ~ c_Orderings_Oord__class_Oless(U_2743,U_2745,c_Groups_Ozero__class_Ozero(U_2743))
| ~ c_Orderings_Oord__class_Oless(U_2743,U_2744,c_Groups_Ozero__class_Ozero(U_2743))
| ~ class_Rings_Olinordered__ring__strict(U_2743) ),
inference(clausify,[status(thm)],[f_946_2]) ).
fof(f_947_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono]) ).
fof(f_947_2,plain,
! [U_2749,U_2748,U_2747,U_2746] :
( c_Orderings_Oord__class_Oless(U_2746,c_Groups_Otimes__class_Otimes(U_2746,U_2747,U_2749),c_Groups_Otimes__class_Otimes(U_2746,U_2748,U_2749))
| ~ c_Orderings_Oord__class_Oless(U_2746,c_Groups_Ozero__class_Ozero(U_2746),U_2749)
| ~ c_Orderings_Oord__class_Oless(U_2746,U_2747,U_2748)
| ~ class_Rings_Olinordered__semiring__strict(U_2746) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
cnf(f_947_3,plain,
( c_Orderings_Oord__class_Oless(U_2746,c_Groups_Otimes__class_Otimes(U_2746,U_2747,U_2749),c_Groups_Otimes__class_Otimes(U_2746,U_2748,U_2749))
| ~ c_Orderings_Oord__class_Oless(U_2746,c_Groups_Ozero__class_Ozero(U_2746),U_2749)
| ~ c_Orderings_Oord__class_Oless(U_2746,U_2747,U_2748)
| ~ class_Rings_Olinordered__semiring__strict(U_2746) ),
inference(clausify,[status(thm)],[f_947_2]) ).
fof(f_948_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono]) ).
fof(f_948_2,plain,
! [U_2753,U_2752,U_2751,U_2750] :
( c_Orderings_Oord__class_Oless(U_2750,c_Groups_Otimes__class_Otimes(U_2750,U_2753,U_2751),c_Groups_Otimes__class_Otimes(U_2750,U_2753,U_2752))
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Ozero__class_Ozero(U_2750),U_2753)
| ~ c_Orderings_Oord__class_Oless(U_2750,U_2751,U_2752)
| ~ class_Rings_Olinordered__semiring__strict(U_2750) ),
inference(variable_rename,[status(thm)],[f_948_1]) ).
cnf(f_948_3,plain,
( c_Orderings_Oord__class_Oless(U_2750,c_Groups_Otimes__class_Otimes(U_2750,U_2753,U_2751),c_Groups_Otimes__class_Otimes(U_2750,U_2753,U_2752))
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Ozero__class_Ozero(U_2750),U_2753)
| ~ c_Orderings_Oord__class_Oless(U_2750,U_2751,U_2752)
| ~ class_Rings_Olinordered__semiring__strict(U_2750) ),
inference(clausify,[status(thm)],[f_948_2]) ).
fof(f_949_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__comm__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono]) ).
fof(f_949_2,plain,
! [U_2757,U_2756,U_2755,U_2754] :
( c_Orderings_Oord__class_Oless(U_2754,c_Groups_Otimes__class_Otimes(U_2754,U_2757,U_2755),c_Groups_Otimes__class_Otimes(U_2754,U_2757,U_2756))
| ~ c_Orderings_Oord__class_Oless(U_2754,c_Groups_Ozero__class_Ozero(U_2754),U_2757)
| ~ c_Orderings_Oord__class_Oless(U_2754,U_2755,U_2756)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_2754) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
cnf(f_949_3,plain,
( c_Orderings_Oord__class_Oless(U_2754,c_Groups_Otimes__class_Otimes(U_2754,U_2757,U_2755),c_Groups_Otimes__class_Otimes(U_2754,U_2757,U_2756))
| ~ c_Orderings_Oord__class_Oless(U_2754,c_Groups_Ozero__class_Ozero(U_2754),U_2757)
| ~ c_Orderings_Oord__class_Oless(U_2754,U_2755,U_2756)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_2754) ),
inference(clausify,[status(thm)],[f_949_2]) ).
fof(f_950_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg]) ).
fof(f_950_2,plain,
! [U_2761,U_2760,U_2759,U_2758] :
( c_Orderings_Oord__class_Oless(U_2758,c_Groups_Otimes__class_Otimes(U_2758,U_2760,U_2761),c_Groups_Otimes__class_Otimes(U_2758,U_2759,U_2761))
| ~ c_Orderings_Oord__class_Oless(U_2758,U_2761,c_Groups_Ozero__class_Ozero(U_2758))
| ~ c_Orderings_Oord__class_Oless(U_2758,U_2759,U_2760)
| ~ class_Rings_Olinordered__ring__strict(U_2758) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
cnf(f_950_3,plain,
( c_Orderings_Oord__class_Oless(U_2758,c_Groups_Otimes__class_Otimes(U_2758,U_2760,U_2761),c_Groups_Otimes__class_Otimes(U_2758,U_2759,U_2761))
| ~ c_Orderings_Oord__class_Oless(U_2758,U_2761,c_Groups_Ozero__class_Ozero(U_2758))
| ~ c_Orderings_Oord__class_Oless(U_2758,U_2759,U_2760)
| ~ class_Rings_Olinordered__ring__strict(U_2758) ),
inference(clausify,[status(thm)],[f_950_2]) ).
fof(f_951_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg]) ).
fof(f_951_2,plain,
! [U_2765,U_2764,U_2763,U_2762] :
( c_Orderings_Oord__class_Oless(U_2762,c_Groups_Otimes__class_Otimes(U_2762,U_2765,U_2764),c_Groups_Otimes__class_Otimes(U_2762,U_2765,U_2763))
| ~ c_Orderings_Oord__class_Oless(U_2762,U_2765,c_Groups_Ozero__class_Ozero(U_2762))
| ~ c_Orderings_Oord__class_Oless(U_2762,U_2763,U_2764)
| ~ class_Rings_Olinordered__ring__strict(U_2762) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
cnf(f_951_3,plain,
( c_Orderings_Oord__class_Oless(U_2762,c_Groups_Otimes__class_Otimes(U_2762,U_2765,U_2764),c_Groups_Otimes__class_Otimes(U_2762,U_2765,U_2763))
| ~ c_Orderings_Oord__class_Oless(U_2762,U_2765,c_Groups_Ozero__class_Ozero(U_2762))
| ~ c_Orderings_Oord__class_Oless(U_2762,U_2763,U_2764)
| ~ class_Rings_Olinordered__ring__strict(U_2762) ),
inference(clausify,[status(thm)],[f_951_2]) ).
fof(f_952_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le]) ).
fof(f_952_2,plain,
! [U_2768,U_2767,U_2766] :
( c_Orderings_Oord__class_Oless__eq(U_2766,c_Groups_Otimes__class_Otimes(U_2766,U_2767,U_2768),c_Groups_Ozero__class_Ozero(U_2766))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2766,c_Groups_Ozero__class_Ozero(U_2766),U_2768)
| ~ c_Orderings_Oord__class_Oless__eq(U_2766,U_2767,c_Groups_Ozero__class_Ozero(U_2766)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_2766,U_2768,c_Groups_Ozero__class_Ozero(U_2766))
| ~ c_Orderings_Oord__class_Oless__eq(U_2766,c_Groups_Ozero__class_Ozero(U_2766),U_2767) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_2766) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
cnf(f_952_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2766,U_2768,c_Groups_Ozero__class_Ozero(U_2766))
| ~ c_Orderings_Oord__class_Oless__eq(U_2766,c_Groups_Ozero__class_Ozero(U_2766),U_2767)
| c_Orderings_Oord__class_Oless__eq(U_2766,c_Groups_Otimes__class_Otimes(U_2766,U_2767,U_2768),c_Groups_Ozero__class_Ozero(U_2766))
| ~ class_Rings_Oordered__cancel__semiring(U_2766) ),
inference(clausify,[status(thm)],[f_952_2]) ).
cnf(f_952_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2766,c_Groups_Ozero__class_Ozero(U_2766),U_2768)
| ~ c_Orderings_Oord__class_Oless__eq(U_2766,U_2767,c_Groups_Ozero__class_Ozero(U_2766))
| c_Orderings_Oord__class_Oless__eq(U_2766,c_Groups_Otimes__class_Otimes(U_2766,U_2767,U_2768),c_Groups_Ozero__class_Ozero(U_2766))
| ~ class_Rings_Oordered__cancel__semiring(U_2766) ),
inference(clausify,[status(thm)],[f_952_2]) ).
fof(f_953_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le]) ).
fof(f_953_2,plain,
! [U_2771,U_2770,U_2769] :
( c_Orderings_Oord__class_Oless__eq(U_2769,c_Groups_Ozero__class_Ozero(U_2769),c_Groups_Otimes__class_Otimes(U_2769,U_2770,U_2771))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2769,U_2771,c_Groups_Ozero__class_Ozero(U_2769))
| ~ c_Orderings_Oord__class_Oless__eq(U_2769,U_2770,c_Groups_Ozero__class_Ozero(U_2769)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_2769,c_Groups_Ozero__class_Ozero(U_2769),U_2771)
| ~ c_Orderings_Oord__class_Oless__eq(U_2769,c_Groups_Ozero__class_Ozero(U_2769),U_2770) ) )
| ~ class_Rings_Oordered__ring(U_2769) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
cnf(f_953_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2769,c_Groups_Ozero__class_Ozero(U_2769),U_2771)
| ~ c_Orderings_Oord__class_Oless__eq(U_2769,c_Groups_Ozero__class_Ozero(U_2769),U_2770)
| c_Orderings_Oord__class_Oless__eq(U_2769,c_Groups_Ozero__class_Ozero(U_2769),c_Groups_Otimes__class_Otimes(U_2769,U_2770,U_2771))
| ~ class_Rings_Oordered__ring(U_2769) ),
inference(clausify,[status(thm)],[f_953_2]) ).
cnf(f_953_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2769,U_2771,c_Groups_Ozero__class_Ozero(U_2769))
| ~ c_Orderings_Oord__class_Oless__eq(U_2769,U_2770,c_Groups_Ozero__class_Ozero(U_2769))
| c_Orderings_Oord__class_Oless__eq(U_2769,c_Groups_Ozero__class_Ozero(U_2769),c_Groups_Otimes__class_Otimes(U_2769,U_2770,U_2771))
| ~ class_Rings_Oordered__ring(U_2769) ),
inference(clausify,[status(thm)],[f_953_2]) ).
fof(f_954_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__mono]) ).
fof(f_954_2,plain,
! [U_2776,U_2775,U_2774,U_2773,U_2772] :
( c_Orderings_Oord__class_Oless__eq(U_2772,c_Groups_Otimes__class_Otimes(U_2772,U_2773,U_2775),c_Groups_Otimes__class_Otimes(U_2772,U_2774,U_2776))
| ~ c_Orderings_Oord__class_Oless__eq(U_2772,c_Groups_Ozero__class_Ozero(U_2772),U_2775)
| ~ c_Orderings_Oord__class_Oless__eq(U_2772,c_Groups_Ozero__class_Ozero(U_2772),U_2774)
| ~ c_Orderings_Oord__class_Oless__eq(U_2772,U_2775,U_2776)
| ~ c_Orderings_Oord__class_Oless__eq(U_2772,U_2773,U_2774)
| ~ class_Rings_Oordered__semiring(U_2772) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
cnf(f_954_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2772,c_Groups_Otimes__class_Otimes(U_2772,U_2773,U_2775),c_Groups_Otimes__class_Otimes(U_2772,U_2774,U_2776))
| ~ c_Orderings_Oord__class_Oless__eq(U_2772,c_Groups_Ozero__class_Ozero(U_2772),U_2775)
| ~ c_Orderings_Oord__class_Oless__eq(U_2772,c_Groups_Ozero__class_Ozero(U_2772),U_2774)
| ~ c_Orderings_Oord__class_Oless__eq(U_2772,U_2775,U_2776)
| ~ c_Orderings_Oord__class_Oless__eq(U_2772,U_2773,U_2774)
| ~ class_Rings_Oordered__semiring(U_2772) ),
inference(clausify,[status(thm)],[f_954_2]) ).
fof(f_955_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__mono_H]) ).
fof(f_955_2,plain,
! [U_2781,U_2780,U_2779,U_2778,U_2777] :
( c_Orderings_Oord__class_Oless__eq(U_2777,c_Groups_Otimes__class_Otimes(U_2777,U_2778,U_2780),c_Groups_Otimes__class_Otimes(U_2777,U_2779,U_2781))
| ~ c_Orderings_Oord__class_Oless__eq(U_2777,c_Groups_Ozero__class_Ozero(U_2777),U_2780)
| ~ c_Orderings_Oord__class_Oless__eq(U_2777,c_Groups_Ozero__class_Ozero(U_2777),U_2778)
| ~ c_Orderings_Oord__class_Oless__eq(U_2777,U_2780,U_2781)
| ~ c_Orderings_Oord__class_Oless__eq(U_2777,U_2778,U_2779)
| ~ class_Rings_Oordered__semiring(U_2777) ),
inference(variable_rename,[status(thm)],[f_955_1]) ).
cnf(f_955_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2777,c_Groups_Otimes__class_Otimes(U_2777,U_2778,U_2780),c_Groups_Otimes__class_Otimes(U_2777,U_2779,U_2781))
| ~ c_Orderings_Oord__class_Oless__eq(U_2777,c_Groups_Ozero__class_Ozero(U_2777),U_2780)
| ~ c_Orderings_Oord__class_Oless__eq(U_2777,c_Groups_Ozero__class_Ozero(U_2777),U_2778)
| ~ c_Orderings_Oord__class_Oless__eq(U_2777,U_2780,U_2781)
| ~ c_Orderings_Oord__class_Oless__eq(U_2777,U_2778,U_2779)
| ~ class_Rings_Oordered__semiring(U_2777) ),
inference(clausify,[status(thm)],[f_955_2]) ).
fof(f_956_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg]) ).
fof(f_956_2,plain,
! [U_2785,U_2784,U_2783,U_2782] :
( c_Orderings_Oord__class_Oless__eq(U_2782,c_Groups_Otimes__class_Otimes(U_2782,U_2785,U_2784),c_Groups_Otimes__class_Otimes(U_2782,U_2785,U_2783))
| ~ c_Orderings_Oord__class_Oless__eq(U_2782,U_2785,c_Groups_Ozero__class_Ozero(U_2782))
| ~ c_Orderings_Oord__class_Oless__eq(U_2782,U_2783,U_2784)
| ~ class_Rings_Oordered__ring(U_2782) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
cnf(f_956_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2782,c_Groups_Otimes__class_Otimes(U_2782,U_2785,U_2784),c_Groups_Otimes__class_Otimes(U_2782,U_2785,U_2783))
| ~ c_Orderings_Oord__class_Oless__eq(U_2782,U_2785,c_Groups_Ozero__class_Ozero(U_2782))
| ~ c_Orderings_Oord__class_Oless__eq(U_2782,U_2783,U_2784)
| ~ class_Rings_Oordered__ring(U_2782) ),
inference(clausify,[status(thm)],[f_956_2]) ).
fof(f_957_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg]) ).
fof(f_957_2,plain,
! [U_2789,U_2788,U_2787,U_2786] :
( c_Orderings_Oord__class_Oless__eq(U_2786,c_Groups_Otimes__class_Otimes(U_2786,U_2788,U_2789),c_Groups_Otimes__class_Otimes(U_2786,U_2787,U_2789))
| ~ c_Orderings_Oord__class_Oless__eq(U_2786,U_2789,c_Groups_Ozero__class_Ozero(U_2786))
| ~ c_Orderings_Oord__class_Oless__eq(U_2786,U_2787,U_2788)
| ~ class_Rings_Oordered__ring(U_2786) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
cnf(f_957_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2786,c_Groups_Otimes__class_Otimes(U_2786,U_2788,U_2789),c_Groups_Otimes__class_Otimes(U_2786,U_2787,U_2789))
| ~ c_Orderings_Oord__class_Oless__eq(U_2786,U_2789,c_Groups_Ozero__class_Ozero(U_2786))
| ~ c_Orderings_Oord__class_Oless__eq(U_2786,U_2787,U_2788)
| ~ class_Rings_Oordered__ring(U_2786) ),
inference(clausify,[status(thm)],[f_957_2]) ).
fof(f_958_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__comm__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono]) ).
fof(f_958_2,plain,
! [U_2793,U_2792,U_2791,U_2790] :
( c_Orderings_Oord__class_Oless__eq(U_2790,c_Groups_Otimes__class_Otimes(U_2790,U_2793,U_2791),c_Groups_Otimes__class_Otimes(U_2790,U_2793,U_2792))
| ~ c_Orderings_Oord__class_Oless__eq(U_2790,c_Groups_Ozero__class_Ozero(U_2790),U_2793)
| ~ c_Orderings_Oord__class_Oless__eq(U_2790,U_2791,U_2792)
| ~ class_Rings_Oordered__comm__semiring(U_2790) ),
inference(variable_rename,[status(thm)],[f_958_1]) ).
cnf(f_958_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2790,c_Groups_Otimes__class_Otimes(U_2790,U_2793,U_2791),c_Groups_Otimes__class_Otimes(U_2790,U_2793,U_2792))
| ~ c_Orderings_Oord__class_Oless__eq(U_2790,c_Groups_Ozero__class_Ozero(U_2790),U_2793)
| ~ c_Orderings_Oord__class_Oless__eq(U_2790,U_2791,U_2792)
| ~ class_Rings_Oordered__comm__semiring(U_2790) ),
inference(clausify,[status(thm)],[f_958_2]) ).
fof(f_959_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__mono]) ).
fof(f_959_2,plain,
! [U_2797,U_2796,U_2795,U_2794] :
( c_Orderings_Oord__class_Oless__eq(U_2794,c_Groups_Otimes__class_Otimes(U_2794,U_2797,U_2795),c_Groups_Otimes__class_Otimes(U_2794,U_2797,U_2796))
| ~ c_Orderings_Oord__class_Oless__eq(U_2794,c_Groups_Ozero__class_Ozero(U_2794),U_2797)
| ~ c_Orderings_Oord__class_Oless__eq(U_2794,U_2795,U_2796)
| ~ class_Rings_Oordered__semiring(U_2794) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
cnf(f_959_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2794,c_Groups_Otimes__class_Otimes(U_2794,U_2797,U_2795),c_Groups_Otimes__class_Otimes(U_2794,U_2797,U_2796))
| ~ c_Orderings_Oord__class_Oless__eq(U_2794,c_Groups_Ozero__class_Ozero(U_2794),U_2797)
| ~ c_Orderings_Oord__class_Oless__eq(U_2794,U_2795,U_2796)
| ~ class_Rings_Oordered__semiring(U_2794) ),
inference(clausify,[status(thm)],[f_959_2]) ).
fof(f_960_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__mono]) ).
fof(f_960_2,plain,
! [U_2801,U_2800,U_2799,U_2798] :
( c_Orderings_Oord__class_Oless__eq(U_2798,c_Groups_Otimes__class_Otimes(U_2798,U_2799,U_2801),c_Groups_Otimes__class_Otimes(U_2798,U_2800,U_2801))
| ~ c_Orderings_Oord__class_Oless__eq(U_2798,c_Groups_Ozero__class_Ozero(U_2798),U_2801)
| ~ c_Orderings_Oord__class_Oless__eq(U_2798,U_2799,U_2800)
| ~ class_Rings_Oordered__semiring(U_2798) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
cnf(f_960_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2798,c_Groups_Otimes__class_Otimes(U_2798,U_2799,U_2801),c_Groups_Otimes__class_Otimes(U_2798,U_2800,U_2801))
| ~ c_Orderings_Oord__class_Oless__eq(U_2798,c_Groups_Ozero__class_Ozero(U_2798),U_2801)
| ~ c_Orderings_Oord__class_Oless__eq(U_2798,U_2799,U_2800)
| ~ class_Rings_Oordered__semiring(U_2798) ),
inference(clausify,[status(thm)],[f_960_2]) ).
fof(f_961_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos]) ).
fof(f_961_2,plain,
! [U_2804,U_2803,U_2802] :
( c_Orderings_Oord__class_Oless__eq(U_2802,c_Groups_Ozero__class_Ozero(U_2802),c_Groups_Otimes__class_Otimes(U_2802,U_2803,U_2804))
| ~ c_Orderings_Oord__class_Oless__eq(U_2802,U_2804,c_Groups_Ozero__class_Ozero(U_2802))
| ~ c_Orderings_Oord__class_Oless__eq(U_2802,U_2803,c_Groups_Ozero__class_Ozero(U_2802))
| ~ class_Rings_Oordered__ring(U_2802) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
cnf(f_961_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2802,c_Groups_Ozero__class_Ozero(U_2802),c_Groups_Otimes__class_Otimes(U_2802,U_2803,U_2804))
| ~ c_Orderings_Oord__class_Oless__eq(U_2802,U_2804,c_Groups_Ozero__class_Ozero(U_2802))
| ~ c_Orderings_Oord__class_Oless__eq(U_2802,U_2803,c_Groups_Ozero__class_Ozero(U_2802))
| ~ class_Rings_Oordered__ring(U_2802) ),
inference(clausify,[status(thm)],[f_961_2]) ).
fof(f_962_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg]) ).
fof(f_962_2,plain,
! [U_2807,U_2806,U_2805] :
( c_Orderings_Oord__class_Oless__eq(U_2805,c_Groups_Otimes__class_Otimes(U_2805,U_2806,U_2807),c_Groups_Ozero__class_Ozero(U_2805))
| ~ c_Orderings_Oord__class_Oless__eq(U_2805,c_Groups_Ozero__class_Ozero(U_2805),U_2807)
| ~ c_Orderings_Oord__class_Oless__eq(U_2805,U_2806,c_Groups_Ozero__class_Ozero(U_2805))
| ~ class_Rings_Oordered__cancel__semiring(U_2805) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
cnf(f_962_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2805,c_Groups_Otimes__class_Otimes(U_2805,U_2806,U_2807),c_Groups_Ozero__class_Ozero(U_2805))
| ~ c_Orderings_Oord__class_Oless__eq(U_2805,c_Groups_Ozero__class_Ozero(U_2805),U_2807)
| ~ c_Orderings_Oord__class_Oless__eq(U_2805,U_2806,c_Groups_Ozero__class_Ozero(U_2805))
| ~ class_Rings_Oordered__cancel__semiring(U_2805) ),
inference(clausify,[status(thm)],[f_962_2]) ).
fof(f_963_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2]) ).
fof(f_963_2,plain,
! [U_2810,U_2809,U_2808] :
( c_Orderings_Oord__class_Oless__eq(U_2808,c_Groups_Otimes__class_Otimes(U_2808,U_2810,U_2809),c_Groups_Ozero__class_Ozero(U_2808))
| ~ c_Orderings_Oord__class_Oless__eq(U_2808,U_2810,c_Groups_Ozero__class_Ozero(U_2808))
| ~ c_Orderings_Oord__class_Oless__eq(U_2808,c_Groups_Ozero__class_Ozero(U_2808),U_2809)
| ~ class_Rings_Oordered__cancel__semiring(U_2808) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
cnf(f_963_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2808,c_Groups_Otimes__class_Otimes(U_2808,U_2810,U_2809),c_Groups_Ozero__class_Ozero(U_2808))
| ~ c_Orderings_Oord__class_Oless__eq(U_2808,U_2810,c_Groups_Ozero__class_Ozero(U_2808))
| ~ c_Orderings_Oord__class_Oless__eq(U_2808,c_Groups_Ozero__class_Ozero(U_2808),U_2809)
| ~ class_Rings_Oordered__cancel__semiring(U_2808) ),
inference(clausify,[status(thm)],[f_963_2]) ).
fof(f_964_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos]) ).
fof(f_964_2,plain,
! [U_2813,U_2812,U_2811] :
( c_Orderings_Oord__class_Oless__eq(U_2811,c_Groups_Otimes__class_Otimes(U_2811,U_2812,U_2813),c_Groups_Ozero__class_Ozero(U_2811))
| ~ c_Orderings_Oord__class_Oless__eq(U_2811,U_2813,c_Groups_Ozero__class_Ozero(U_2811))
| ~ c_Orderings_Oord__class_Oless__eq(U_2811,c_Groups_Ozero__class_Ozero(U_2811),U_2812)
| ~ class_Rings_Oordered__cancel__semiring(U_2811) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
cnf(f_964_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2811,c_Groups_Otimes__class_Otimes(U_2811,U_2812,U_2813),c_Groups_Ozero__class_Ozero(U_2811))
| ~ c_Orderings_Oord__class_Oless__eq(U_2811,U_2813,c_Groups_Ozero__class_Ozero(U_2811))
| ~ c_Orderings_Oord__class_Oless__eq(U_2811,c_Groups_Ozero__class_Ozero(U_2811),U_2812)
| ~ class_Rings_Oordered__cancel__semiring(U_2811) ),
inference(clausify,[status(thm)],[f_964_2]) ).
fof(f_965_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg]) ).
fof(f_965_2,plain,
! [U_2816,U_2815,U_2814] :
( c_Orderings_Oord__class_Oless__eq(U_2814,c_Groups_Ozero__class_Ozero(U_2814),c_Groups_Otimes__class_Otimes(U_2814,U_2815,U_2816))
| ~ c_Orderings_Oord__class_Oless__eq(U_2814,c_Groups_Ozero__class_Ozero(U_2814),U_2816)
| ~ c_Orderings_Oord__class_Oless__eq(U_2814,c_Groups_Ozero__class_Ozero(U_2814),U_2815)
| ~ class_Rings_Oordered__cancel__semiring(U_2814) ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
cnf(f_965_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2814,c_Groups_Ozero__class_Ozero(U_2814),c_Groups_Otimes__class_Otimes(U_2814,U_2815,U_2816))
| ~ c_Orderings_Oord__class_Oless__eq(U_2814,c_Groups_Ozero__class_Ozero(U_2814),U_2816)
| ~ c_Orderings_Oord__class_Oless__eq(U_2814,c_Groups_Ozero__class_Ozero(U_2814),U_2815)
| ~ class_Rings_Oordered__cancel__semiring(U_2814) ),
inference(clausify,[status(thm)],[f_965_2]) ).
fof(f_966_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).
fof(f_966_2,plain,
! [U_2819,U_2818,U_2817] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Otimes__class_Otimes(U_2817,U_2818,U_2819),c_Groups_Ozero__class_Ozero(U_2817))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2819)
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,U_2818,c_Groups_Ozero__class_Ozero(U_2817)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_2817,U_2819,c_Groups_Ozero__class_Ozero(U_2817))
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2818) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2819)
& c_Orderings_Oord__class_Oless__eq(U_2817,U_2818,c_Groups_Ozero__class_Ozero(U_2817)) )
| ( c_Orderings_Oord__class_Oless__eq(U_2817,U_2819,c_Groups_Ozero__class_Ozero(U_2817))
& c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2818) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Otimes__class_Otimes(U_2817,U_2818,U_2819),c_Groups_Ozero__class_Ozero(U_2817)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2817) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
cnf(f_966_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2817,U_2818,c_Groups_Ozero__class_Ozero(U_2817))
| c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2818)
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Otimes__class_Otimes(U_2817,U_2818,U_2819),c_Groups_Ozero__class_Ozero(U_2817))
| ~ class_Rings_Olinordered__ring__strict(U_2817) ),
inference(clausify,[status(thm)],[f_966_2]) ).
cnf(f_966_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2819)
| c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2818)
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Otimes__class_Otimes(U_2817,U_2818,U_2819),c_Groups_Ozero__class_Ozero(U_2817))
| ~ class_Rings_Olinordered__ring__strict(U_2817) ),
inference(clausify,[status(thm)],[f_966_2]) ).
cnf(f_966_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2817,U_2818,c_Groups_Ozero__class_Ozero(U_2817))
| c_Orderings_Oord__class_Oless__eq(U_2817,U_2819,c_Groups_Ozero__class_Ozero(U_2817))
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Otimes__class_Otimes(U_2817,U_2818,U_2819),c_Groups_Ozero__class_Ozero(U_2817))
| ~ class_Rings_Olinordered__ring__strict(U_2817) ),
inference(clausify,[status(thm)],[f_966_2]) ).
cnf(f_966_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2819)
| c_Orderings_Oord__class_Oless__eq(U_2817,U_2819,c_Groups_Ozero__class_Ozero(U_2817))
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Otimes__class_Otimes(U_2817,U_2818,U_2819),c_Groups_Ozero__class_Ozero(U_2817))
| ~ class_Rings_Olinordered__ring__strict(U_2817) ),
inference(clausify,[status(thm)],[f_966_2]) ).
cnf(f_966_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2817,U_2819,c_Groups_Ozero__class_Ozero(U_2817))
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2818)
| c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Otimes__class_Otimes(U_2817,U_2818,U_2819),c_Groups_Ozero__class_Ozero(U_2817))
| ~ class_Rings_Olinordered__ring__strict(U_2817) ),
inference(clausify,[status(thm)],[f_966_2]) ).
cnf(f_966_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Ozero__class_Ozero(U_2817),U_2819)
| ~ c_Orderings_Oord__class_Oless__eq(U_2817,U_2818,c_Groups_Ozero__class_Ozero(U_2817))
| c_Orderings_Oord__class_Oless__eq(U_2817,c_Groups_Otimes__class_Otimes(U_2817,U_2818,U_2819),c_Groups_Ozero__class_Ozero(U_2817))
| ~ class_Rings_Olinordered__ring__strict(U_2817) ),
inference(clausify,[status(thm)],[f_966_2]) ).
fof(f_967_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).
fof(f_967_2,plain,
! [U_2822,U_2821,U_2820] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),c_Groups_Otimes__class_Otimes(U_2820,U_2821,U_2822))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2820,U_2822,c_Groups_Ozero__class_Ozero(U_2820))
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,U_2821,c_Groups_Ozero__class_Ozero(U_2820)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2822)
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2821) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_2820,U_2822,c_Groups_Ozero__class_Ozero(U_2820))
& c_Orderings_Oord__class_Oless__eq(U_2820,U_2821,c_Groups_Ozero__class_Ozero(U_2820)) )
| ( c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2822)
& c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2821) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),c_Groups_Otimes__class_Otimes(U_2820,U_2821,U_2822)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2820) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
cnf(f_967_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2820,U_2821,c_Groups_Ozero__class_Ozero(U_2820))
| c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2821)
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),c_Groups_Otimes__class_Otimes(U_2820,U_2821,U_2822))
| ~ class_Rings_Olinordered__ring__strict(U_2820) ),
inference(clausify,[status(thm)],[f_967_2]) ).
cnf(f_967_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2820,U_2822,c_Groups_Ozero__class_Ozero(U_2820))
| c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2821)
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),c_Groups_Otimes__class_Otimes(U_2820,U_2821,U_2822))
| ~ class_Rings_Olinordered__ring__strict(U_2820) ),
inference(clausify,[status(thm)],[f_967_2]) ).
cnf(f_967_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2820,U_2821,c_Groups_Ozero__class_Ozero(U_2820))
| c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2822)
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),c_Groups_Otimes__class_Otimes(U_2820,U_2821,U_2822))
| ~ class_Rings_Olinordered__ring__strict(U_2820) ),
inference(clausify,[status(thm)],[f_967_2]) ).
cnf(f_967_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2820,U_2822,c_Groups_Ozero__class_Ozero(U_2820))
| c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2822)
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),c_Groups_Otimes__class_Otimes(U_2820,U_2821,U_2822))
| ~ class_Rings_Olinordered__ring__strict(U_2820) ),
inference(clausify,[status(thm)],[f_967_2]) ).
cnf(f_967_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2822)
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),U_2821)
| c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),c_Groups_Otimes__class_Otimes(U_2820,U_2821,U_2822))
| ~ class_Rings_Olinordered__ring__strict(U_2820) ),
inference(clausify,[status(thm)],[f_967_2]) ).
cnf(f_967_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2820,U_2822,c_Groups_Ozero__class_Ozero(U_2820))
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,U_2821,c_Groups_Ozero__class_Ozero(U_2820))
| c_Orderings_Oord__class_Oless__eq(U_2820,c_Groups_Ozero__class_Ozero(U_2820),c_Groups_Otimes__class_Otimes(U_2820,U_2821,U_2822))
| ~ class_Rings_Olinordered__ring__strict(U_2820) ),
inference(clausify,[status(thm)],[f_967_2]) ).
fof(f_968_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__square]) ).
fof(f_968_2,plain,
! [U_2824,U_2823] :
( c_Orderings_Oord__class_Oless__eq(U_2823,c_Groups_Ozero__class_Ozero(U_2823),c_Groups_Otimes__class_Otimes(U_2823,U_2824,U_2824))
| ~ class_Rings_Olinordered__ring(U_2823) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
cnf(f_968_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2823,c_Groups_Ozero__class_Ozero(U_2823),c_Groups_Otimes__class_Otimes(U_2823,U_2824,U_2824))
| ~ class_Rings_Olinordered__ring(U_2823) ),
inference(clausify,[status(thm)],[f_968_2]) ).
fof(f_969_1,plain,
! [V_y,V_x] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__mult]) ).
fof(f_969_2,plain,
! [U_2826,U_2825] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2825,U_2826)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2825),c_NthRoot_Osqrt(U_2826)),
inference(variable_rename,[status(thm)],[f_969_1]) ).
cnf(f_969_3,plain,
c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2825,U_2826)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2825),c_NthRoot_Osqrt(U_2826)),
inference(clausify,[status(thm)],[f_969_2]) ).
fof(f_970_1,plain,
! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_a),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r),
inference(fof_nnf,[status(thm)],[fact_real__divide__square__eq]) ).
fof(f_970_2,plain,
! [U_2828,U_2827] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2827,U_2828),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2827,U_2827)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2828,U_2827),
inference(variable_rename,[status(thm)],[f_970_1]) ).
cnf(f_970_3,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2827,U_2828),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2827,U_2827)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2828,U_2827),
inference(clausify,[status(thm)],[f_970_2]) ).
fof(f_971_1,plain,
! [V_z] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z) = V_z,
inference(fof_nnf,[status(thm)],[fact_real__mult__1]) ).
fof(f_971_2,plain,
! [U_2829] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2829) = U_2829,
inference(variable_rename,[status(thm)],[f_971_1]) ).
cnf(f_971_3,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2829) = U_2829,
inference(clausify,[status(thm)],[f_971_2]) ).
fof(f_972_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Groups_Ocomm__monoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral]) ).
fof(f_972_2,plain,
! [U_2831,U_2830] :
( c_Groups_Otimes__class_Otimes(U_2830,U_2831,c_Groups_Oone__class_Oone(U_2830)) = U_2831
| ~ class_Groups_Ocomm__monoid__mult(U_2830) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
cnf(f_972_3,plain,
( c_Groups_Otimes__class_Otimes(U_2830,U_2831,c_Groups_Oone__class_Oone(U_2830)) = U_2831
| ~ class_Groups_Ocomm__monoid__mult(U_2830) ),
inference(clausify,[status(thm)],[f_972_2]) ).
fof(f_973_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__1__right]) ).
fof(f_973_2,plain,
! [U_2833,U_2832] :
( c_Groups_Otimes__class_Otimes(U_2832,U_2833,c_Groups_Oone__class_Oone(U_2832)) = U_2833
| ~ class_Groups_Omonoid__mult(U_2832) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
cnf(f_973_3,plain,
( c_Groups_Otimes__class_Otimes(U_2832,U_2833,c_Groups_Oone__class_Oone(U_2832)) = U_2833
| ~ class_Groups_Omonoid__mult(U_2832) ),
inference(clausify,[status(thm)],[f_973_2]) ).
fof(f_974_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a
| ~ class_Groups_Ocomm__monoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__1]) ).
fof(f_974_2,plain,
! [U_2835,U_2834] :
( c_Groups_Otimes__class_Otimes(U_2834,c_Groups_Oone__class_Oone(U_2834),U_2835) = U_2835
| ~ class_Groups_Ocomm__monoid__mult(U_2834) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
cnf(f_974_3,plain,
( c_Groups_Otimes__class_Otimes(U_2834,c_Groups_Oone__class_Oone(U_2834),U_2835) = U_2835
| ~ class_Groups_Ocomm__monoid__mult(U_2834) ),
inference(clausify,[status(thm)],[f_974_2]) ).
fof(f_975_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__1__left]) ).
fof(f_975_2,plain,
! [U_2837,U_2836] :
( c_Groups_Otimes__class_Otimes(U_2836,c_Groups_Oone__class_Oone(U_2836),U_2837) = U_2837
| ~ class_Groups_Omonoid__mult(U_2836) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
cnf(f_975_3,plain,
( c_Groups_Otimes__class_Otimes(U_2836,c_Groups_Oone__class_Oone(U_2836),U_2837) = U_2837
| ~ class_Groups_Omonoid__mult(U_2836) ),
inference(clausify,[status(thm)],[f_975_2]) ).
fof(f_976_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
fof(f_976_2,plain,
! [U_2839,U_2838] :
( c_Groups_Otimes__class_Otimes(U_2838,c_Groups_Oone__class_Oone(U_2838),U_2839) = U_2839
| ~ class_Rings_Ocomm__semiring__1(U_2838) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
cnf(f_976_3,plain,
( c_Groups_Otimes__class_Otimes(U_2838,c_Groups_Oone__class_Oone(U_2838),U_2839) = U_2839
| ~ class_Rings_Ocomm__semiring__1(U_2838) ),
inference(clausify,[status(thm)],[f_976_2]) ).
fof(f_977_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
fof(f_977_2,plain,
! [U_2841,U_2840] :
( c_Groups_Otimes__class_Otimes(U_2840,U_2841,c_Groups_Oone__class_Oone(U_2840)) = U_2841
| ~ class_Rings_Ocomm__semiring__1(U_2840) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
cnf(f_977_3,plain,
( c_Groups_Otimes__class_Otimes(U_2840,U_2841,c_Groups_Oone__class_Oone(U_2840)) = U_2841
| ~ class_Rings_Ocomm__semiring__1(U_2840) ),
inference(clausify,[status(thm)],[f_977_2]) ).
fof(f_978_1,plain,
! [V_q,V_y,V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_q) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),c_Power_Opower__class_Opower(T_a,V_y,V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_978_2,plain,
! [U_2845,U_2844,U_2843,U_2842] :
( c_Power_Opower__class_Opower(U_2842,c_Groups_Otimes__class_Otimes(U_2842,U_2843,U_2844),U_2845) = c_Groups_Otimes__class_Otimes(U_2842,c_Power_Opower__class_Opower(U_2842,U_2843,U_2845),c_Power_Opower__class_Opower(U_2842,U_2844,U_2845))
| ~ class_Rings_Ocomm__semiring__1(U_2842) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
cnf(f_978_3,plain,
( c_Power_Opower__class_Opower(U_2842,c_Groups_Otimes__class_Otimes(U_2842,U_2843,U_2844),U_2845) = c_Groups_Otimes__class_Otimes(U_2842,c_Power_Opower__class_Opower(U_2842,U_2843,U_2845),c_Power_Opower__class_Opower(U_2842,U_2844,U_2845))
| ~ class_Rings_Ocomm__semiring__1(U_2842) ),
inference(clausify,[status(thm)],[f_978_2]) ).
fof(f_979_1,plain,
! [V_q,V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)) = c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J]) ).
fof(f_979_2,plain,
! [U_2848,U_2847,U_2846] :
( c_Power_Opower__class_Opower(U_2846,U_2847,c_Nat_OSuc(U_2848)) = c_Groups_Otimes__class_Otimes(U_2846,U_2847,c_Power_Opower__class_Opower(U_2846,U_2847,U_2848))
| ~ class_Rings_Ocomm__semiring__1(U_2846) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
cnf(f_979_3,plain,
( c_Power_Opower__class_Opower(U_2846,U_2847,c_Nat_OSuc(U_2848)) = c_Groups_Otimes__class_Otimes(U_2846,U_2847,c_Power_Opower__class_Opower(U_2846,U_2847,U_2848))
| ~ class_Rings_Ocomm__semiring__1(U_2846) ),
inference(clausify,[status(thm)],[f_979_2]) ).
fof(f_980_1,plain,
! [V_q,V_x,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q)) = c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J]) ).
fof(f_980_2,plain,
! [U_2851,U_2850,U_2849] :
( c_Groups_Otimes__class_Otimes(U_2849,U_2850,c_Power_Opower__class_Opower(U_2849,U_2850,U_2851)) = c_Power_Opower__class_Opower(U_2849,U_2850,c_Nat_OSuc(U_2851))
| ~ class_Rings_Ocomm__semiring__1(U_2849) ),
inference(variable_rename,[status(thm)],[f_980_1]) ).
cnf(f_980_3,plain,
( c_Groups_Otimes__class_Otimes(U_2849,U_2850,c_Power_Opower__class_Opower(U_2849,U_2850,U_2851)) = c_Power_Opower__class_Opower(U_2849,U_2850,c_Nat_OSuc(U_2851))
| ~ class_Rings_Ocomm__semiring__1(U_2849) ),
inference(clausify,[status(thm)],[f_980_2]) ).
fof(f_981_1,plain,
! [V_q,V_x,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J]) ).
fof(f_981_2,plain,
! [U_2854,U_2853,U_2852] :
( c_Groups_Otimes__class_Otimes(U_2852,c_Power_Opower__class_Opower(U_2852,U_2853,U_2854),U_2853) = c_Power_Opower__class_Opower(U_2852,U_2853,c_Nat_OSuc(U_2854))
| ~ class_Rings_Ocomm__semiring__1(U_2852) ),
inference(variable_rename,[status(thm)],[f_981_1]) ).
cnf(f_981_3,plain,
( c_Groups_Otimes__class_Otimes(U_2852,c_Power_Opower__class_Opower(U_2852,U_2853,U_2854),U_2853) = c_Power_Opower__class_Opower(U_2852,U_2853,c_Nat_OSuc(U_2854))
| ~ class_Rings_Ocomm__semiring__1(U_2852) ),
inference(clausify,[status(thm)],[f_981_2]) ).
fof(f_982_1,plain,
! [V_n,V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_x,V_n))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_982_2,plain,
! [U_2857,U_2856,U_2855] :
( c_Power_Opower__class_Opower(U_2855,U_2856,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_2857)) = c_Groups_Otimes__class_Otimes(U_2855,c_Power_Opower__class_Opower(U_2855,U_2856,U_2857),c_Power_Opower__class_Opower(U_2855,U_2856,U_2857))
| ~ class_Rings_Ocomm__semiring__1(U_2855) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
cnf(f_982_3,plain,
( c_Power_Opower__class_Opower(U_2855,U_2856,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_2857)) = c_Groups_Otimes__class_Otimes(U_2855,c_Power_Opower__class_Opower(U_2855,U_2856,U_2857),c_Power_Opower__class_Opower(U_2855,U_2856,U_2857))
| ~ class_Rings_Ocomm__semiring__1(U_2855) ),
inference(clausify,[status(thm)],[f_982_2]) ).
fof(f_983_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
fof(f_983_2,plain,
! [U_2859,U_2858] :
( c_Groups_Otimes__class_Otimes(U_2858,c_Groups_Ozero__class_Ozero(U_2858),U_2859) = c_Groups_Ozero__class_Ozero(U_2858)
| ~ class_Rings_Ocomm__semiring__1(U_2858) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
cnf(f_983_3,plain,
( c_Groups_Otimes__class_Otimes(U_2858,c_Groups_Ozero__class_Ozero(U_2858),U_2859) = c_Groups_Ozero__class_Ozero(U_2858)
| ~ class_Rings_Ocomm__semiring__1(U_2858) ),
inference(clausify,[status(thm)],[f_983_2]) ).
fof(f_984_1,plain,
! [V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(f_984_2,plain,
! [U_2861,U_2860] :
( c_Groups_Otimes__class_Otimes(U_2860,U_2861,c_Groups_Ozero__class_Ozero(U_2860)) = c_Groups_Ozero__class_Ozero(U_2860)
| ~ class_Rings_Ocomm__semiring__1(U_2860) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
cnf(f_984_3,plain,
( c_Groups_Otimes__class_Otimes(U_2860,U_2861,c_Groups_Ozero__class_Ozero(U_2860)) = c_Groups_Ozero__class_Ozero(U_2860)
| ~ class_Rings_Ocomm__semiring__1(U_2860) ),
inference(clausify,[status(thm)],[f_984_2]) ).
fof(f_985_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),c_Groups_Otimes__class_Otimes(T_a,V_ly,V_ry))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(f_985_2,plain,
! [U_2866,U_2865,U_2864,U_2863,U_2862] :
( c_Groups_Otimes__class_Otimes(U_2862,c_Groups_Otimes__class_Otimes(U_2862,U_2863,U_2864),c_Groups_Otimes__class_Otimes(U_2862,U_2865,U_2866)) = c_Groups_Otimes__class_Otimes(U_2862,c_Groups_Otimes__class_Otimes(U_2862,U_2863,U_2865),c_Groups_Otimes__class_Otimes(U_2862,U_2864,U_2866))
| ~ class_Rings_Ocomm__semiring__1(U_2862) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
cnf(f_985_3,plain,
( c_Groups_Otimes__class_Otimes(U_2862,c_Groups_Otimes__class_Otimes(U_2862,U_2863,U_2864),c_Groups_Otimes__class_Otimes(U_2862,U_2865,U_2866)) = c_Groups_Otimes__class_Otimes(U_2862,c_Groups_Otimes__class_Otimes(U_2862,U_2863,U_2865),c_Groups_Otimes__class_Otimes(U_2862,U_2864,U_2866))
| ~ class_Rings_Ocomm__semiring__1(U_2862) ),
inference(clausify,[status(thm)],[f_985_2]) ).
fof(f_986_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_ry))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(f_986_2,plain,
! [U_2871,U_2870,U_2869,U_2868,U_2867] :
( c_Groups_Otimes__class_Otimes(U_2867,c_Groups_Otimes__class_Otimes(U_2867,U_2868,U_2869),c_Groups_Otimes__class_Otimes(U_2867,U_2870,U_2871)) = c_Groups_Otimes__class_Otimes(U_2867,U_2870,c_Groups_Otimes__class_Otimes(U_2867,c_Groups_Otimes__class_Otimes(U_2867,U_2868,U_2869),U_2871))
| ~ class_Rings_Ocomm__semiring__1(U_2867) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
cnf(f_986_3,plain,
( c_Groups_Otimes__class_Otimes(U_2867,c_Groups_Otimes__class_Otimes(U_2867,U_2868,U_2869),c_Groups_Otimes__class_Otimes(U_2867,U_2870,U_2871)) = c_Groups_Otimes__class_Otimes(U_2867,U_2870,c_Groups_Otimes__class_Otimes(U_2867,c_Groups_Otimes__class_Otimes(U_2867,U_2868,U_2869),U_2871))
| ~ class_Rings_Ocomm__semiring__1(U_2867) ),
inference(clausify,[status(thm)],[f_986_2]) ).
fof(f_987_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(f_987_2,plain,
! [U_2876,U_2875,U_2874,U_2873,U_2872] :
( c_Groups_Otimes__class_Otimes(U_2872,c_Groups_Otimes__class_Otimes(U_2872,U_2873,U_2874),c_Groups_Otimes__class_Otimes(U_2872,U_2875,U_2876)) = c_Groups_Otimes__class_Otimes(U_2872,U_2873,c_Groups_Otimes__class_Otimes(U_2872,U_2874,c_Groups_Otimes__class_Otimes(U_2872,U_2875,U_2876)))
| ~ class_Rings_Ocomm__semiring__1(U_2872) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
cnf(f_987_3,plain,
( c_Groups_Otimes__class_Otimes(U_2872,c_Groups_Otimes__class_Otimes(U_2872,U_2873,U_2874),c_Groups_Otimes__class_Otimes(U_2872,U_2875,U_2876)) = c_Groups_Otimes__class_Otimes(U_2872,U_2873,c_Groups_Otimes__class_Otimes(U_2872,U_2874,c_Groups_Otimes__class_Otimes(U_2872,U_2875,U_2876)))
| ~ class_Rings_Ocomm__semiring__1(U_2872) ),
inference(clausify,[status(thm)],[f_987_2]) ).
fof(f_988_1,plain,
! [V_rx,V_ly,V_lx,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ly)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(f_988_2,plain,
! [U_2880,U_2879,U_2878,U_2877] :
( c_Groups_Otimes__class_Otimes(U_2877,c_Groups_Otimes__class_Otimes(U_2877,U_2878,U_2879),U_2880) = c_Groups_Otimes__class_Otimes(U_2877,c_Groups_Otimes__class_Otimes(U_2877,U_2878,U_2880),U_2879)
| ~ class_Rings_Ocomm__semiring__1(U_2877) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
cnf(f_988_3,plain,
( c_Groups_Otimes__class_Otimes(U_2877,c_Groups_Otimes__class_Otimes(U_2877,U_2878,U_2879),U_2880) = c_Groups_Otimes__class_Otimes(U_2877,c_Groups_Otimes__class_Otimes(U_2877,U_2878,U_2880),U_2879)
| ~ class_Rings_Ocomm__semiring__1(U_2877) ),
inference(clausify,[status(thm)],[f_988_2]) ).
fof(f_989_1,plain,
! [V_rx,V_ly,V_lx,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,V_rx))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(f_989_2,plain,
! [U_2884,U_2883,U_2882,U_2881] :
( c_Groups_Otimes__class_Otimes(U_2881,c_Groups_Otimes__class_Otimes(U_2881,U_2882,U_2883),U_2884) = c_Groups_Otimes__class_Otimes(U_2881,U_2882,c_Groups_Otimes__class_Otimes(U_2881,U_2883,U_2884))
| ~ class_Rings_Ocomm__semiring__1(U_2881) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
cnf(f_989_3,plain,
( c_Groups_Otimes__class_Otimes(U_2881,c_Groups_Otimes__class_Otimes(U_2881,U_2882,U_2883),U_2884) = c_Groups_Otimes__class_Otimes(U_2881,U_2882,c_Groups_Otimes__class_Otimes(U_2881,U_2883,U_2884))
| ~ class_Rings_Ocomm__semiring__1(U_2881) ),
inference(clausify,[status(thm)],[f_989_2]) ).
fof(f_990_1,plain,
! [V_ry,V_rx,V_lx,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ry)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(f_990_2,plain,
! [U_2888,U_2887,U_2886,U_2885] :
( c_Groups_Otimes__class_Otimes(U_2885,U_2886,c_Groups_Otimes__class_Otimes(U_2885,U_2887,U_2888)) = c_Groups_Otimes__class_Otimes(U_2885,c_Groups_Otimes__class_Otimes(U_2885,U_2886,U_2887),U_2888)
| ~ class_Rings_Ocomm__semiring__1(U_2885) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
cnf(f_990_3,plain,
( c_Groups_Otimes__class_Otimes(U_2885,U_2886,c_Groups_Otimes__class_Otimes(U_2885,U_2887,U_2888)) = c_Groups_Otimes__class_Otimes(U_2885,c_Groups_Otimes__class_Otimes(U_2885,U_2886,U_2887),U_2888)
| ~ class_Rings_Ocomm__semiring__1(U_2885) ),
inference(clausify,[status(thm)],[f_990_2]) ).
fof(f_991_1,plain,
! [V_ry,V_rx,V_lx,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(f_991_2,plain,
! [U_2892,U_2891,U_2890,U_2889] :
( c_Groups_Otimes__class_Otimes(U_2889,U_2890,c_Groups_Otimes__class_Otimes(U_2889,U_2891,U_2892)) = c_Groups_Otimes__class_Otimes(U_2889,U_2891,c_Groups_Otimes__class_Otimes(U_2889,U_2890,U_2892))
| ~ class_Rings_Ocomm__semiring__1(U_2889) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
cnf(f_991_3,plain,
( c_Groups_Otimes__class_Otimes(U_2889,U_2890,c_Groups_Otimes__class_Otimes(U_2889,U_2891,U_2892)) = c_Groups_Otimes__class_Otimes(U_2889,U_2891,c_Groups_Otimes__class_Otimes(U_2889,U_2890,U_2892))
| ~ class_Rings_Ocomm__semiring__1(U_2889) ),
inference(clausify,[status(thm)],[f_991_2]) ).
fof(f_992_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(f_992_2,plain,
! [U_2895,U_2894,U_2893] :
( c_Groups_Otimes__class_Otimes(U_2893,U_2894,U_2895) = c_Groups_Otimes__class_Otimes(U_2893,U_2895,U_2894)
| ~ class_Rings_Ocomm__semiring__1(U_2893) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
cnf(f_992_3,plain,
( c_Groups_Otimes__class_Otimes(U_2893,U_2894,U_2895) = c_Groups_Otimes__class_Otimes(U_2893,U_2895,U_2894)
| ~ class_Rings_Ocomm__semiring__1(U_2893) ),
inference(clausify,[status(thm)],[f_992_2]) ).
fof(f_993_1,plain,
! [V_n,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),V_a)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc2]) ).
fof(f_993_2,plain,
! [U_2898,U_2897,U_2896] :
( c_Power_Opower__class_Opower(U_2896,U_2897,c_Nat_OSuc(U_2898)) = c_Groups_Otimes__class_Otimes(U_2896,c_Power_Opower__class_Opower(U_2896,U_2897,U_2898),U_2897)
| ~ class_Groups_Omonoid__mult(U_2896) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
cnf(f_993_3,plain,
( c_Power_Opower__class_Opower(U_2896,U_2897,c_Nat_OSuc(U_2898)) = c_Groups_Otimes__class_Otimes(U_2896,c_Power_Opower__class_Opower(U_2896,U_2897,U_2898),U_2897)
| ~ class_Groups_Omonoid__mult(U_2896) ),
inference(clausify,[status(thm)],[f_993_2]) ).
fof(f_994_1,plain,
! [V_n,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc]) ).
fof(f_994_2,plain,
! [U_2901,U_2900,U_2899] :
( c_Power_Opower__class_Opower(U_2899,U_2900,c_Nat_OSuc(U_2901)) = c_Groups_Otimes__class_Otimes(U_2899,U_2900,c_Power_Opower__class_Opower(U_2899,U_2900,U_2901))
| ~ class_Power_Opower(U_2899) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
cnf(f_994_3,plain,
( c_Power_Opower__class_Opower(U_2899,U_2900,c_Nat_OSuc(U_2901)) = c_Groups_Otimes__class_Otimes(U_2899,U_2900,c_Power_Opower__class_Opower(U_2899,U_2900,U_2901))
| ~ class_Power_Opower(U_2899) ),
inference(clausify,[status(thm)],[f_994_2]) ).
fof(f_995_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_x)
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J]) ).
fof(f_995_2,plain,
! [U_2903,U_2902] :
( c_Groups_Ouminus__class_Ouminus(U_2902,U_2903) = c_Groups_Otimes__class_Otimes(U_2902,c_Groups_Ouminus__class_Ouminus(U_2902,c_Groups_Oone__class_Oone(U_2902)),U_2903)
| ~ class_Rings_Ocomm__ring__1(U_2902) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
cnf(f_995_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_2902,U_2903) = c_Groups_Otimes__class_Otimes(U_2902,c_Groups_Ouminus__class_Ouminus(U_2902,c_Groups_Oone__class_Oone(U_2902)),U_2903)
| ~ class_Rings_Ocomm__ring__1(U_2902) ),
inference(clausify,[status(thm)],[f_995_2]) ).
fof(f_996_1,plain,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add]) ).
fof(f_996_2,plain,
! [U_2904] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_2904))
| ~ class_Groups_Ocancel__comm__monoid__add(U_2904) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
cnf(f_996_3,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_2904))
| ~ class_Groups_Ocancel__comm__monoid__add(U_2904) ),
inference(clausify,[status(thm)],[f_996_2]) ).
fof(f_997_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add]) ).
cnf(f_997_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_997_1]) ).
fof(f_998_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add]) ).
cnf(f_998_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_998_1]) ).
fof(f_999_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]) ).
cnf(f_999_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_999_1]) ).
fof(f_1000_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]) ).
cnf(f_1000_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1000_1]) ).
fof(f_1001_1,plain,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra]) ).
fof(f_1001_2,plain,
! [U_2906,U_2905] :
( class_Lattices_Oboolean__algebra(tc_fun(U_2906,U_2905))
| ~ class_Lattices_Oboolean__algebra(U_2905) ),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
cnf(f_1001_3,plain,
( class_Lattices_Oboolean__algebra(tc_fun(U_2906,U_2905))
| ~ class_Lattices_Oboolean__algebra(U_2905) ),
inference(clausify,[status(thm)],[f_1001_2]) ).
fof(f_1002_1,plain,
! [T_2,T_1] :
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder]) ).
fof(f_1002_2,plain,
! [U_2908,U_2907] :
( class_Orderings_Opreorder(tc_fun(U_2908,U_2907))
| ~ class_Orderings_Opreorder(U_2907) ),
inference(variable_rename,[status(thm)],[f_1002_1]) ).
cnf(f_1002_3,plain,
( class_Orderings_Opreorder(tc_fun(U_2908,U_2907))
| ~ class_Orderings_Opreorder(U_2907) ),
inference(clausify,[status(thm)],[f_1002_2]) ).
fof(f_1003_1,plain,
! [T_2,T_1] :
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder]) ).
fof(f_1003_2,plain,
! [U_2910,U_2909] :
( class_Orderings_Oorder(tc_fun(U_2910,U_2909))
| ~ class_Orderings_Oorder(U_2909) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
cnf(f_1003_3,plain,
( class_Orderings_Oorder(tc_fun(U_2910,U_2909))
| ~ class_Orderings_Oorder(U_2909) ),
inference(clausify,[status(thm)],[f_1003_2]) ).
fof(f_1004_1,plain,
! [T_2,T_1] :
( class_Orderings_Oord(tc_fun(T_2,T_1))
| ~ class_Orderings_Oord(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord]) ).
fof(f_1004_2,plain,
! [U_2912,U_2911] :
( class_Orderings_Oord(tc_fun(U_2912,U_2911))
| ~ class_Orderings_Oord(U_2911) ),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
cnf(f_1004_3,plain,
( class_Orderings_Oord(tc_fun(U_2912,U_2911))
| ~ class_Orderings_Oord(U_2911) ),
inference(clausify,[status(thm)],[f_1004_2]) ).
fof(f_1005_1,plain,
! [T_2,T_1] :
( class_Groups_Ouminus(tc_fun(T_2,T_1))
| ~ class_Groups_Ouminus(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus]) ).
fof(f_1005_2,plain,
! [U_2914,U_2913] :
( class_Groups_Ouminus(tc_fun(U_2914,U_2913))
| ~ class_Groups_Ouminus(U_2913) ),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
cnf(f_1005_3,plain,
( class_Groups_Ouminus(tc_fun(U_2914,U_2913))
| ~ class_Groups_Ouminus(U_2913) ),
inference(clausify,[status(thm)],[f_1005_2]) ).
fof(f_1006_1,plain,
! [T_2,T_1] :
( class_Groups_Ominus(tc_fun(T_2,T_1))
| ~ class_Groups_Ominus(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus]) ).
fof(f_1006_2,plain,
! [U_2916,U_2915] :
( class_Groups_Ominus(tc_fun(U_2916,U_2915))
| ~ class_Groups_Ominus(U_2915) ),
inference(variable_rename,[status(thm)],[f_1006_1]) ).
cnf(f_1006_3,plain,
( class_Groups_Ominus(tc_fun(U_2916,U_2915))
| ~ class_Groups_Ominus(U_2915) ),
inference(clausify,[status(thm)],[f_1006_2]) ).
fof(f_1007_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(f_1007_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1007_1]) ).
fof(f_1008_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]) ).
cnf(f_1008_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1008_1]) ).
fof(f_1009_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(f_1009_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1009_1]) ).
fof(f_1010_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1010_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1010_1]) ).
fof(f_1011_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).
cnf(f_1011_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1011_1]) ).
fof(f_1012_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1012_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1012_1]) ).
fof(f_1013_1,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]) ).
cnf(f_1013_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1013_1]) ).
fof(f_1014_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1014_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1014_1]) ).
fof(f_1015_1,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).
cnf(f_1015_2,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1015_1]) ).
fof(f_1016_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1016_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1016_1]) ).
fof(f_1017_1,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]) ).
cnf(f_1017_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1017_1]) ).
fof(f_1018_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).
cnf(f_1018_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1018_1]) ).
fof(f_1019_1,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).
cnf(f_1019_2,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1019_1]) ).
fof(f_1020_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).
cnf(f_1020_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1020_1]) ).
fof(f_1021_1,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).
cnf(f_1021_2,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1021_1]) ).
fof(f_1022_1,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).
cnf(f_1022_2,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1022_1]) ).
fof(f_1023_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).
cnf(f_1023_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1023_1]) ).
fof(f_1024_1,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).
cnf(f_1024_2,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1024_1]) ).
fof(f_1025_1,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).
cnf(f_1025_2,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1025_1]) ).
fof(f_1026_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).
cnf(f_1026_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1026_1]) ).
fof(f_1027_1,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).
cnf(f_1027_2,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1027_1]) ).
fof(f_1028_1,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).
cnf(f_1028_2,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1028_1]) ).
fof(f_1029_1,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).
cnf(f_1029_2,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1029_1]) ).
fof(f_1030_1,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).
cnf(f_1030_2,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1030_1]) ).
fof(f_1031_1,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).
cnf(f_1031_2,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1031_1]) ).
fof(f_1032_1,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).
cnf(f_1032_2,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1032_1]) ).
fof(f_1033_1,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).
cnf(f_1033_2,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1033_1]) ).
fof(f_1034_1,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]) ).
cnf(f_1034_2,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1034_1]) ).
fof(f_1035_1,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).
cnf(f_1035_2,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1035_1]) ).
fof(f_1036_1,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).
cnf(f_1036_2,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1036_1]) ).
fof(f_1037_1,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).
cnf(f_1037_2,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1037_1]) ).
fof(f_1038_1,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).
cnf(f_1038_2,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1038_1]) ).
fof(f_1039_1,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).
cnf(f_1039_2,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1039_1]) ).
fof(f_1040_1,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).
cnf(f_1040_2,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1040_1]) ).
fof(f_1041_1,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).
cnf(f_1041_2,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1041_1]) ).
fof(f_1042_1,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).
cnf(f_1042_2,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1042_1]) ).
fof(f_1043_1,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).
cnf(f_1043_2,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1043_1]) ).
fof(f_1044_1,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]) ).
cnf(f_1044_2,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1044_1]) ).
fof(f_1045_1,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).
cnf(f_1045_2,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1045_1]) ).
fof(f_1046_1,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).
cnf(f_1046_2,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1046_1]) ).
fof(f_1047_1,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).
cnf(f_1047_2,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1047_1]) ).
fof(f_1048_1,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]) ).
cnf(f_1048_2,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1048_1]) ).
fof(f_1049_1,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).
cnf(f_1049_2,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1049_1]) ).
fof(f_1050_1,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).
cnf(f_1050_2,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1050_1]) ).
fof(f_1051_1,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).
cnf(f_1051_2,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1051_1]) ).
fof(f_1052_1,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).
cnf(f_1052_2,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1052_1]) ).
fof(f_1053_1,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).
cnf(f_1053_2,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1053_1]) ).
fof(f_1054_1,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).
cnf(f_1054_2,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1054_1]) ).
fof(f_1055_1,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]) ).
cnf(f_1055_2,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1055_1]) ).
fof(f_1056_1,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).
cnf(f_1056_2,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1056_1]) ).
fof(f_1057_1,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ominus]) ).
cnf(f_1057_2,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1057_1]) ).
fof(f_1058_1,plain,
class_Power_Opower(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).
cnf(f_1058_2,plain,
class_Power_Opower(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1058_1]) ).
fof(f_1059_1,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).
cnf(f_1059_2,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1059_1]) ).
fof(f_1060_1,plain,
class_Rings_Oring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).
cnf(f_1060_2,plain,
class_Rings_Oring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1060_1]) ).
fof(f_1061_1,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).
cnf(f_1061_2,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1061_1]) ).
fof(f_1062_1,plain,
class_Int_Onumber(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber]) ).
cnf(f_1062_2,plain,
class_Int_Onumber(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1062_1]) ).
fof(f_1063_1,plain,
class_Groups_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).
cnf(f_1063_2,plain,
class_Groups_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1063_1]) ).
fof(f_1064_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(f_1064_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1064_1]) ).
fof(f_1065_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]) ).
cnf(f_1065_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1065_1]) ).
fof(f_1066_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(f_1066_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1066_1]) ).
fof(f_1067_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1067_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1067_1]) ).
fof(f_1068_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).
cnf(f_1068_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1068_1]) ).
fof(f_1069_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1069_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1069_1]) ).
fof(f_1070_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1070_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1070_1]) ).
fof(f_1071_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1071_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1071_1]) ).
fof(f_1072_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).
cnf(f_1072_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1072_1]) ).
fof(f_1073_1,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).
cnf(f_1073_2,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1073_1]) ).
fof(f_1074_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
cnf(f_1074_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1074_1]) ).
fof(f_1075_1,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).
cnf(f_1075_2,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1075_1]) ).
fof(f_1076_1,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).
cnf(f_1076_2,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1076_1]) ).
fof(f_1077_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).
cnf(f_1077_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1077_1]) ).
fof(f_1078_1,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).
cnf(f_1078_2,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1078_1]) ).
fof(f_1079_1,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).
cnf(f_1079_2,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1079_1]) ).
fof(f_1080_1,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).
cnf(f_1080_2,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1080_1]) ).
fof(f_1081_1,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).
cnf(f_1081_2,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1081_1]) ).
fof(f_1082_1,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
cnf(f_1082_2,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1082_1]) ).
fof(f_1083_1,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]) ).
cnf(f_1083_2,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1083_1]) ).
fof(f_1084_1,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).
cnf(f_1084_2,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1084_1]) ).
fof(f_1085_1,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).
cnf(f_1085_2,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1085_1]) ).
fof(f_1086_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
cnf(f_1086_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1086_1]) ).
fof(f_1087_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
cnf(f_1087_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1087_1]) ).
fof(f_1088_1,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).
cnf(f_1088_2,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1088_1]) ).
fof(f_1089_1,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).
cnf(f_1089_2,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1089_1]) ).
fof(f_1090_1,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]) ).
cnf(f_1090_2,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1090_1]) ).
fof(f_1091_1,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).
cnf(f_1091_2,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1091_1]) ).
fof(f_1092_1,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).
cnf(f_1092_2,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1092_1]) ).
fof(f_1093_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
cnf(f_1093_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1093_1]) ).
fof(f_1094_1,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).
cnf(f_1094_2,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1094_1]) ).
fof(f_1095_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
cnf(f_1095_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1095_1]) ).
fof(f_1096_1,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ominus]) ).
cnf(f_1096_2,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1096_1]) ).
fof(f_1097_1,plain,
class_Power_Opower(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).
cnf(f_1097_2,plain,
class_Power_Opower(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1097_1]) ).
fof(f_1098_1,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).
cnf(f_1098_2,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1098_1]) ).
fof(f_1099_1,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Int_Onumber]) ).
cnf(f_1099_2,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1099_1]) ).
fof(f_1100_1,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).
cnf(f_1100_2,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1100_1]) ).
fof(f_1101_1,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
cnf(f_1101_2,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1101_1]) ).
fof(f_1102_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
cnf(f_1102_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1102_1]) ).
fof(f_1103_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
cnf(f_1103_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1103_1]) ).
fof(f_1104_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
cnf(f_1104_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1104_1]) ).
fof(f_1105_1,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).
cnf(f_1105_2,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1105_1]) ).
fof(f_1106_1,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ominus]) ).
cnf(f_1106_2,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1106_1]) ).
fof(f_1107_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(f_1107_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1107_1]) ).
fof(f_1108_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add]) ).
cnf(f_1108_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1108_1]) ).
fof(f_1109_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(f_1109_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1109_1]) ).
fof(f_1110_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1110_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1110_1]) ).
fof(f_1111_1,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(f_1111_2,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1111_1]) ).
fof(f_1112_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]) ).
cnf(f_1112_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1112_1]) ).
fof(f_1113_1,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).
cnf(f_1113_2,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1113_1]) ).
fof(f_1114_1,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]) ).
cnf(f_1114_2,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1114_1]) ).
fof(f_1115_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]) ).
cnf(f_1115_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1115_1]) ).
fof(f_1116_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1116_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1116_1]) ).
fof(f_1117_1,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(f_1117_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1117_1]) ).
fof(f_1118_1,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(f_1118_2,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1118_1]) ).
fof(f_1119_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1119_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1119_1]) ).
fof(f_1120_1,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
cnf(f_1120_2,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1120_1]) ).
fof(f_1121_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1121_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1121_1]) ).
fof(f_1122_1,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]) ).
cnf(f_1122_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1122_1]) ).
fof(f_1123_1,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]) ).
cnf(f_1123_2,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1123_1]) ).
fof(f_1124_1,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(f_1124_2,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1124_1]) ).
fof(f_1125_1,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
cnf(f_1125_2,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1125_1]) ).
fof(f_1126_1,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__field]) ).
cnf(f_1126_2,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1126_1]) ).
fof(f_1127_1,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__no__zero__divisors]) ).
cnf(f_1127_2,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1127_1]) ).
fof(f_1128_1,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]) ).
cnf(f_1128_2,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1128_1]) ).
fof(f_1129_1,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]) ).
cnf(f_1129_2,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1129_1]) ).
fof(f_1130_1,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).
cnf(f_1130_2,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1130_1]) ).
fof(f_1131_1,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
cnf(f_1131_2,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1131_1]) ).
fof(f_1132_1,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(f_1132_2,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1132_1]) ).
fof(f_1133_1,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]) ).
cnf(f_1133_2,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1133_1]) ).
fof(f_1134_1,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]) ).
cnf(f_1134_2,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1134_1]) ).
fof(f_1135_1,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).
cnf(f_1135_2,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1135_1]) ).
fof(f_1136_1,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
cnf(f_1136_2,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1136_1]) ).
fof(f_1137_1,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]) ).
cnf(f_1137_2,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1137_1]) ).
fof(f_1138_1,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]) ).
cnf(f_1138_2,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1138_1]) ).
fof(f_1139_1,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
cnf(f_1139_2,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1139_1]) ).
fof(f_1140_1,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]) ).
cnf(f_1140_2,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1140_1]) ).
fof(f_1141_1,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(f_1141_2,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1141_1]) ).
fof(f_1142_1,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(f_1142_2,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1142_1]) ).
fof(f_1143_1,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]) ).
cnf(f_1143_2,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1143_1]) ).
fof(f_1144_1,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
cnf(f_1144_2,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1144_1]) ).
fof(f_1145_1,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]) ).
cnf(f_1145_2,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1145_1]) ).
fof(f_1146_1,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).
cnf(f_1146_2,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1146_1]) ).
fof(f_1147_1,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]) ).
cnf(f_1147_2,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1147_1]) ).
fof(f_1148_1,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).
cnf(f_1148_2,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1148_1]) ).
fof(f_1149_1,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(f_1149_2,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1149_1]) ).
fof(f_1150_1,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(f_1150_2,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1150_1]) ).
fof(f_1151_1,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
cnf(f_1151_2,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1151_1]) ).
fof(f_1152_1,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]) ).
cnf(f_1152_2,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1152_1]) ).
fof(f_1153_1,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
cnf(f_1153_2,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1153_1]) ).
fof(f_1154_1,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]) ).
cnf(f_1154_2,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1154_1]) ).
fof(f_1155_1,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]) ).
cnf(f_1155_2,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1155_1]) ).
fof(f_1156_1,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(f_1156_2,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1156_1]) ).
fof(f_1157_1,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]) ).
cnf(f_1157_2,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1157_1]) ).
fof(f_1158_1,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]) ).
cnf(f_1158_2,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1158_1]) ).
fof(f_1159_1,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(f_1159_2,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1159_1]) ).
fof(f_1160_1,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]) ).
cnf(f_1160_2,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1160_1]) ).
fof(f_1161_1,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
cnf(f_1161_2,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1161_1]) ).
fof(f_1162_1,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]) ).
cnf(f_1162_2,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1162_1]) ).
fof(f_1163_1,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]) ).
cnf(f_1163_2,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1163_1]) ).
fof(f_1164_1,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]) ).
cnf(f_1164_2,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1164_1]) ).
fof(f_1165_1,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]) ).
cnf(f_1165_2,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1165_1]) ).
fof(f_1166_1,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]) ).
cnf(f_1166_2,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1166_1]) ).
fof(f_1167_1,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ominus]) ).
cnf(f_1167_2,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1167_1]) ).
fof(f_1168_1,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]) ).
cnf(f_1168_2,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1168_1]) ).
fof(f_1169_1,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Power_Opower]) ).
cnf(f_1169_2,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1169_1]) ).
fof(f_1170_1,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]) ).
cnf(f_1170_2,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1170_1]) ).
fof(f_1171_1,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]) ).
cnf(f_1171_2,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1171_1]) ).
fof(f_1172_1,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]) ).
cnf(f_1172_2,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1172_1]) ).
fof(f_1173_1,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]) ).
cnf(f_1173_2,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1173_1]) ).
fof(f_1174_1,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]) ).
cnf(f_1174_2,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1174_1]) ).
fof(f_1175_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(f_1175_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1175_1]) ).
fof(f_1176_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
cnf(f_1176_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1176_1]) ).
fof(f_1177_1,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero]) ).
cnf(f_1177_2,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1177_1]) ).
fof(f_1178_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).
cnf(f_1178_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1178_1]) ).
fof(f_1179_1,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
cnf(f_1179_2,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1179_1]) ).
fof(f_1180_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1180_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1180_1]) ).
fof(f_1181_1,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors]) ).
cnf(f_1181_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1181_1]) ).
fof(f_1182_1,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(f_1182_2,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1182_1]) ).
fof(f_1183_1,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__field]) ).
cnf(f_1183_2,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1183_1]) ).
fof(f_1184_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]) ).
cnf(f_1184_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1184_1]) ).
fof(f_1185_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).
cnf(f_1185_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1185_1]) ).
fof(f_1186_1,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield__inverse__zero]) ).
cnf(f_1186_2,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1186_1]) ).
fof(f_1187_1,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]) ).
cnf(f_1187_2,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1187_1]) ).
fof(f_1188_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).
cnf(f_1188_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1188_1]) ).
fof(f_1189_1,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).
cnf(f_1189_2,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1189_1]) ).
fof(f_1190_1,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
cnf(f_1190_2,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1190_1]) ).
fof(f_1191_1,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
cnf(f_1191_2,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1191_1]) ).
fof(f_1192_1,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(f_1192_2,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1192_1]) ).
fof(f_1193_1,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
cnf(f_1193_2,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1193_1]) ).
fof(f_1194_1,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]) ).
cnf(f_1194_2,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1194_1]) ).
fof(f_1195_1,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).
cnf(f_1195_2,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1195_1]) ).
fof(f_1196_1,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).
cnf(f_1196_2,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1196_1]) ).
fof(f_1197_1,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).
cnf(f_1197_2,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1197_1]) ).
fof(f_1198_1,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
cnf(f_1198_2,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1198_1]) ).
fof(f_1199_1,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).
cnf(f_1199_2,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1199_1]) ).
fof(f_1200_1,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).
cnf(f_1200_2,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1200_1]) ).
fof(f_1201_1,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__1]) ).
cnf(f_1201_2,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1201_1]) ).
fof(f_1202_1,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).
cnf(f_1202_2,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1202_1]) ).
fof(f_1203_1,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(f_1203_2,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1203_1]) ).
fof(f_1204_1,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).
cnf(f_1204_2,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1204_1]) ).
fof(f_1205_1,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]) ).
cnf(f_1205_2,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1205_1]) ).
fof(f_1206_1,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
cnf(f_1206_2,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1206_1]) ).
fof(f_1207_1,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]) ).
cnf(f_1207_2,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1207_1]) ).
fof(f_1208_1,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).
cnf(f_1208_2,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1208_1]) ).
fof(f_1209_1,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]) ).
cnf(f_1209_2,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1209_1]) ).
fof(f_1210_1,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).
cnf(f_1210_2,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1210_1]) ).
fof(f_1211_1,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]) ).
cnf(f_1211_2,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1211_1]) ).
fof(f_1212_1,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
cnf(f_1212_2,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1212_1]) ).
fof(f_1213_1,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
cnf(f_1213_2,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1213_1]) ).
fof(f_1214_1,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
cnf(f_1214_2,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1214_1]) ).
fof(f_1215_1,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).
cnf(f_1215_2,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1215_1]) ).
fof(f_1216_1,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
cnf(f_1216_2,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1216_1]) ).
fof(f_1217_1,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]) ).
cnf(f_1217_2,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1217_1]) ).
fof(f_1218_1,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).
cnf(f_1218_2,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1218_1]) ).
fof(f_1219_1,plain,
! [T_1] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(f_1219_2,plain,
! [U_2917] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_2917))
| ~ class_Rings_Oidom(U_2917) ),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
cnf(f_1219_3,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_2917))
| ~ class_Rings_Oidom(U_2917) ),
inference(clausify,[status(thm)],[f_1219_2]) ).
fof(f_1220_1,plain,
! [T_1] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add]) ).
fof(f_1220_2,plain,
! [U_2918] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_2918))
| ~ class_Rings_Olinordered__idom(U_2918) ),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
cnf(f_1220_3,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_2918))
| ~ class_Rings_Olinordered__idom(U_2918) ),
inference(clausify,[status(thm)],[f_1220_2]) ).
fof(f_1221_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le]) ).
fof(f_1221_2,plain,
! [U_2919] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_2919))
| ~ class_Rings_Olinordered__idom(U_2919) ),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
cnf(f_1221_3,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_2919))
| ~ class_Rings_Olinordered__idom(U_2919) ),
inference(clausify,[status(thm)],[f_1221_2]) ).
fof(f_1222_1,plain,
! [T_1] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1222_2,plain,
! [U_2920] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_2920))
| ~ class_Rings_Olinordered__idom(U_2920) ),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
cnf(f_1222_3,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_2920))
| ~ class_Rings_Olinordered__idom(U_2920) ),
inference(clausify,[status(thm)],[f_1222_2]) ).
fof(f_1223_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict]) ).
fof(f_1223_2,plain,
! [U_2921] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_2921))
| ~ class_Rings_Olinordered__idom(U_2921) ),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
cnf(f_1223_3,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_2921))
| ~ class_Rings_Olinordered__idom(U_2921) ),
inference(clausify,[status(thm)],[f_1223_2]) ).
fof(f_1224_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1224_2,plain,
! [U_2922] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_2922))
| ~ class_Rings_Olinordered__idom(U_2922) ),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
cnf(f_1224_3,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_2922))
| ~ class_Rings_Olinordered__idom(U_2922) ),
inference(clausify,[status(thm)],[f_1224_2]) ).
fof(f_1225_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs]) ).
fof(f_1225_2,plain,
! [U_2923] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_2923))
| ~ class_Rings_Olinordered__idom(U_2923) ),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
cnf(f_1225_3,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_2923))
| ~ class_Rings_Olinordered__idom(U_2923) ),
inference(clausify,[status(thm)],[f_1225_2]) ).
fof(f_1226_1,plain,
! [T_1] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add]) ).
fof(f_1226_2,plain,
! [U_2924] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_2924))
| ~ class_Rings_Olinordered__idom(U_2924) ),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
cnf(f_1226_3,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_2924))
| ~ class_Rings_Olinordered__idom(U_2924) ),
inference(clausify,[status(thm)],[f_1226_2]) ).
fof(f_1227_1,plain,
! [T_1] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add]) ).
fof(f_1227_2,plain,
! [U_2925] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_2925))
| ~ class_Rings_Olinordered__idom(U_2925) ),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
cnf(f_1227_3,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_2925))
| ~ class_Rings_Olinordered__idom(U_2925) ),
inference(clausify,[status(thm)],[f_1227_2]) ).
fof(f_1228_1,plain,
! [T_1] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1228_2,plain,
! [U_2926] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_2926))
| ~ class_Groups_Ocancel__comm__monoid__add(U_2926) ),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
cnf(f_1228_3,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_2926))
| ~ class_Groups_Ocancel__comm__monoid__add(U_2926) ),
inference(clausify,[status(thm)],[f_1228_2]) ).
fof(f_1229_1,plain,
! [T_1] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors]) ).
fof(f_1229_2,plain,
! [U_2927] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_2927))
| ~ class_Rings_Oidom(U_2927) ),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
cnf(f_1229_3,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_2927))
| ~ class_Rings_Oidom(U_2927) ),
inference(clausify,[status(thm)],[f_1229_2]) ).
fof(f_1230_1,plain,
! [T_1] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring]) ).
fof(f_1230_2,plain,
! [U_2928] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_2928))
| ~ class_Rings_Olinordered__idom(U_2928) ),
inference(variable_rename,[status(thm)],[f_1230_1]) ).
cnf(f_1230_3,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_2928))
| ~ class_Rings_Olinordered__idom(U_2928) ),
inference(clausify,[status(thm)],[f_1230_2]) ).
fof(f_1231_1,plain,
! [T_1] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict]) ).
fof(f_1231_2,plain,
! [U_2929] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_2929))
| ~ class_Rings_Olinordered__idom(U_2929) ),
inference(variable_rename,[status(thm)],[f_1231_1]) ).
cnf(f_1231_3,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_2929))
| ~ class_Rings_Olinordered__idom(U_2929) ),
inference(clausify,[status(thm)],[f_1231_2]) ).
fof(f_1232_1,plain,
! [T_1] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors]) ).
fof(f_1232_2,plain,
! [U_2930] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_2930))
| ~ class_Rings_Oidom(U_2930) ),
inference(variable_rename,[status(thm)],[f_1232_1]) ).
cnf(f_1232_3,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_2930))
| ~ class_Rings_Oidom(U_2930) ),
inference(clausify,[status(thm)],[f_1232_2]) ).
fof(f_1233_1,plain,
! [T_1] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring]) ).
fof(f_1233_2,plain,
! [U_2931] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_2931))
| ~ class_Rings_Olinordered__idom(U_2931) ),
inference(variable_rename,[status(thm)],[f_1233_1]) ).
cnf(f_1233_3,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_2931))
| ~ class_Rings_Olinordered__idom(U_2931) ),
inference(clausify,[status(thm)],[f_1233_2]) ).
fof(f_1234_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add]) ).
fof(f_1234_2,plain,
! [U_2932] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_2932))
| ~ class_Rings_Olinordered__idom(U_2932) ),
inference(variable_rename,[status(thm)],[f_1234_1]) ).
cnf(f_1234_3,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_2932))
| ~ class_Rings_Olinordered__idom(U_2932) ),
inference(clausify,[status(thm)],[f_1234_2]) ).
fof(f_1235_1,plain,
! [T_1] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add]) ).
fof(f_1235_2,plain,
! [U_2933] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_2933))
| ~ class_Groups_Ocancel__comm__monoid__add(U_2933) ),
inference(variable_rename,[status(thm)],[f_1235_1]) ).
cnf(f_1235_3,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_2933))
| ~ class_Groups_Ocancel__comm__monoid__add(U_2933) ),
inference(clausify,[status(thm)],[f_1235_2]) ).
fof(f_1236_1,plain,
! [T_1] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom]) ).
fof(f_1236_2,plain,
! [U_2934] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_2934))
| ~ class_Rings_Olinordered__idom(U_2934) ),
inference(variable_rename,[status(thm)],[f_1236_1]) ).
cnf(f_1236_3,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_2934))
| ~ class_Rings_Olinordered__idom(U_2934) ),
inference(clausify,[status(thm)],[f_1236_2]) ).
fof(f_1237_1,plain,
! [T_1] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult]) ).
fof(f_1237_2,plain,
! [U_2935] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_2935))
| ~ class_Rings_Ocomm__semiring__0(U_2935) ),
inference(variable_rename,[status(thm)],[f_1237_1]) ).
cnf(f_1237_3,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_2935))
| ~ class_Rings_Ocomm__semiring__0(U_2935) ),
inference(clausify,[status(thm)],[f_1237_2]) ).
fof(f_1238_1,plain,
! [T_1] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult]) ).
fof(f_1238_2,plain,
! [U_2936] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_2936))
| ~ class_Rings_Ocomm__semiring__1(U_2936) ),
inference(variable_rename,[status(thm)],[f_1238_1]) ).
cnf(f_1238_3,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_2936))
| ~ class_Rings_Ocomm__semiring__1(U_2936) ),
inference(clausify,[status(thm)],[f_1238_2]) ).
fof(f_1239_1,plain,
! [T_1] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add]) ).
fof(f_1239_2,plain,
! [U_2937] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_2937))
| ~ class_Groups_Ocomm__monoid__add(U_2937) ),
inference(variable_rename,[status(thm)],[f_1239_1]) ).
cnf(f_1239_3,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_2937))
| ~ class_Groups_Ocomm__monoid__add(U_2937) ),
inference(clausify,[status(thm)],[f_1239_2]) ).
fof(f_1240_1,plain,
! [T_1] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring]) ).
fof(f_1240_2,plain,
! [U_2938] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_2938))
| ~ class_Rings_Olinordered__idom(U_2938) ),
inference(variable_rename,[status(thm)],[f_1240_1]) ).
cnf(f_1240_3,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_2938))
| ~ class_Rings_Olinordered__idom(U_2938) ),
inference(clausify,[status(thm)],[f_1240_2]) ).
fof(f_1241_1,plain,
! [T_1] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors]) ).
fof(f_1241_2,plain,
! [U_2939] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_2939))
| ~ class_Rings_Oidom(U_2939) ),
inference(variable_rename,[status(thm)],[f_1241_1]) ).
cnf(f_1241_3,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_2939))
| ~ class_Rings_Oidom(U_2939) ),
inference(clausify,[status(thm)],[f_1241_2]) ).
fof(f_1242_1,plain,
! [T_1] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add]) ).
fof(f_1242_2,plain,
! [U_2940] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_2940))
| ~ class_Groups_Ocomm__monoid__add(U_2940) ),
inference(variable_rename,[status(thm)],[f_1242_1]) ).
cnf(f_1242_3,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_2940))
| ~ class_Groups_Ocomm__monoid__add(U_2940) ),
inference(clausify,[status(thm)],[f_1242_2]) ).
fof(f_1243_1,plain,
! [T_1] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring]) ).
fof(f_1243_2,plain,
! [U_2941] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_2941))
| ~ class_Rings_Olinordered__idom(U_2941) ),
inference(variable_rename,[status(thm)],[f_1243_1]) ).
cnf(f_1243_3,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_2941))
| ~ class_Rings_Olinordered__idom(U_2941) ),
inference(clausify,[status(thm)],[f_1243_2]) ).
fof(f_1244_1,plain,
! [T_1] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom]) ).
fof(f_1244_2,plain,
! [U_2942] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_2942))
| ~ class_Rings_Olinordered__idom(U_2942) ),
inference(variable_rename,[status(thm)],[f_1244_1]) ).
cnf(f_1244_3,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_2942))
| ~ class_Rings_Olinordered__idom(U_2942) ),
inference(clausify,[status(thm)],[f_1244_2]) ).
fof(f_1245_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1]) ).
fof(f_1245_2,plain,
! [U_2943] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_2943))
| ~ class_Rings_Ocomm__semiring__1(U_2943) ),
inference(variable_rename,[status(thm)],[f_1245_1]) ).
cnf(f_1245_3,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_2943))
| ~ class_Rings_Ocomm__semiring__1(U_2943) ),
inference(clausify,[status(thm)],[f_1245_2]) ).
fof(f_1246_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0]) ).
fof(f_1246_2,plain,
! [U_2944] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_2944))
| ~ class_Rings_Ocomm__semiring__0(U_2944) ),
inference(variable_rename,[status(thm)],[f_1246_1]) ).
cnf(f_1246_3,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_2944))
| ~ class_Rings_Ocomm__semiring__0(U_2944) ),
inference(clausify,[status(thm)],[f_1246_2]) ).
fof(f_1247_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring]) ).
fof(f_1247_2,plain,
! [U_2945] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_2945))
| ~ class_Rings_Ocomm__semiring__0(U_2945) ),
inference(variable_rename,[status(thm)],[f_1247_1]) ).
cnf(f_1247_3,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_2945))
| ~ class_Rings_Ocomm__semiring__0(U_2945) ),
inference(clausify,[status(thm)],[f_1247_2]) ).
fof(f_1248_1,plain,
! [T_1] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add]) ).
fof(f_1248_2,plain,
! [U_2946] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_2946))
| ~ class_Groups_Oab__group__add(U_2946) ),
inference(variable_rename,[status(thm)],[f_1248_1]) ).
cnf(f_1248_3,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_2946))
| ~ class_Groups_Oab__group__add(U_2946) ),
inference(clausify,[status(thm)],[f_1248_2]) ).
fof(f_1249_1,plain,
! [T_1] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one]) ).
fof(f_1249_2,plain,
! [U_2947] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_2947))
| ~ class_Rings_Ocomm__semiring__1(U_2947) ),
inference(variable_rename,[status(thm)],[f_1249_1]) ).
cnf(f_1249_3,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_2947))
| ~ class_Rings_Ocomm__semiring__1(U_2947) ),
inference(clausify,[status(thm)],[f_1249_2]) ).
fof(f_1250_1,plain,
! [T_1] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring]) ).
fof(f_1250_2,plain,
! [U_2948] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_2948))
| ~ class_Rings_Olinordered__idom(U_2948) ),
inference(variable_rename,[status(thm)],[f_1250_1]) ).
cnf(f_1250_3,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_2948))
| ~ class_Rings_Olinordered__idom(U_2948) ),
inference(clausify,[status(thm)],[f_1250_2]) ).
fof(f_1251_1,plain,
! [T_1] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder]) ).
fof(f_1251_2,plain,
! [U_2949] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_2949))
| ~ class_Rings_Olinordered__idom(U_2949) ),
inference(variable_rename,[status(thm)],[f_1251_1]) ).
cnf(f_1251_3,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_2949))
| ~ class_Rings_Olinordered__idom(U_2949) ),
inference(clausify,[status(thm)],[f_1251_2]) ).
fof(f_1252_1,plain,
! [T_1] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder]) ).
fof(f_1252_2,plain,
! [U_2950] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_2950))
| ~ class_Rings_Olinordered__idom(U_2950) ),
inference(variable_rename,[status(thm)],[f_1252_1]) ).
cnf(f_1252_3,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_2950))
| ~ class_Rings_Olinordered__idom(U_2950) ),
inference(clausify,[status(thm)],[f_1252_2]) ).
fof(f_1253_1,plain,
! [T_1] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult]) ).
fof(f_1253_2,plain,
! [U_2951] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_2951))
| ~ class_Rings_Ocomm__semiring__1(U_2951) ),
inference(variable_rename,[status(thm)],[f_1253_1]) ).
cnf(f_1253_3,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_2951))
| ~ class_Rings_Ocomm__semiring__1(U_2951) ),
inference(clausify,[status(thm)],[f_1253_2]) ).
fof(f_1254_1,plain,
! [T_1] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1]) ).
fof(f_1254_2,plain,
! [U_2952] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_2952))
| ~ class_Rings_Ocomm__ring__1(U_2952) ),
inference(variable_rename,[status(thm)],[f_1254_1]) ).
cnf(f_1254_3,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_2952))
| ~ class_Rings_Ocomm__ring__1(U_2952) ),
inference(clausify,[status(thm)],[f_1254_2]) ).
fof(f_1255_1,plain,
! [T_1] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add]) ).
fof(f_1255_2,plain,
! [U_2953] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_2953))
| ~ class_Groups_Ocomm__monoid__add(U_2953) ),
inference(variable_rename,[status(thm)],[f_1255_1]) ).
cnf(f_1255_3,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_2953))
| ~ class_Groups_Ocomm__monoid__add(U_2953) ),
inference(clausify,[status(thm)],[f_1255_2]) ).
fof(f_1256_1,plain,
! [T_1] :
( class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__1]) ).
fof(f_1256_2,plain,
! [U_2954] :
( class_Rings_Osemiring__1(tc_Polynomial_Opoly(U_2954))
| ~ class_Rings_Ocomm__semiring__1(U_2954) ),
inference(variable_rename,[status(thm)],[f_1256_1]) ).
cnf(f_1256_3,plain,
( class_Rings_Osemiring__1(tc_Polynomial_Opoly(U_2954))
| ~ class_Rings_Ocomm__semiring__1(U_2954) ),
inference(clausify,[status(thm)],[f_1256_2]) ).
fof(f_1257_1,plain,
! [T_1] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0]) ).
fof(f_1257_2,plain,
! [U_2955] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_2955))
| ~ class_Rings_Ocomm__semiring__0(U_2955) ),
inference(variable_rename,[status(thm)],[f_1257_1]) ).
cnf(f_1257_3,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_2955))
| ~ class_Rings_Ocomm__semiring__0(U_2955) ),
inference(clausify,[status(thm)],[f_1257_2]) ).
fof(f_1258_1,plain,
! [T_1] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add]) ).
fof(f_1258_2,plain,
! [U_2956] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_2956))
| ~ class_Groups_Oab__group__add(U_2956) ),
inference(variable_rename,[status(thm)],[f_1258_1]) ).
cnf(f_1258_3,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_2956))
| ~ class_Groups_Oab__group__add(U_2956) ),
inference(clausify,[status(thm)],[f_1258_2]) ).
fof(f_1259_1,plain,
! [T_1] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero]) ).
fof(f_1259_2,plain,
! [U_2957] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_2957))
| ~ class_Rings_Ocomm__semiring__0(U_2957) ),
inference(variable_rename,[status(thm)],[f_1259_1]) ).
cnf(f_1259_3,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_2957))
| ~ class_Rings_Ocomm__semiring__0(U_2957) ),
inference(clausify,[status(thm)],[f_1259_2]) ).
fof(f_1260_1,plain,
! [T_1] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring]) ).
fof(f_1260_2,plain,
! [U_2958] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_2958))
| ~ class_Rings_Ocomm__ring(U_2958) ),
inference(variable_rename,[status(thm)],[f_1260_1]) ).
cnf(f_1260_3,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_2958))
| ~ class_Rings_Ocomm__ring(U_2958) ),
inference(clausify,[status(thm)],[f_1260_2]) ).
fof(f_1261_1,plain,
! [T_1] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder]) ).
fof(f_1261_2,plain,
! [U_2959] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_2959))
| ~ class_Rings_Olinordered__idom(U_2959) ),
inference(variable_rename,[status(thm)],[f_1261_1]) ).
cnf(f_1261_3,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_2959))
| ~ class_Rings_Olinordered__idom(U_2959) ),
inference(clausify,[status(thm)],[f_1261_2]) ).
fof(f_1262_1,plain,
! [T_1] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0]) ).
fof(f_1262_2,plain,
! [U_2960] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_2960))
| ~ class_Rings_Olinordered__idom(U_2960) ),
inference(variable_rename,[status(thm)],[f_1262_1]) ).
cnf(f_1262_3,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_2960))
| ~ class_Rings_Olinordered__idom(U_2960) ),
inference(clausify,[status(thm)],[f_1262_2]) ).
fof(f_1263_1,plain,
! [T_1] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Onumber__ring]) ).
fof(f_1263_2,plain,
! [U_2961] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(U_2961))
| ~ class_Rings_Ocomm__ring__1(U_2961) ),
inference(variable_rename,[status(thm)],[f_1263_1]) ).
cnf(f_1263_3,plain,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(U_2961))
| ~ class_Rings_Ocomm__ring__1(U_2961) ),
inference(clausify,[status(thm)],[f_1263_2]) ).
fof(f_1264_1,plain,
! [T_1] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring]) ).
fof(f_1264_2,plain,
! [U_2962] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_2962))
| ~ class_Rings_Ocomm__semiring__0(U_2962) ),
inference(variable_rename,[status(thm)],[f_1264_1]) ).
cnf(f_1264_3,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_2962))
| ~ class_Rings_Ocomm__semiring__0(U_2962) ),
inference(clausify,[status(thm)],[f_1264_2]) ).
fof(f_1265_1,plain,
! [T_1] :
( class_Orderings_Oord(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord]) ).
fof(f_1265_2,plain,
! [U_2963] :
( class_Orderings_Oord(tc_Polynomial_Opoly(U_2963))
| ~ class_Rings_Olinordered__idom(U_2963) ),
inference(variable_rename,[status(thm)],[f_1265_1]) ).
cnf(f_1265_3,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(U_2963))
| ~ class_Rings_Olinordered__idom(U_2963) ),
inference(clausify,[status(thm)],[f_1265_2]) ).
fof(f_1266_1,plain,
! [T_1] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus]) ).
fof(f_1266_2,plain,
! [U_2964] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_2964))
| ~ class_Groups_Oab__group__add(U_2964) ),
inference(variable_rename,[status(thm)],[f_1266_1]) ).
cnf(f_1266_3,plain,
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_2964))
| ~ class_Groups_Oab__group__add(U_2964) ),
inference(clausify,[status(thm)],[f_1266_2]) ).
fof(f_1267_1,plain,
! [T_1] :
( class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oabs__if]) ).
fof(f_1267_2,plain,
! [U_2965] :
( class_Groups_Oabs__if(tc_Polynomial_Opoly(U_2965))
| ~ class_Rings_Olinordered__idom(U_2965) ),
inference(variable_rename,[status(thm)],[f_1267_1]) ).
cnf(f_1267_3,plain,
( class_Groups_Oabs__if(tc_Polynomial_Opoly(U_2965))
| ~ class_Rings_Olinordered__idom(U_2965) ),
inference(clausify,[status(thm)],[f_1267_2]) ).
fof(f_1268_1,plain,
! [T_1] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1]) ).
fof(f_1268_2,plain,
! [U_2966] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_2966))
| ~ class_Rings_Ocomm__ring__1(U_2966) ),
inference(variable_rename,[status(thm)],[f_1268_1]) ).
cnf(f_1268_3,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_2966))
| ~ class_Rings_Ocomm__ring__1(U_2966) ),
inference(clausify,[status(thm)],[f_1268_2]) ).
fof(f_1269_1,plain,
! [T_1] :
( class_Groups_Ominus(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus]) ).
fof(f_1269_2,plain,
! [U_2967] :
( class_Groups_Ominus(tc_Polynomial_Opoly(U_2967))
| ~ class_Groups_Oab__group__add(U_2967) ),
inference(variable_rename,[status(thm)],[f_1269_1]) ).
cnf(f_1269_3,plain,
( class_Groups_Ominus(tc_Polynomial_Opoly(U_2967))
| ~ class_Groups_Oab__group__add(U_2967) ),
inference(clausify,[status(thm)],[f_1269_2]) ).
fof(f_1270_1,plain,
! [T_1] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower]) ).
fof(f_1270_2,plain,
! [U_2968] :
( class_Power_Opower(tc_Polynomial_Opoly(U_2968))
| ~ class_Rings_Ocomm__semiring__1(U_2968) ),
inference(variable_rename,[status(thm)],[f_1270_1]) ).
cnf(f_1270_3,plain,
( class_Power_Opower(tc_Polynomial_Opoly(U_2968))
| ~ class_Rings_Ocomm__semiring__1(U_2968) ),
inference(clausify,[status(thm)],[f_1270_2]) ).
fof(f_1271_1,plain,
! [T_1] :
( class_Groups_Ozero(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ozero(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero]) ).
fof(f_1271_2,plain,
! [U_2969] :
( class_Groups_Ozero(tc_Polynomial_Opoly(U_2969))
| ~ class_Groups_Ozero(U_2969) ),
inference(variable_rename,[status(thm)],[f_1271_1]) ).
cnf(f_1271_3,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(U_2969))
| ~ class_Groups_Ozero(U_2969) ),
inference(clausify,[status(thm)],[f_1271_2]) ).
fof(f_1272_1,plain,
! [T_1] :
( class_Rings_Oring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring]) ).
fof(f_1272_2,plain,
! [U_2970] :
( class_Rings_Oring(tc_Polynomial_Opoly(U_2970))
| ~ class_Rings_Ocomm__ring(U_2970) ),
inference(variable_rename,[status(thm)],[f_1272_1]) ).
cnf(f_1272_3,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(U_2970))
| ~ class_Rings_Ocomm__ring(U_2970) ),
inference(clausify,[status(thm)],[f_1272_2]) ).
fof(f_1273_1,plain,
! [T_1] :
( class_Rings_Oidom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom]) ).
fof(f_1273_2,plain,
! [U_2971] :
( class_Rings_Oidom(tc_Polynomial_Opoly(U_2971))
| ~ class_Rings_Oidom(U_2971) ),
inference(variable_rename,[status(thm)],[f_1273_1]) ).
cnf(f_1273_3,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(U_2971))
| ~ class_Rings_Oidom(U_2971) ),
inference(clausify,[status(thm)],[f_1273_2]) ).
fof(f_1274_1,plain,
! [T_1] :
( class_Int_Onumber(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Onumber]) ).
fof(f_1274_2,plain,
! [U_2972] :
( class_Int_Onumber(tc_Polynomial_Opoly(U_2972))
| ~ class_Rings_Ocomm__ring__1(U_2972) ),
inference(variable_rename,[status(thm)],[f_1274_1]) ).
cnf(f_1274_3,plain,
( class_Int_Onumber(tc_Polynomial_Opoly(U_2972))
| ~ class_Rings_Ocomm__ring__1(U_2972) ),
inference(clausify,[status(thm)],[f_1274_2]) ).
fof(f_1275_1,plain,
! [T_1] :
( class_Groups_Oone(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone]) ).
fof(f_1275_2,plain,
! [U_2973] :
( class_Groups_Oone(tc_Polynomial_Opoly(U_2973))
| ~ class_Rings_Ocomm__semiring__1(U_2973) ),
inference(variable_rename,[status(thm)],[f_1275_1]) ).
cnf(f_1275_3,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(U_2973))
| ~ class_Rings_Ocomm__semiring__1(U_2973) ),
inference(clausify,[status(thm)],[f_1275_2]) ).
fof(f_1276_1,plain,
! [B_d] :
( v_thesis____
| ? [B_w] :
( ~ 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_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_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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ),
inference(fof_nnf,[status(thm)],[conj_0]) ).
fof(f_1276_2,plain,
! [U_2975] :
( v_thesis____
| ? [U_2974] :
( ~ 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),U_2974),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2974,v_z____)),U_2975)
& 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,U_2974,v_z____))) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2975) ),
inference(variable_rename,[status(thm)],[f_1276_1]) ).
fof(f_1276_3,plain,
! [U_2975] :
( v_thesis____
| ( ~ 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),sK42(U_2975)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,sK42(U_2975),v_z____)),U_2975)
& 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,sK42(U_2975),v_z____))) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2975) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2974,sK42(U_2975))],[f_1276_2]) ).
cnf(f_1276_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,sK42(U_2975),v_z____)))
| v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2975) ),
inference(clausify,[status(thm)],[f_1276_3]) ).
cnf(f_1276_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,sK42(U_2975),v_z____)),U_2975)
| v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2975) ),
inference(clausify,[status(thm)],[f_1276_3]) ).
cnf(f_1276_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK42(U_2975)),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),U_2975) ),
inference(clausify,[status(thm)],[f_1276_3]) ).
fof(f_1277_1,negated_conjecture,
~ v_thesis____,
inference(negate,[status(cth)],[conj_1]) ).
fof(f_1277_2,negated_conjecture,
~ v_thesis____,
inference(definitional_conversion,[status(esa)],[f_1277_1]) ).
cnf(f_1277_3,negated_conjecture,
~ v_thesis____,
inference(clausify,[status(thm)],[f_1277_2]) ).
cnf(f_108_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_108_6]) ).
cnf(f_222_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_222_4]) ).
cnf(f_222_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_222_5]) ).
cnf(f_222_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_222_6]) ).
cnf(f_222_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_222_7]) ).
cnf(f_222_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_222_8]) ).
cnf(f_222_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_222_9]) ).
cnf(f_222_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_222_10]) ).
cnf(f_888_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_888_5]) ).
cnf(f_889_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_889_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_Groups_Ozero__class_Ozero(Eq_x_0) = c_Groups_Ozero__class_Ozero(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( c_Polynomial_Opoly(Eq_x_0,Eq_x_1) = c_Polynomial_Opoly(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( c_RealVector_Onorm__class_Onorm(Eq_x_0,Eq_x_1) = c_RealVector_Onorm__class_Onorm(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_Groups_Ouminus__class_Ouminus(Eq_x_0,Eq_x_1) = c_Groups_Ouminus__class_Ouminus(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_Groups_Ominus__class_Ominus(Eq_x_0,Eq_x_1,Eq_x_2) = c_Groups_Ominus__class_Ominus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( c_Groups_Oabs__class_Oabs(Eq_x_0,Eq_x_1) = c_Groups_Oabs__class_Oabs(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( c_Int_OBit1(Eq_x_0) = c_Int_OBit1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_Int_OBit0(Eq_x_0) = c_Int_OBit0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_Int_Onumber__class_Onumber__of(Eq_x_0,Eq_x_1) = c_Int_Onumber__class_Onumber__of(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_Rings_Oinverse__class_Odivide(Eq_x_0,Eq_x_1,Eq_x_2) = c_Rings_Oinverse__class_Odivide(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( v_g____(Eq_x_0) = v_g____(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( tc_Polynomial_Opoly(Eq_x_0) = tc_Polynomial_Opoly(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(Eq_x_0,Eq_x_1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Polynomial_Oorder(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Oorder(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_Groups_Oone__class_Oone(Eq_x_0) = c_Groups_Oone__class_Oone(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( c_Nat__Transfer_Otsub(Eq_x_0,Eq_x_1) = c_Nat__Transfer_Otsub(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_Power_Opower__class_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower__class_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( c_Nat_OSuc(Eq_x_0) = c_Nat_OSuc(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( c_RealDef_Oreal(Eq_x_0,Eq_x_1) = c_RealDef_Oreal(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_Groups_Oplus__class_Oplus(Eq_x_0,Eq_x_1,Eq_x_2) = c_Groups_Oplus__class_Oplus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( c_NthRoot_Osqrt(Eq_x_0) = c_NthRoot_Osqrt(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(Eq_x_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( c_RComplete_Onatceiling(Eq_x_0) = c_RComplete_Onatceiling(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_Groups_Otimes__class_Otimes(Eq_x_0,Eq_x_1,Eq_x_2) = c_Groups_Otimes__class_Otimes(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK24(Eq_x_0,Eq_x_1) = sK24(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK26(Eq_x_0,Eq_x_1) = sK26(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( sK29(Eq_x_0,Eq_x_1,Eq_x_2) = sK29(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK33(Eq_x_0) = sK33(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK34(Eq_x_0) = sK34(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK36(Eq_x_0) = sK36(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK42(Eq_x_0) = sK42(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( c_SEQ_Osubseq(Eq_y_0)
| ~ c_SEQ_Osubseq(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_65,axiom,
( c_Orderings_Oord__class_Oless(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Orderings_Oord__class_Oless(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( class_Fields_Olinordered__field__inverse__zero(Eq_y_0)
| ~ class_Fields_Olinordered__field__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( class_Int_Onumber__ring(Eq_y_0)
| ~ class_Int_Onumber__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( class_Rings_Olinordered__idom(Eq_y_0)
| ~ class_Rings_Olinordered__idom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( class_RealVector_Oreal__normed__algebra__1(Eq_y_0)
| ~ class_RealVector_Oreal__normed__algebra__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,axiom,
( class_RealVector_Oreal__normed__field(Eq_y_0)
| ~ class_RealVector_Oreal__normed__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_71,axiom,
( class_Fields_Ofield(Eq_y_0)
| ~ class_Fields_Ofield(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,axiom,
( class_RealVector_Oreal__normed__vector(Eq_y_0)
| ~ class_RealVector_Oreal__normed__vector(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_73,axiom,
( class_Fields_Ofield__inverse__zero(Eq_y_0)
| ~ class_Fields_Ofield__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_74,axiom,
( class_Int_Oring__char__0(Eq_y_0)
| ~ class_Int_Oring__char__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_75,axiom,
( class_Int_Onumber(Eq_y_0)
| ~ class_Int_Onumber(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_76,axiom,
( class_Fields_Olinordered__field(Eq_y_0)
| ~ class_Fields_Olinordered__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_77,axiom,
( class_Groups_Oordered__ab__group__add__abs(Eq_y_0)
| ~ class_Groups_Oordered__ab__group__add__abs(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_78,axiom,
( class_Groups_Oabs__if(Eq_y_0)
| ~ class_Groups_Oabs__if(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_79,axiom,
( class_Rings_Odivision__ring(Eq_y_0)
| ~ class_Rings_Odivision__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_80,axiom,
( class_Groups_Ogroup__add(Eq_y_0)
| ~ class_Groups_Ogroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_81,axiom,
( class_Groups_Olinordered__ab__group__add(Eq_y_0)
| ~ class_Groups_Olinordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_82,axiom,
( class_Groups_Ozero(Eq_y_0)
| ~ class_Groups_Ozero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,axiom,
( class_Groups_Oab__group__add(Eq_y_0)
| ~ class_Groups_Oab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_84,axiom,
( class_Groups_Oordered__ab__group__add(Eq_y_0)
| ~ class_Groups_Oordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_85,axiom,
( class_Rings_Odivision__ring__inverse__zero(Eq_y_0)
| ~ class_Rings_Odivision__ring__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_86,axiom,
( c_Orderings_Oord__class_Oless__eq(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_87,axiom,
( class_Rings_Ocomm__ring(Eq_y_0)
| ~ class_Rings_Ocomm__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_88,axiom,
( class_Rings_Ocomm__semiring__0(Eq_y_0)
| ~ class_Rings_Ocomm__semiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( class_Orderings_Olinorder(Eq_y_0)
| ~ class_Orderings_Olinorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_90,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_91,axiom,
( class_Rings_Oidom(Eq_y_0)
| ~ class_Rings_Oidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_92,axiom,
( class_Orderings_Opreorder(Eq_y_0)
| ~ class_Orderings_Opreorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_93,axiom,
( class_Orderings_Oorder(Eq_y_0)
| ~ class_Orderings_Oorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_94,axiom,
( c_SEQ_Odecseq(Eq_y_0,Eq_y_1)
| ~ c_SEQ_Odecseq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_95,axiom,
( class_Lattices_Oboolean__algebra(Eq_y_0)
| ~ class_Lattices_Oboolean__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_96,axiom,
( class_Orderings_Oord(Eq_y_0)
| ~ class_Orderings_Oord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_97,axiom,
( class_Groups_Ominus(Eq_y_0)
| ~ class_Groups_Ominus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_98,axiom,
( class_Groups_Ouminus(Eq_y_0)
| ~ class_Groups_Ouminus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_99,axiom,
( class_Groups_Oone(Eq_y_0)
| ~ class_Groups_Oone(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_100,axiom,
( class_Rings_Ocomm__semiring__1(Eq_y_0)
| ~ class_Rings_Ocomm__semiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_101,axiom,
( class_Rings_Ozero__neq__one(Eq_y_0)
| ~ class_Rings_Ozero__neq__one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_102,axiom,
( class_Rings_Olinordered__semidom(Eq_y_0)
| ~ class_Rings_Olinordered__semidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_103,axiom,
( class_RealVector_Oreal__normed__div__algebra(Eq_y_0)
| ~ class_RealVector_Oreal__normed__div__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_104,axiom,
( class_Groups_Oab__semigroup__add(Eq_y_0)
| ~ class_Groups_Oab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_105,axiom,
( class_Groups_Ocancel__semigroup__add(Eq_y_0)
| ~ class_Groups_Ocancel__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_106,axiom,
( class_Groups_Ocancel__ab__semigroup__add(Eq_y_0)
| ~ class_Groups_Ocancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_107,axiom,
( class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_y_0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_108,axiom,
( class_Groups_Oordered__cancel__ab__semigroup__add(Eq_y_0)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_109,axiom,
( class_Groups_Oordered__ab__semigroup__add(Eq_y_0)
| ~ class_Groups_Oordered__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_110,axiom,
( class_Groups_Ocomm__monoid__add(Eq_y_0)
| ~ class_Groups_Ocomm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_111,axiom,
( class_Groups_Omonoid__add(Eq_y_0)
| ~ class_Groups_Omonoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_112,axiom,
( class_Groups_Oordered__comm__monoid__add(Eq_y_0)
| ~ class_Groups_Oordered__comm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_113,axiom,
( class_Rings_Osemiring__1(Eq_y_0)
| ~ class_Rings_Osemiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_114,axiom,
( class_Rings_Oring__1__no__zero__divisors(Eq_y_0)
| ~ class_Rings_Oring__1__no__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_115,axiom,
( class_Rings_Oring__1(Eq_y_0)
| ~ class_Rings_Oring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_116,axiom,
( class_Groups_Omonoid__mult(Eq_y_0)
| ~ class_Groups_Omonoid__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_117,axiom,
( class_Power_Opower(Eq_y_0)
| ~ class_Power_Opower(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_118,axiom,
( class_Rings_Omult__zero(Eq_y_0)
| ~ class_Rings_Omult__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_119,axiom,
( class_Rings_Ono__zero__divisors(Eq_y_0)
| ~ class_Rings_Ono__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_120,axiom,
( class_Rings_Osemiring__0(Eq_y_0)
| ~ class_Rings_Osemiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_121,axiom,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_y_0)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_122,axiom,
( class_Rings_Ocomm__ring__1(Eq_y_0)
| ~ class_Rings_Ocomm__ring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_123,axiom,
( c_Int_Oiszero(Eq_y_0,Eq_y_1)
| ~ c_Int_Oiszero(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_124,axiom,
( class_RealVector_Oreal__normed__algebra(Eq_y_0)
| ~ class_RealVector_Oreal__normed__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_125,axiom,
( class_Rings_Ocomm__semiring(Eq_y_0)
| ~ class_Rings_Ocomm__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_126,axiom,
( class_Rings_Osemiring(Eq_y_0)
| ~ class_Rings_Osemiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_127,axiom,
( class_Rings_Olinordered__ring__strict(Eq_y_0)
| ~ class_Rings_Olinordered__ring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_128,axiom,
( class_Rings_Oring(Eq_y_0)
| ~ class_Rings_Oring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_129,axiom,
( class_Lattices_Oab__semigroup__idem__mult(Eq_y_0)
| ~ class_Lattices_Oab__semigroup__idem__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_130,axiom,
( class_Groups_Oab__semigroup__mult(Eq_y_0)
| ~ class_Groups_Oab__semigroup__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_131,axiom,
( class_Rings_Oring__no__zero__divisors(Eq_y_0)
| ~ class_Rings_Oring__no__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_132,axiom,
( class_Rings_Olinordered__ring(Eq_y_0)
| ~ class_Rings_Olinordered__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_133,axiom,
( class_Rings_Olinordered__semiring__strict(Eq_y_0)
| ~ class_Rings_Olinordered__semiring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_134,axiom,
( class_Rings_Olinordered__comm__semiring__strict(Eq_y_0)
| ~ class_Rings_Olinordered__comm__semiring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_135,axiom,
( class_Rings_Oordered__cancel__semiring(Eq_y_0)
| ~ class_Rings_Oordered__cancel__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_136,axiom,
( class_Rings_Oordered__ring(Eq_y_0)
| ~ class_Rings_Oordered__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,axiom,
( class_Rings_Oordered__semiring(Eq_y_0)
| ~ class_Rings_Oordered__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_138,axiom,
( class_Rings_Oordered__comm__semiring(Eq_y_0)
| ~ class_Rings_Oordered__comm__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_139,axiom,
( class_Groups_Ocomm__monoid__mult(Eq_y_0)
| ~ class_Groups_Ocomm__monoid__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_140,axiom,
( class_Groups_Ocancel__comm__monoid__add(Eq_y_0)
| ~ class_Groups_Ocancel__comm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW221+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 05:10:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 142.24/142.55 % SZS status Theorem for theBenchmark
% 142.24/142.55 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------